experimental techniques for multiphase flows

Experimental techniques for multiphase flowsRobert L. Powell

Citation: Physics of Fluids (1994-present) 20, 040605 (2008); doi: 10.1063/1.2911023 View online: http://dx.doi.org/10.1063/1.2911023 View Table of Contents: http://scitation.aip.org/content/aip/journal/pof2/20/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Study on electrodynamic sensor of multi-modality system for multiphase flow measurement Rev. Sci. Instrum. 82, 124701 (2011); 10.1063/1.3665207 Development of a compact x-ray particle image velocimetry for measuring opaque flows Rev. Sci. Instrum. 80, 033706 (2009); 10.1063/1.3103644 Application of Extended Imaging Techniques for Analyzing Elementary Processes in Multiphase Flow AIP Conf. Proc. 914, 20 (2007); 10.1063/1.2747409 Viscous resuspension in a tube: The impact of secondary flows resulting from second normal stress differences Phys. Fluids 19, 053301 (2007); 10.1063/1.2720533 Bifurcation phenomena in a Taylor–Couette flow with asymmetric boundary conditions Phys. Fluids 13, 136 (2001); 10.1063/1.1329906

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Experimental techniques for multiphase flowsRobert L. Powella�

Department of Chemical Engineering and Materials Science and Department of Food Scienceand Technology, University of California, Davis, California 95616, USA

�Received 5 October 2007; accepted 8 February 2008; published online 30 April 2008�

This review discusses experimental techniques that provide an accurate spatial and temporalmeasurement of the fields used to describe multiphase systems for a wide range of concentrations,velocities, and chemical constituents. Five methods are discussed: magnetic resonance imaging�MRI�, ultrasonic pulsed Doppler velocimetry �UPDV�, electrical impedance tomography �EIT�,x-ray radiography, and neutron radiography. All of the techniques are capable of measuring thedistribution of solids in suspensions. The most versatile technique is MRI, which can be used forspatially resolved measurements of concentration, velocity, chemical constituents, and diffusivity.The ability to measure concentration allows for the study of sedimentation and shear-inducedmigration. One-dimensional and two-dimensional velocity profiles have been measured withsuspensions, emulsions, and a range of other complex liquids. Chemical shift MRI can discriminatebetween different constituents in an emulsion where diffusivity measurements allow the particle sizeto be determined. UPDV is an alternative technique for velocity measurement. There are somelimitations regarding the ability to map complex flow fields as a result of the attenuation of theultrasonic wave in concentrated systems that have high viscosities or where multiple scatteringeffects may be present. When combined with measurements of the pressure drop, both MRI andUPDV can provide local values of viscosity in pipe flow. EIT is a low cost means of measuringconcentration profiles and has been used to study shear-induced migration in pipe flow. Both x-rayand neutron radiographes are used to image structures in flowing suspensions, but both requirehighly specialized facilities. © 2008 American Institute of Physics. �DOI: 10.1063/1.2911023�

I. INTRODUCTION

This paper reviews methods for studying flows of mul-tiphase fluids. These systems are typically a solid phase sus-pended in a liquid but could also include emulsions, suspen-sions of gas bubbles in a liquid, solids fluidized by a gas, ora three-phase �gas/liquid/solid� system. The focus is on tech-niques that can be applied to a wide range of multiphasefluids, especially those of immediate practical interest in-cluding paper pulp suspensions, foodstuffs, such as tomatopaste and starch suspensions, and, generally, highly concen-trated suspensions. The two principal measurements to beconsidered are the concentration of the dispersed phase andthe velocity. The techniques may measure the velocity ofeither the continuous or discontinuous phase �or both�. Forthe purposes of this review, it is assumed that the particlesand fluid have the same velocity. Given the size of the par-ticles and the viscosity of the continuous phase for most ofthe work discussed here, this is a reasonable assumption butone that would benefit from comparative measurements onsome systems. For emulsions, an additional important char-acteristic is the particle size distribution which may changewith flow, temperature, or chemical reactions. This is of lessinterest in solid particle suspensions, where, usually, the par-ticle sizes remain constant and can be readily measured off-line. This paper may then be summarized as the review oftechniques that provide an accurate spatial and temporal

measurement of the fields used to describe multiphase sys-tems for wide ranges of concentrations, velocities, andchemical constituents.

There are many techniques that may fit within the frame-work being considered. At the outset, some are eliminated asa result of not providing the possibility of the wide-rangingapplicability as specified above. For example, although avery well-established technique, laser Doppler anemometry�LDA� cannot be used with highly concentrated suspensionswithout considerable effort to match the refractive indices ofthe suspended phase and the liquid. Experiments with LDAare useful for gaining a basic understanding of the flow ofmodel suspensions, but there is no possibility of making itgenerally applicable for suspensions found in many process-ing industries. Other velocity measurement techniques fallinto a similar category, such as hot film anemometry andparticle image velocimetry. It is not the intent of this paper toprovide a critique of those methodologies but rather to pro-vide insights into techniques that have been demonstrated toovercome the limitations of instruments such as the LDA andat the same time discuss their applicability and limitations.

In this review, two techniques are discussed in detail,magnetic resonance imaging �MRI� and ultrasonic pulsedDoppler velocimetry �UPDV�. Three other methods are alsoincluded, x-ray radiography, neutron radiography, and elec-trical impedance tomography �EIT�. MRI and UPDV receivethe most attention for two reasons. They have been used by alarge number of investigators and they are based on equip-ment that is readily available. In the case of MRI, the equip-a�Electronic mail: [email protected].

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ment used for the studies described herein are either the sameas or direct analogs of those used in medicine. MRI instru-mentation is usually housed in a facility with trained techni-cal support or in the research laboratory of a person with astrong background in NMR or MRI. The equipment is ex-pensive and requires that the experimental apparatus used tostudy flows of multiphase fluids be designed around the in-strument. UPDV offers some of the same advantages as MRIbut at a much lower cost in terms of equipment, training, andstaffing. At the same time, it is not as flexible and does notoffer the potential to obtain information about, for example,chemical constituents. X-ray radiography is quite specializedand has been used in a limited number of studies of multi-phase systems. The same is true for neutron radiographywhich has a special niche in the study of multiphase systemsinvolving liquid metals. EIT has been pioneered for studiesof multiphase fluids by Bonnecaze and coworkers.1–3 How-ever, although the instrument is easy to set up, the actualmeasurements are difficult to interpret, requiring extensiveanalysis and processing of the acquired data. This has limitedthe widespread use of the technique.

In the cases of both MRI and UPDV, one reason formaintained interest has been the potential for their use asviscometers that are very flexible and could be implementedas an in-line viscometer in an industrial setting. The prin-ciples behind both instruments are the same as first describedfor MRI by Powell et al.4 A steady, fully developed, pressuredriven laminar flow in a pipe with a circular cross section isconsidered. Two measurements are performed: the pressuredrop, �P, and the velocity profile, vz�r�, r being the radialposition and z being the coordinate along the axis of the pipe.The shear rate, �̇, as a function of r is calculated from thevelocity profile:

�̇�r� = −dvz�r�

dr. �1�

For a unidirectional flow, the conservation of linear momen-tum is

0 = −dP

dz+

d��r�dr

, �2�

where P is the pressure and ��r� is the radial shear stressdistribution. Since the pressure gradient is constant, Eq. �2�can be solved independently of the constitutive relation toobtain

��r� =�P

2Lr , �3�

where L is the distance over which the pressure drop is mea-sured. At every point r in the flow, it is possible to calculateboth the shear stress and the shear rate to determine the ra-dial distribution of viscosity:

��r� =��r��̇�r�

. �4�

Since �̇�r� is known, Eq. �4� can be recast as ��̇� or the

shear viscosity as a function of shear rate, which is the typi-cal representation of this viscometric function.5,6 Throughoutthis paper, the symbol � is used to denote the viscosity ofcomplex fluids which are expected to have viscosities thatvary with shear rate. For Newtonian fluids, the viscosity isdenoted by �.

The development represented by Eqs. �1�–�4� is based onthe assumption that the fluid is incompressible and that theflow is isothermal. Typically, these equations result from atheory that has been developed for polymeric fluids forwhich these assumptions are valid.5,6 In the case of particu-late suspensions, the established formulas of the viscometricflow theory are used to determine properties such as viscos-ity. At the same time, the dynamics of suspensions may giverise to effects not anticipated by these theories. For example,shear-induced particle migration leads to a nonuniform con-centration profile in a fully developed laminar pipe flow.2

Equations �1�–�4� are valid only if the concentration profilesare fully developed. If the particles and fluid have the samedensities, this will eliminate any density gradients that maygive rise to additional body forces which would make theunderlying conservation laws more complicated than in thestandard viscometric theory. The remaining issue is in theinterpretation of the measured viscosity. Clearly, if the par-ticle concentration depends on the radius, so does the viscos-ity. By using simultaneous measurements of concentration�Sec. II B� on a point-by-point basis, it is possible to charac-terize the viscosity as a function of concentration, whichwould appear to be a more rigorous interpretation of the datathan viscosity versus shear rate given the strong viscositydependence with particle loading at a high concentration.

It is important to draw a sharp line between the use ofultrasonics for measuring viscosity described above andmore traditional techniques. Physical acoustics provides the-oretical relationships between wave speed and attenuationand the physical properties, including viscosity.7,8 As will beseen in Sec. III A, the wave speed is an important parameterin the UPDV viscosity measurement, which is determinedover the course of an experiment. Neither theory nor corre-lation is used to extract physical property information di-rectly from the wave speed. There needs to be no theoryconnecting this with physical properties to fully implementthe technique described above.

Section II reviews results for MRI. This technique isunique in the context of this paper. The versatility of MRIpermits the determination of concentration distributions,two- and even three-dimensional velocity profiles, spatialmapping of chemical constituents, and emulsion drop sizes.Section III discusses the use of UPDV to determine velocity.X-radiography, neutron radiography, and EIT �Sec. IV� areall techniques that principally provide ways of visualizingconcentration distributions. While each might be applied tovelocity measurements, these may require the use of tracerparticles that will act as contrast agents. When such an ap-proach is required, it must go against the tenor of this review,which is that the experimental techniques must work withreal systems without the need to modify those in order tomake a measurement. Section V discusses areas where

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changes in technologies might make the different instru-ments more widely applied. There is also a discussion of theapplicability of the different instruments.

II. MAGNETIC RESONANCE IMAGING

A. Technique and scope

The use of MRI to study problems in fluid and suspen-sion mechanics began in the late 1980s and early 1990s.9–14

The technique offers many advantages for measurements ofconcentration profiles, velocity distributions, and spatialmapping of chemical constituents in multiphase flows. Someexcellent recent summaries provide a comprehensive pictureof the current status of the technology and the usefulness ofthe technique.15–18 It would be presumptuous to attempt toprovide a comprehensive review that recapitulates the find-ings of those studies, not all of which relate to multiphaseflows. This paper focuses on research that particularly relatesto flows of suspensions and droplets. Application of MRI toflows of granular materials is not explicitly discussed. Thereview by Fukushima15 comprehensively covers this area.The granular materials that are generally used in these stud-ies contain an oil or some other liquid that can be imaged.Much of the discussion in this paper relating to MRI tech-niques apply to such systems directly.

This review focuses on three aspects of MRI:

�1� Determination of concentration distributions in suspen-sions and emulsions, both under steady-state and dy-namic conditions. For emulsions, there is also the possi-bility of imaging the two phases separately.

�2� Measurement of velocity fields and applications of suchmeasurements.

�3� Determination of size distributions of droplets and spa-tial distributions of sizes.

The basic principle that sets MRI apart from �nuclear�magnetic resonance �MR� is shown schematically in Fig. 1.Two tubes of water �upper left� are placed in a magnet. Thelower left schematic shows the result of applying a constant

magnetic field pulse and detecting the response of thesample. A signal centered at a frequency proportional to themagnetic field B0, is measured. The exact frequency is foundusing the Larmor relation, �=�B0, where � is the gyromag-netic ratio, which is a property of the sample. For most sys-tems of interest in multiphase flows, proton imaging is usedfor which �=267.64�106 �T s�−1. If instead of a constantmagnetic field, a field with a linear gradient is applied �upperright�, B0+Gxx, where Gx is the applied magnetic field gra-dient, a signal with two peaks is obtained. The frequenciesassociated with the peaks are mapped onto the locations ofthe samples in the magnet by using the same Larmor rela-tion, �=��B0+Gxx�. The frequency difference �a−�b corre-sponds to a spatial separation of �Gx�xa−xb�. The magnitudeof the signal centered at that frequency directly reflects theamount of liquid in each tube. In terms of imaging multi-phase systems, this is critical. When using MRI to imagesuspensions of solid particles, the volume fraction � of thesolid phase is determined by measuring the amount of liquidpresent in a sample. This offers a noninvasive means of mea-suring � as a function of position even for highly concen-trated suspensions.

In practice, samples are divided into volume elements or“voxels.” The dimension of a voxel determines the resolutionof the experiment. For MR microscopy, a voxel may be assmall as 20 �m on a side. A voxel must contain enoughsample to give a detectable signal. To obtain a high reso-lution in two dimensions, a noncubic voxel can be used. Itmay have two dimensions as small as 5 �m with the thirddimension being larger. In most applications, it is possible topicture the voxel as being formed by first choosing a “slicethickness” and then setting the image resolution. The ac-quired image represents the average over the slice thicknessand the image pixel size. In general, the resolution is speci-fied by the applied magnetic field gradients, the size of thecoils, and, the relaxation times of the samples.16 Further,there are many developments with MRI using novel pulsesequences that decrease the acquisition time or increase themaximum speed that can be imaged �see Sec. II C�. Althoughthese are of interest for studies of multiphase fluids, they arebeyond the scope of this review.

B. Concentration distribution

One of the simplest MRI measurements is the concen-tration distribution of solid particles in a liquid sample. A“phantom” consisting of 100% liquid is used to obtain animage of signal intensity as a function of position. Ideally,this should be uniform over the entire image. A sample con-sisting of liquid and solids is placed in the magnetic field andthe two images are compared. The image containing solidparticles will be less intense because it contains less liquid.The decrease in signal intensity is directly proportional to thevolume fraction of particles. As indicated in Fig. 1, for MRI,this is localized to obtain the concentration distribution,which can be measured under static or dynamic conditions.Some of the first researchers to make dynamic measurementsexamined the sedimentation of particles.19,20 Experiments byTurney et al.20 studied bulk sedimentation for suspensions of

FIG. 1. �Color online� Schematic of MR and MRI experiments. Differentmasses of water are placed in two tubes that are placed inside a magnet. Theapplication of a constant magnetic field �lower left� results in a signal cen-tered at a frequency determined by the Larmor relation, �=�B0. If themagnetic field also includes a constant gradient, Gx �upper right�, where x isthe direction that is defined by the line separating the two tubes, the signalhas two peaks centered at two frequencies determined by �=��B0+Gxx�.

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nearly monodisperse spheres. Typical results are shown inFig. 2�a� for a suspension of polystyrene spheres, with anaverage diameter of 488 �m, in a viscous Newtonian oil.The bottom of the container is located at a normalized heightof zero. The initial volume fraction � is 0.42, as representedby the nearly vertical line at that volume fraction. As timeprogresses, the height of the region with the highest volumefraction, �=0.550.02, increases. The interface remainssharp during the entire sedimentation process, reflecting theself-sharpening associated with sedimentation at these highconcentrations.20 At lower concentrations, the effects ofpolydispersity and self-diffusion lead to interfacial spread-ing. Figure 2�b� shows the dynamics of sedimentation for asuspension with �=0.11. As sedimentation proceeds, theconcentration does not vary sharply with height. Data suchas these can be used to calculate the hindered settling func-tion and the effects of polydispersity and self-induced hydro-dynamic diffusivity. The advantage of MRI for such experi-ments is that volume fractions from dilute to concentratedcan be measured and also that it can be applied to systemsthat do not require matching the refractive indices of theliquid and the particles. It is also possible to study the dy-namics of fan formation. Indeed, MRI is almost uniquelysituated for such studies, especially for nonideal suspensions.This flexibility led to studies of sedimentation of bimodalsuspensions21 and fibers22 as well as studies of creaming andseparation of populations of spheres that contain particlesthat are more and less dense than the suspending fluid.23,24

The ability to measure volume fraction as a function ofposition is directly relevant to one of the major areas ofresearch on suspensions over the past 20 years: shear-induced migration. The prototype experiment is the study ofthe steady-state concentration profile in suspensions under-going a flow without a uniform shear rate, such as pipe flowor a pressure driven channel flow. Shear-induced migrationleads to the particles moving from regions with a high shearrate to those with a low shear rate, causing the particle con-centration near the center of a pipe to be higher than that atthe walls.25 Hampton et al.26 used MRI to show that thiseffect could be directly measured with concentrated suspen-sions of spherical particles. Figure 3 shows � as a functionof the dimensionless radius for two different average valuesof �, 0.3 and 0.4. It also shows the actual MRI images thatwere used to calculate the values of the volume fraction. Theratio of the particle diameter to the pipe diameter is 0.0625.In the images, the bright areas represent regions where theconcentration of the suspending liquid is high. In both cases,the lightest regions are near the walls of the pipe and thedarkest regions are near the pipe center. The concentrationprofiles are shown for the region near the wall where � de-creases. Near the pipe center, the concentration approaches avalue that depends on both the overall volume fraction andthe ratio of the particle radius to that of the pipe.

More recently, MRI has been used to provide valuableinsights into the development of particle concentration pro-files in complex geometries, especially the effect of upstreamconditions on the flow through an abrupt annular expansion.Moraczewski and Shapley27 obtained radial concentrationprofiles at two axial positions downstream of an abrupt, axi-symmetric 1:4 expansion �z /d2=0, where d2 is the diameterof the tube downstream from the expansion�. Radial concen-tration profiles for both the long and short inlet tubes areshown in Fig. 4, and longitudinal cross sections of thesesystems are shown in the inset. As in the results of Hamptonet al.,26 the darker areas in the NMR images indicate higherparticle volume fractions. Similar features appear in the ra-

FIG. 2. �Turney et al. �Ref. 20�; reprinted with permission from AmericanInstitute of Physics� MRI-measured volume fraction profiles for a suspen-sion of polystyrene spheres �diameter=48831 �m� in a viscous Newton-ian fluid with an initially uniform concentration. Profiles were acquired at59.65 min intervals for suspensions with �a� �=0.42 and �b� �=0.11. Eachprofile is differentiated by the type of line �solid, dashed, dotted, etc.�. Spa-tial resolution is 240 �m /pixel and the uncertainty in the measured volumefraction is within 0.02. The measured volume fractions of the sedimentsare 0.550.02, indicating that the sediments have disordered structures.

FIG. 3. �Hampton et al. �Ref. 26�; reprinted with permission from the So-ciety of Rheology� Fully developed radial volume fraction profiles �left� andvolume fraction intensity images for flow of a suspension in a pipe. Darkerregions indicate a lower amount of liquid than in the brighter regions andhence a higher volume fraction of particles. �a� �=0.3 and �b� �=0.4.



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dial profiles, which were obtained after steady flow at Rey-nolds number NRe=0.04 for a suspension at �=0.45 �widetube to particle radius ratio, d2 /a=75�. In each radial profile,two regions of close to uniform particle volume fraction areapparent, where the central region is more concentrated thanthe surrounding annulus. The concentration difference be-tween the core and annular regions is more pronounced forthe cases with a long narrow upstream tube than in caseswith a short narrow upstream tube. This can be attributed tothe higher degree of shear-induced particle migration occur-ring in the long narrow tube preceding the expansion. Thecomparison illustrates the importance of inlet conditions inthe flow of suspensions in complex geometries.

C. Velocity fields

The direct connection between MRI and other measure-ment techniques used in fluid mechanics is the ability tomeasure velocity fields. The unique aspects of MRI includeits application to multiphase fluids, especially to systemswith a wide range of concentrations of the dispersed phase,multidimensional flows, and opaque systems. It is also non-invasive and does not require the addition of tracers. There isan excellent review by Fukushima that discusses thisliterature15 and a recent book by Stapf and Han16 that alsodeals with aspects of these measurements. The goal here is toshow some results that have provided insights that were dif-ficult or not possible to obtain by other means and to dem-onstrate the flexibility for a number of suspensions and othercomplex systems.

There are two techniques that are regularly used for MRIvelocity imaging that will be described here. The first may beconsidered as a classical tracer experiment where a line isdrawn in a fluid at time t=0 and “photographed” as it moves.

Consider such an experiment in a laminar pipe flow. For aMRI experiment, at t=0, a cross section of the pipe is selec-tively excited so that the spins associated with the protonsare tipped relative to the remaining spins. After a specifieddelay, these spins are imaged. This technique produces ex-cellent one-dimensional velocity profiles for a laminar flow.It is also an analog to the classical Taylor–Aris dispersion.28

The second technique, which is called the phase encodeimaging,15 uses the unique aspects of a MRI experiment.Consider the motion of a fluid element initially located at r0

that moves to r�t� at time t. This motion occurs during theimposition of a magnetic field gradient G�t�. The direction ofG determines which component of velocity is measured. Theapplication of the gradient pulse over the pulse echo time Tpe

changes the rotation of the proton spins and results in anaccumulated phase of

= ��0

Tpe

r�t� · G�t�dt . �5�

The evolution of the position vector is represented by

r�t� = r0 + v0t + �a0/2�t2, �6�

where v0 is the velocity vector and a0 is the accelerationvector. Equation �6� is substituted into Eq. �5� to obtain

= ��r0 · m0 + v0 · m1 +a0

2· m2� , �7�

where m0, m1, and m2 are the zeroth, first, and second mo-ments of the applied gradient, respectively,

m0 = ��0

Tpe

G�t�dt, m1 = ��0

Tpe

G�t�tdt,

�8�

m2 = ��0

Tpe

G�t�t2dt .

Equation �7� is the basis for phase encode velocity measure-ments. The applied pulse may be designed so that two of thethree moments are zero. For velocity measurements, m0

=m2=0, which leaves the phase proportional to the velocityvector. This permits multiple components of the velocity tobe determined depending on the direction of G. Typically,instruments are able to apply gradients in three orthogonaldirections providing the capability to measure all three com-ponents of velocity.

Equation �7� shows that choosing the gradient pulse sothat m0=m1=0 results in a relationship between the phaseand the acceleration. This provides a direct technique for thestudy of acceleration, which is a unique feature of MRI mea-surements.

The measurements made with MRI are averages over avolume element that is set by the experiment parameters.29

Typically, for a “slice” in an experiment involving pipe flow,the thickness of the volume normal to the axis of the pipe isover 1 mm and may be as much as a centimeter. The reso-lution in the cross section perpendicular to the pipe axis isusually 20–100 �m and may be as small as 5 �m. The ex-perimental trade-off is the number acquisitions �NA� result-

FIG. 4. �Moraczewski and Shapley �Ref. 27�; reprinted with permissionfrom American Institute of Physics� Effect of upstream tube length onsteady state radial concentration distributions downstream of 1:4 expansionplane for �=0.45, d2 /a=150 after flow at NRe=0.04. Open points corre-spond to the long upstream tube �L1 /d1=128� and filled points represent theshort inlet �L1 /d1=10�. Spin-echo intensity images are shown in the inset.



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ing in signal coadditions that may be needed in order toobtain a high signal-to-noise ratio �SNR�. The important pa-rameters for an experiment include the velocity and spatialresolutions, �vz and �r, respectively. The SNR is related to�vz, �r, and NA. The functional behavior is of the formSNR��vz�rNA. The total experimental time, again usingthe example of pipe flow and imaging the velocity in onedimension, is the number of discrete points used to define thevelocity field �usually Nz=128� times the repetition time be-tween pulses, TR0.2 s, times NA �typically a minimum of2�. This results in an experiment time of about 51 s, which istypical for standard pulse sequences. Expressions for �vz and�r are given in Sec. II D.

Results using both velocity imaging techniques are pre-sented in Fig. 5, which shows Couette flow between a sta-tionary inner cylinder and an outer cylinder rotating clock-wise at a linear velocity of 2 cm /s. The system is an oil-in-water emulsion at �=0.4.30 Figure 5�a� shows the result ofexciting a vertical cross section of the flow and then imagingthose protons at a later time. The inner cylinder is hollow andthe fluid in that region does not move. When the image istaken, the fluid in this region shows a vertical stripe of se-lectively excited protons since no motion in this region hasoccurred. Between the two cylinders, the emulsion hasmoved clockwise. The no-slip condition is apparent at theinner cylinder where there has been no movement. At theouter cylinder, the emulsion moves with the boundary andhas rotated relative to the initial position by a distance equalto the linear velocity of the wall times the time since theprotons were initially excited. Knowing the time between theexcitation and the detection, it is possible to find the velocityprofile at each radial position.

Figures 5�b� and 5�c� show the phase encode images forthe same flow. These are color-coded images that are two-dimensional velocity fields. In Fig. 5�b�, the dark red regions

near the wall correspond to the highest velocities in theclockwise direction. Near the inner cylinder, the green arearepresents flow at a very low velocity. At each point in theflow, the actual velocity vector has been measured. This isclearly seen in Fig. 5�c�, which is an expanded section be-tween the cylinders. The velocity has been measured usingtwo orthogonal gradients and the resulting velocity vectorsare referred to a Cartesian coordinate system.

One of the first applications of MRI to a multiphasesystem that has been difficult to study was presented in aseries of papers examining the flow of paper pulpsuspensions.14,31–35 Figure 6 shows images for the flow of a0.5% suspension of bleached hardwood fibers in a 25 mmdiameter pipe. This is a nondilute suspension, as indicated bythe concentration in terms of ncl

3, where nc is the numberconcentration and l is the fiber length, which is about 1.5.Starting in the upper left �image A�, each successive imagerepresents an increasing volume flow rate. Along the hori-zontal axis, the velocity is represented in cm/s. The verticalaxis represents the distance across the pipe. The velocityprofiles are seen as bright lines against the dark background.In image �A�, the velocity profile is clearly observed to beblunt near the center of the pipe with all of the shearingoccurring near the wall. The profile is quite pronounced andclearly identified. For this and all of the images, two signalaverages were used to increase the SNR. As the volume flowrate is increased �images �B�–�D��, the width of the blunt,plug flow region decreases. As described below, this can beinterpreted in terms of the yield stress of the suspension.Equation �3� clearly shows that the shear stress decreases asthe radius decreases. If the material is assumed to have ayield stress, near the pipe center, it is not exceeded and thesuspension is not sheared. As the overall flow rate is in-creased, the radial position in the pipe that has an associatedshear stress equal to the yield stress moves closer to the

FIG. 5. �Color online� �Shapley et al. �Ref. 30�; reprinted with permission from American Institute of Physics� MRI velocity images of a �=0.4 oil-in-wateremulsion being sheared in a Couette cell. �a� Time-of-flight velocity image; dark line shows the motion of the emulsion in response to the rotation of the outercylinder. �b� Phase encode image. �c� Enlargement of a portion of �b� that shows the local two-dimensional velocity vector field.



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center, qualitatively following the behavior found in images�A�–�D�. In images �A�–�D�, the velocity profile, indicatedby the bright line, is somewhat less intense near the pipewall. Near the center of the pipe, where there is little shear-ing, the fibers form a network. Closer to the wall, this net-work is disrupted due to the higher shear stresses near thewall. Also, near the wall, it is generally accepted that there isa water layer with a relatively low concentration of fibersthat are free to move36 and impart small-scale fluid motionsthat affect the signal intensity.37 This effect is also evident athigher flow rates, images �E�–�G�, until a transition occursthat is seen in images �H� and �I�. Here, the intensity of theimage near the wall starts to increase and the intensity nearthe center decreases. In these and subsequent images, a lami-nar boundary layer near the wall results in a well-defined,bright flow image in that region. Near the pipe center, thenetwork is completely disrupted and the fibers create second-ary flows that reduce the signal intensity. Averaging overmore images at a particular flow rate provides an image ofthe mean velocity profile with a higher SNR.37

The observation that small fluctuations in the fluid ve-locity decrease the intensity of the signal of the mean veloc-ity profile has led to ways of estimating the turbulence inten-sity. Li et al.37 developed a technique to measure theturbulence intensity from the intensity distribution of theMRI-measured averaged velocity profile. The techniquegives values of velocity fluctuations that are averaged alongthe path length of a particle trajectory: a Lagrangian average.The actual measurement compares the intensity distributionof the imaged velocity profile to the intensity of an imagetaken at zero velocity. Li et al.37 showed that this techniqueprovided values of the turbulence intensity in pipe flow ofwater at NRe4000 that compared well to those obtained byconventional means.

Seymour38 extended the methodology of Li et al.37 to a

laminar flow of particle suspensions. He obtained an expres-sion relating the mean square fluctuations of the ensembleaverage velocity to the intensity ratio of the flow and no flowimages:

�uz2��x� = −

I�x,vz�/I�x,vz = 0�8�2G2�2Tpe

2 . �9�

Here, uz is the velocity fluctuation in the z direction, thebrackets represent the ensemble average, I is the signal in-tensity as a function of the position x and mean velocity vz,and G is the magnitude of the imposed gradient pulse. Theparameter � is the duration of the flow encoding gradient.The parameters �, G, �, and Tpe in Eq. �9� are set by theexperiment. Two signal intensity distributions, with andwithout flow, are measured. This technique allows the fluc-tuation intensity to be directly determined. Results from thiswork are shown in Fig. 7. Here, the intensity ratios are com-pared to check for experimental effects. The parameters �and G are fixed and the product of � and Tpe is kept constant.Figure 7�a� shows that there is no effect of varying either thespatial resolution or the number of signal averages on themeasured ensemble-averaged fluctuation. The maximum in-tensity occurs close to the wall, at r /R of roughly 0.85,which is consistent with the work of Nott and Brady.39 Whenthe timing parameters are varied, Fig. 7�b�, the magnitudesof the measured fluctuations change although the overall be-havior, i.e., the form of the curves in Fig. 7�b�, does notchange. Changing the timing parameters affects the frequen-cies that can be observed, so some effect is expected. Clearly,this technique can be used to estimate the fluctuations butthere is more work to be done to fully elucidate the interplaybetween the time scales associated with the measurementsand those associated with the flow. Still, this is one of twotechniques40 that have been used to measure velocity fluctua-

FIG. 6. Flow of a 0.5% pulp suspension in a pipe. Foreach image, along the horizontal axis the velocity andalong the vertical axis, the distance across the pipe. Thevolume flow rate increases in going from image �A� to�L�.



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tions in concentrated suspensions and the only one that canbe applied over a wide range of concentrations and for mostmultiphase fluids of interest from both fundamental and ap-plied standpoints.

A unique application of MRI derives from the observa-tion based on Eq. �7� that, by the appropriate choice of thepulse gradient, both m0 and m1 can be set to zero, making theacquired phase proportional to the local acceleration. Alltechniques typically used in fluid dynamics experiments—pitot tubes, hot wire anemometers, LDAs, particle image ve-locimetry, UPDV—measure the velocity field. The local ac-celeration can be derived from these measurements but thatinvolves differentiating the instantaneous velocity with re-spect to time. The frequency response of some of these tech-niques would allow accurate acceleration determinations, butthey are not independent of the original velocity measure-ment. MRI acceleration imaging gives the acceleration fieldindependently of the velocity. To demonstrate the applicabil-ity of this technique it is useful to have a flow with a well-defined acceleration. One way to achieve this is to createplug flow in a conical contraction, which has a linear changein cross section along the axis of symmetry. For example,consider a conical contraction where z=0 is the location ofthe inlet and A�z� is the cross-sectional area. At any point inthe contraction, A�z�=A�0�−sz, where s is the slope of thecontraction. By assuming a plug flow behavior and that theflow is steady, the axial velocity depends on z only. It can befound from an overall mass balance to be

vz�z� =A�0�A�z�

vz�0� . �10�

The axial acceleration az�z� is found from the general defi-nition a�t�=�v /�t+v· ·v which for an axial symmetric steadyflow and �vz /�r=0 reduces to

az�z� = vz�vz

�z. �11�

Substituting Eq. �10� into Eq. �11� gives a theoretical expres-sion for az�z�,

az�z� = vz�0�2 sA�0�2

�A�0� − sz�3 . �12�

From Fig. 6, it is observed that at low enough velocities, apaper pulp suspension exhibits plug flow. The suspensionconsists of a network of highly entangled fibers flowing on alubricating layer next to the pipe wall. Such a suspensionmakes an excellent candidate for experiments to test the ac-celeration imaging technique. The actual geometry used wasa conical contraction with a 26 mm inlet and a 6.5 mm outlet100 mm downstream.41 A 1% by weight hardwood pulp wasused. Figure 8 shows the velocity and acceleration images.Figure 8�A� clearly demonstrates that the pulp suspensionflows as a plug at the velocities experienced in the contrac-tion. The acceleration image, Fig. 8�B�, shows a similar be-havior: over the entire cross section, the acceleration is es-sentially constant as predicted by Eq. �12�. The results in Fig.8 are compared to the predictions of Eqs. �10� and �12� inFig. 9. There is good agreement between the predicted andexperimental velocities and accelerations. This verifies that itis possible to make direct acceleration measurements andpotentially derive from these new insights about multiphaseflow, recognizing that the data are directly obtained with noadjustable parameters or calibrations.

The application of MRI to flows of complex and multi-phase liquids has produced results that have led to acceptedtechniques for measuring properties or specific characteris-tics of a system. For example, Arola et al.35 showed thatMRI could be used to determine the flocculation time of pulpsuspensions. This was measured by flowing a suspensioncontaining 0.5% by weight hardwood fibers �aspectratio=25, ncl

33� through an abrupt expansion. Upstreamof the expansion, a steady fully developed flow was estab-lished over a 3.1 m section of a 1.53 cm diameter pipe. Atthe flow rates studied, the suspension was fluidized.33 Down-stream from the expansion, over a 4 m length, the diameterwas 2.62 cm. MRI was used to determine at what pointdownstream from the expansion the velocity profile showedplug flow behavior, implying that the suspension had refloc-

FIG. 7. �Seymour �Ref. 38�� Axial velocity fluctuation distributions for a �=0.36 suspension of spheres in oil. The velocity fluctuation distribution iscalculated from the image signal intensities by using Eq. �9�. The fluctuations are normalized by the experimental parameters. The distributions shown in �a�were obtained for different values of the number of signal acquisitions used in the averages and the spatial resolution of the data. They demonstrate theinsensitivity of the measurements to both of these parameters. Those in �b� show sensitivity to the time scales of the measurement while holding their product�Tpe constant, which limits the overall frequency range that is being accessed.



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culated. The slope of the line showing the average flow rateversus the reflocculation length gives the reflocculation time,which was found to be 510 ms. This compares favorablywith results from other techniques that are usually based onan optical sensor.33 The advantage of MRI is that it will workover the entire range of concentrations that are of interest inpapermaking, up to 12% and even higher. Indeed, it is pos-sible that it could be used to study flocculation in air formingprocesses, typically used for manufacturing personal careproducts, if enough water remains in the fiber for imaging.The biggest challenge in this case will be the high velocitieswhich makes imaging more difficult.

D. Viscosity measurement

One of the most widely studied applications of MRI forcomplex liquids has been the measurement of viscosity.4,42,43

Equations �1�, �3�, and �4� provide the background for thismethodology. As discussed in Sec. I, this theory can apply toany joint velocity field–pressure drop measurement. MRI is

especially well suited for several reasons: �1� It is noninva-sive. �2� It does not require the addition of a tracer. �3� Itworks with opaque systems. �4� It works with highly concen-trated systems. As with the measurement of viscosity usingUPDV, MRI requires that the pressure drop be determined.For pipe flow, this is relatively straightforward and is typi-cally accomplished by mounting transducers on both sides ofthe magnet and measuring the pressure drop at the same timethat the velocity profiles are determined. If measurements inmore complex geometries are needed, such as across a con-traction or expansion, it may be difficult to place the trans-ducers at the desired locations due to the presence of thelarge magnetic fields and possible interference with the MRIsignals. In these cases, it is possible to make measurementsin the same geometry under the same conditions but with theflow cell outside the magnet. The MRI technique for viscos-ity measurement was recently reviewed by Powell.44 Thecritical elements here are to indicate the capability, empha-size some of the unique characteristics, and discuss the de-sign basis.

Figure 10 provides an excellent example of the capabili-ties and benefits of using an MRI-based viscometer. The fluidused to obtain these data, a 1% by weight aqueous polyeth-ylene oxide solution, shows much of the behavior of manycomplex fluids. At low shear rates, it has a constant viscosityand is considered Newtonian. As the shear rate increases, theviscosity decreases, exhibiting a shear thinning behavior. Atsufficiently high shear rates, it is likely that the fluid could bemodeled as a power-law fluid for which ��̇��̇n−1 where nis the power-law exponent. If n 1, the viscosity decreaseswith increasing shear rate and the velocity profile in pipeflow is blunt relative to that for a Newtonian fluid. Since thisplot is semilogarithmic, it is not apparent that this fluid doesexhibit a power-law behavior. These conclusions regardingthe rheological behavior of the polyethylene oxide solutioncan be drawn from the data in Fig. 10 that were obtainedusing a conventional cone and plate viscometer and usingMRI at different spatial resolutions.

For each MRI data set, consisting of a velocity profile–pressure drop pair, viscosity data are obtained over almosttwo decades of shear rate. Any other technique for measuring

FIG. 8. �Li et al., �Ref. 41�; reprinted with permissionfrom Elsevier� ��A�–�D�� Velocity images of an aqueouscellulose fiber suspension �1 wt. % � at four differentaxial positions and ��E� and �F�� acceleration images attwo different axial positions in a conical contraction:�A� z=4.6 cm, �B� z=5.4 cm, �C� z=6.5 cm, �D� z=7.9 cm, �E� z=5.4 cm, and �F� z=7.0 cm. The posi-tion is given as the relative distance of the selected slicewith respect to the end of the contraction. All the im-ages were obtained by using a slice thickness of 3 mm.

FIG. 9. �Li et al., �Ref. 41�; reprinted with permission from Elsevier� Themean velocity and acceleration as a function of the position in a conicalcontraction. Results from the calculations based on the independently mea-sured volumetric flow rate and the NMRI experimental measurements arepresented. Note that the horizontal axis is the distance from the end of thecontraction.



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the shear viscosity relies on single point measurements in aviscometric flow, such as cone and plate, pipe flow, or Cou-ette flow. In all of these cases, the measurement is made atsteady flow conditions after all inertial effects have decayedand the material has been sheared long enough to ensure thatthe experiment time is much greater than material time con-stants. During a typical experiment, a rotational speed �shearrate� is set and after all transients have decayed, the torque�shear stress� is measured. A viscosity determination at an-other shear rate requires that the rotational speed be changedand the measurement repeated. It is reasonable to expect thata well-characterized material might have six to eight datapoints per decade of shear rate. The 12–16 measurementsrequired to characterize a fluid over two decades might takeover an hour to measure and require that a sample be ob-tained from a process stream. For MRI, the time to acquireand process the data is an order of magnitude shorter and itcan be done under process conditions. This is especially im-portant for materials that may change with time or once theyare removed from the process stream, such as many foodproducts.

Figure 10 clearly shows that MRI has delineated thetransition between the Newtonian and shear thinning behav-iors. The ability to do this rests with the technique used toobtain the shear rate. Although Eqs. �1�, �3�, and �4� providethe framework for data analysis, the specific steps for deter-mining the viscosity are as follows: �1� Measure the velocityprofile and the pressure drop. �2� Fit the velocity data to aneven order polynomial �usually sixth order�. �3� Differentiatethe velocity data to obtain the shear rate. �4� Calculate thelocal shear stress. �5� Use Eq. �4� to determine the viscosity.Step �2� is crucial. Differentiating velocity data to obtain theshear rate is not straightforward. The velocity field is repre-sented as a data matrix, typically 128 velocity and 128 spa-tial points. Even for the most accurate measurements, thedigital nature of the data means that there will be some errorsin taking the derivative. It is tempting to fit data to a particu-lar constitutive model and use the parameters that are found

to calculate the shear rate.45 Rather than determine the vis-cosity, one might skip directly to find the parameters of aparticular model.44 It is important not to do this. As an ex-treme case, suppose that a priori one believes that a 1%polyethylene solution should behave as a power-law fluidand the values of the parameters for this model are directlyobtained from the velocity profile. Then the behavior foundin Fig. 10 could never be observed. The polynomial tech-nique has consistently been shown to be sufficiently generalto follow behavior at low shear rates, in the power-law re-gion, and at very high shear rates where a second Newtonianplateau can be found.43

Figure 10 also shows the effect of the radial resolutionon the acquired data. There are three important parametersthat directly affect the data �ignoring many parameters thatare related to the MRI signal such as the spin-spin and thespin-lattice relaxation times�: the radial resolution, the veloc-ity resolution, and the mass flow rate �average velocity�. Theradial resolution is

�r =2�

�GxNxTDW, �13�

where Gx is the magnitude of the magnetic field gradient inthe cross-flow direction, Nx is the number of data points inthat direction, and TDW is the dwell time which is the timebetween acquisitions, making NxTDW the total signal acqui-sition time. Note that increasing either the gradient or thenumber of data points decreases �r. The velocity resolutionis

�vz =2�

��Gz�NzTpeTGz

, �14�

where �Gz is the incremental change in the z component ofthe magnetic field gradient used for each acquisition, Nz isthe number of samples along the z direction, and TGz

is theduration of the gradient applied at the beginning and the endof the time interval Tpe. The velocity resolution is generallyfound to have a greater effect on the quality of the data thanthe radial resolution.46

The third parameter, the mass flow rate, governs the“window” of shear rates that can be accessed during a par-ticular experiment.46 The maximum shear rate in a flow is theshear rate at the wall, �̇max. The maximum span of shear ratesin an experiment is between zero at the pipe center and �̇max.Since �̇max is approximately proportional to the mass or vol-ume flow rate, the higher the flow rate, the larger the �̇max.This is clearly seen in Fig. 11, which shows data obtainedusing a 0.5% aqueous polyacrylamide solution. Four sets ofMRI and one set of cone and plate viscometer data are in-cluded. The MRI data were obtained at two different volumeflow rates. At the higher flow rate, the MRI data coincidevery well with the cone and plate data over the range ofabout 5–100 s−1. Below 5 s−1, the data start to level off andappear to suggest that the fluid is showing a low shear rateNewtonian plateau. When the volume flow rate is lowered,however, there is a different set of shear rates that agreeswell with the cone and plate data, approximately 0.7–15 s−1.Again, at shear rates below these values, the fluid appears to

FIG. 10. �Color online� �Arola et al. �Ref. 43�; reprinted with permissionfrom the Society of Rheology� Shear viscosity vs shear rate data for a 1%aqueous polyethylene oxide solution. Rotational rheometry ��; MRI: �r=200 �m ��, �r=300 �m ��, �r=400 �m ��, �r=500 �m ��, and �r=1000 �m ��.



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have a Newtonian plateau when, in fact, the cone and platedata clearly show that the viscosity continues to increasewith decreasing shear rate at least to shear rates of 0.1 s−1.The anomalous data in both cases are found from velocitiesmeasured near the center of the pipe. In this region, the ve-locity is nearly constant and it is very difficult to make ac-curate determinations of the shear rate. The resolution of theexperiment causes limitations. Also, the even order polyno-mial fit yields values that are biased toward a parabolic pro-file since, in effect, it is seeking to look for a first ordercorrection to a constant velocity profile using the formC1+C2r2. Another functional form may provide additionalinformation but would also bias the data. Arola et al.46 wereable to determine a design curve that allows a minimumshear rate at which accurate data can be obtained, �̇min to bespecified by the experimental conditions. The design curve�Fig. 6 of Ref. 46� is given in terms of R�̇min / v̄z versus�vz / v̄z where v̄z is the average velocity.

It is well established in food science and engineeringliterature that many suspensions of practical interest, such asmayonnaise, tomato paste, whipped cream, and paper pulpsuspensions, exhibit yield stress behavior.47–50 The manifes-tation of apparent yield behavior in flow is the existence ofregions that do not undergo shearing if the yield stress �y isnot exceeded. A material with a yield stress flowing througha pipe will therefore have a flat profile near the center and allof the shearing will take place near the wall where the shearstress is highest and exceeds the yield stress, see image �A�of Fig. 6. Equation �3� holds regardless of the constitutiverelation although if the suspension behaves as a Binghammaterial, which does not flow or deform at all unless theyield stress is exceeded, the stress in the unyielded region isindeterminate. However, as the plug flow region is ap-proached from the pipe wall where shearing occurs, Eq. �3�does hold and provides the means to calculate the shearstress near the “point” where the transition between shearedand unsheared behaviors occurs.

It is also possible to consider a velocity profile that is“flat” as representing a power-law fluid with a small expo-nent. For example, if n=0.5, at a dimensionless radius r� of0.21, the velocity would be 99% of its maximum; r� increasesto 0.4 and 0.66 for n=0.25 and 0.1, respectively. Indeed, inthe latter two cases, the velocity would be 99.9% of themaximum at r� of 0.25 and 0.53. Measuring such small dif-ferences, one part in a thousand, is difficult and beyond cur-rent MRI capabilities. It is then a matter of interpretation asto whether one chooses to say that the region in the centerof the pipe is unsheared and the material is behaving as aBingham material or the material is a power-law fluid with0 n�1. If the former is chosen, Eq. �3� can be used tocalculate the yield stress once the “yield radius” Ry isdetermined.43 Figure 12 shows a portion of the velocity pro-file for a 0.53% by weight microfibrous cellulose suspension.What can be interpreted as plug flow is observed near thecenter of the pipe. This behavior persists to a radial positionof just over 6 mm, which is about 50% of the distance fromthe center of the pipe. Assuming that the first significantdecrease is about 1% of the maximum implies that a power-law exponent between 0.15 and 0.2 would adequately predictthe profile in Fig. 12. Taking the alternative approach ofmodeling this behavior as a fluid with a yield stress andcalculating �y from the yield radius gives a value of3.420.34 Pa. This compares very favorably with the yieldstress measured using a constant stress rheometer with avane attachment, 3.150.08 Pa.

A complementary use of MRI and NMR but with asomewhat different set of goals is that pursued byCallaghan17,18 who coined the term Rheo-NMR. Much ofthis work seeks to use NMR / MRI to examine the dynamicsof complex fluids, principally polymeric fluids, under rheo-metrical flows and infer from these measurements informa-tion about the dynamics of polymers, liquid crystals, mi-celles, etc., under shear and elongational flow. This work

FIG. 11. �Color online� �Arola et al. �Ref. 43�; reprinted with permissionfrom the Society of Rheology� The viscosity–shear rate relation for a 0.5%aqueous polyacrylamide solution. The triangles are data obtained using acone and plate viscometer. The diamonds are MRI data obtained at a volumeflow rate of 12 ml /s and the circles are data obtained at a volume flow rateof 43 ml /s. The volume flow rate governs the range of shear rates that canbe accessed.

FIG. 12. �Color online� �Arola et al. �Ref. 43�; reprinted with permissionfrom the Society of Rheology� The velocity profile for a 0.53% by weightmicrofibrous cellulose suspension. The velocity profile is flat near the centerof the pipe leading to the possibility of interpreting this as the flow of amaterial with a yield stress. The radial position as which measurable shear-ing occurs, Ry, is associated with a stress, �y, which is interpreted as theyield stress.



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focuses on the use of geometries that typically have dimen-sions in which the flow occurs on the order of 1 mm withsample volumes of 1 cm3. While of interest for imagingflows in microchannels, such geometries cannot be used formany of the problems discussed in the present work. The twoexcellent reviews by Callaghan17,18 provide insights into hiswork as well as that of others. They also discuss a morerecent work that is aimed at the study of colloidal systems.18

E. Emulsion dynamics

As discussed above and shown in Fig. 5, MRI is anexcellent tool for mapping velocity fields in concentratedemulsions. It can also be used to quantify other aspects ofemulsion dynamics including the measurement of drop sizedistributions51–54 and mixing.55 Chemical shift imaging pro-vides an excellent means of discriminating the differentphases in an emulsion by imaging them separately. The pulsesequences are chosen to selectively excite individual chemi-cal species. For example, in an oil-in-water emulsion, thewater phase and the oil phase can be separately imaged,55

which permits the velocities of each phase to bedetermined.56 Figure 13 gives a sequence of images obtainedby MRI chemical shift imaging that demonstrate how mixingoccurs in an emulsion which has been allowed to cream ina horizontal Couette device. The oil-in-water emulsion�average oil drop diameter of 3 �m� with an overall volumefraction of 0.5 was loaded in a flow cell �inner cylinderradius=4 mm; gap/inner cylinder radius=1.75� and allowedto cream for 3 h. The emulsion was stabilized with a surfac-tant. Initially, at a strain � equals zero, the emulsion, repre-sented in red, was concentrated near the top of the cylinderand at the bottom, the blue/teal region was rich in thecontinuous phase �water�. The time-of-flight velocity image,which is shown immediately next to the concentration image,indicates a zero velocity. The image to the immediate rightshows the result of the rotation of the outer cylinder at aconstant speed of 0.05 cm /s after four complete rotations ora total strain of 37.8. Both the droplet-enriched layer near the

top of the flow cell and the droplet depleted water layer nearthe bottom have decreased in size. The flow in the emulsionwas confined to a thin region near the outer cylinder. This isseen more clearly in the �=118 image �12 rotations�, wherethe mixing is nearly complete, but the time-of-flight velocityimage shows that most of the emulsion has not moved. At 21rotations, �=197, the emulsion was completely mixed, butthe steady-state velocity profile was not established until�=437.6, 46 rotations. Further, this steady profile clearlyshows that all of the fluid is not moving in the same directionas the rotating outer cylinder. This flow reversal phenomenonwas identified by Shapley et al.30 and depends on the buoy-ancy parameter

BV̄ �2

9��1 − ��5�� − �p gaRouter

�eV� , �15�

where �e is the emulsion viscosity, � is the density of thecontinuous phase �water, 1.0 g /cm3�, �p is the density of thediscrete phase �oil, 0.69 g /cm3�, g is the gravitational con-stant, a is the particle radius, Router is the outer cylinder ra-dius, and V is the linear velocity of the outer cylinder. Flowreversal has been observed in both emulsions andsuspensions.57 It is reasonable to say that this effect mighthave only been found using MRI. While it is possible toobserve this effect in dilute systems, as low as �=0.02, itwas through experimentation at emulsion volume fractionsup to 0.4 and suspension volume fractions near 0.1 that amechanism was identified.57

The ability to measure droplet size in concentrated emul-sions in situ is one of the unique characteristics of MRI rela-tive to other techniques for drop size determination.51–54 Thistechnique is based on the measurement of the hindered dif-fusion of the constituent in the dispersed phase.52 Both themean drop size and the drop size distribution can be deter-mined. When spatially resolved measurements are made, theamount of material in a voxel limits to some extent the res-olution of the technique and makes the determination of thedrop size distribution in each volume element more difficult.

FIG. 13. �Color online� �D’Avila et al. �Ref. 57�; re-printed with permission from American Institute ofPhysics� Side-by-side oil chemical shift imaging con-centration maps and time-of-flight TOF images for anemulsion with bulk of 0.5 and V of 0.05 cm /s after 3 hof creaming. The series of images shows the progres-sion of mixing as the strain increases from �a� �=0 to�b� �=38, �c� �=118, �d� �=197, �e� �=278, and �f��=438.



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Typical results for the spatial distribution of the mean dropsize is given in Fig. 14 in terms of the mean drop size nor-malized with respect to the gap of the Couette cell versus thedimensionless distance from the bottom of the creamed layer.These data were obtained using a �=0.4 emulsion �averagedrop size of 5.4 �m�, which was allowed to cream in theCouette cell described above. The bottom of the creamedlayer is y=0. The thickness of the creamed layer is y0. Thesedata clearly show that the larger particles cream first due tothe larger buoyancy force acting on them. Conversely, thesmaller particles tend to stay near the bottom of the layer.

F. Summary comments

The use of MRI in research related to suspension me-chanics has matured over the past 15 years. In studies ofparticle migration and emulsion dynamics, MRI is uniquelyable to determine velocities, concentration profiles, and dropsizes in situ. Perhaps the biggest barrier to its further use isthat it remains essentially a technology that requires the ex-perimental apparatus in which a flow experiment is to beperformed to be brought to the equipment rather than havingthe MRI unit readily available for on-going studies in a labo-ratory devoted to fluid mechanics. Typically, MRI instrumen-tation is available in central facilities or at medical centers.Experiments must be scheduled and the flow apparatus mustbe designed within the constraints of the MRI unit as well asthe physical location. Even in those research centers wherededicated instruments are available for use with multiphaseflow studies, it is usually the case that there are numerouscompeting demands being placed on the instrumentation andits technical support staff. In Sec. V these issues are dis-cussed in more detail along with some developments thatmay change the way that MRI experiments are handled.

III. ULTRASONICS

A. Technique

The use of ultrasonics for velocity measurements startedin the 1970s with McLeod and Anliker,58 Barber et al.,59 andBrandestini.60 The original applications were related to themeasurement of blood flow. In the mid-1980s, Takeda61 be-gan to apply this technique to a range of problems in fluidmechanics and heat transfer. The actual velocity determina-

tion is based on the measurement of the Doppler shift in thefrequency of an ultrasonic wave that is scattered from a mov-ing particle. A typical schematic of the implementation ofUPDV is shown in Fig. 15 for a unidirectional laminar flowin a pipe. The transducer emits a pulse of ultrasonic waves,typically in the 1–10 MHz range with 5–10 pulses in thewave packet. In the idealized case, the waves propagatethrough the fluid with little or no attenuation and are scat-tered from a particle in the fluid at position s. The sametransducer is used as the receiving transducer, which is usedto acquire data after each pulse is sent. Information receivedat a particular time � corresponds to a position in the fluidalong the propagation direction. This position is related to sthe wave speed c through

s =c�

2. �16�

In practice, the received signal is continuously monitoredand acquired through a digital data acquisition system. Eachtime is assumed to map onto a unique point in the pipe. Thisignores effects such as multiple scattering and the presenceof overtones that might have different propagation velocities.Also, since data are obtained at discrete points in time, asingle velocity data point actually represents an average ve-locity over the volume element corresponding to a spatial“position” by Eq. �16�. For the geometry in Fig. 15, theequation relating the velocity to the Doppler shift frequencyfD is

vz =cfD

2f0 cos �, �17�

where f0 is the frequency of the incident wave. The angle �explicitly appears in Eq. �17�. This implies that there is an apriori knowledge of the flow direction. This is usually inter-preted as meaning that UPDV will measure the componentof velocity that corresponds to the direction specified by agiven �. For example, UPDV has been used to measure theaverage velocity in turbulent flow by using this interpreta-tion. In Sec. V, recent work is described that is a major steptoward relaxing the requirement that � is known and therebygreatly expanding the applicability of the technique.

The actual measurement of the Doppler frequency re-quires some further considerations. Returning to Fig. 15, ide-ally, each instant of the reflected signal refers to a point inspace. One data point at one position does not provide

FIG. 14. �Color online� Drop size distribution in a creamed emulsion. Theaverage drop diameter is 5.4 �m. The bottom of the creamed layer is y=0and its thickness is y0.

FIG. 15. �Color online� Typical experimental configuration for a UPDVexperiment. The flow represents the fully developed laminar flow of a New-tonian fluid in a pipe. The angle � is the angle between the velocity vectorand direction of ultrasound propagation. The position s represents a point inthe fluid relative to the transducer and along the propagation direction. Theradial position is r.



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enough information to determine the Doppler frequency. Toovercome this, a series of experiments is performed and thecorresponding signals are recorded. For each of these signals,it is possible to identify which times correspond to whichpoints in space. A new time series is created for each spatialposition. This series is populated by points that are equallyspaced in time at the pulse repetition rate �the inverse of thepulse repetition frequency fpr�. It is possible to show thattaking the Fourier transform of this time series yields theDoppler frequency.62

Besides the issue with the angle �, the limitations on thistechnique come from two sources. First, it must be possibleto propagate a high frequency ultrasound in the system withminimal attenuation and scattering. Kytömaa’s review of thepropagation of compressional waves in suspensions providessome insights in this regard.8 He discussed three regimes forwave propagation and provided estimates for the attenuation.This is summarized in Table I, where NRe=a��f0 /� and kis the wavenumber, 2�f0 /c.

The second category of limitations arises from the ex-perimental parameters. As discussed above, the data set isbuilt from signals received from a series of pulses separatedby the pulse repetition time Tpr �=1 /2�fpr�. Clearly, if Tpr istoo small, the scattered and the incident waves will interfere.This means that enough time must be allowed so that thesignal from the most distant point being examined can becollected by the transducer before the next pulse is sent.Considering the geometry in Fig. 15, Eq. �15� can be used tocalculate the depth d into the flow corresponding to time � :

d =c�

2cos � . �18�

The maximum value that � can attain before a new pulsewould interfere with the data being collected is Tpr, whichleads to an expression for the maximum depth in a flow for aparticular Tpr:

dmax =cTpr cos �

2=

c cos �

2fpr. �19�

Another limitation arises from the Nyquist sampling theoremwhich stipulates that fD fpr /2. Combining this with Eq.�17� yields

vmax �cfpr

4f0 cos �. �20�

Eliminating Tpr between Eqs. �19� and �20� shows the trade-off between the maximum depth and the maximum velocity:

dmaxvmax �c2

8f0. �21�

To provide some insights that result from Eq. �21�, considera 5 cm diameter pipe and assume that data are to be collectedat all radial positions. If the pulses consist of 5 MHz wavesand the medium has a wave speed comparable to that ofwater, then the maximum velocity is just over 1 m /s, whichleads to a Reynolds number of 50 000.

The other important parameters are the spatial and ve-locity resolutions. These derive directly from the experimen-tal parameters. The best possible Doppler resolution, �fD, isgiven by

�fD =fpr

NP, �22�

where NP is the number of pulses per scan.63 The radialresolution, �r, is

�r =NPc

2f0. �23�

B. Results

A typical velocity profile measured using UPDV isshown in Fig. 16. These data were obtained using a non-Newtonian fluid in a 20.4 mm pipe. The suspension con-sisted of a blend of microcrystalline cellulose �MCC� andcellulose gum. Two different velocity resolutions were used.The dashed line results from a calculation based on thepower-law model with the material parameters determinedusing a conventional Couette viscometer. Figure 16 shows

TABLE I. Dependence of attenuation on frequency and viscosity for sus-pensions �Ref. 8�.

Regime Physical parameters

Attenuation dependence

Frequency Viscosity

Multiple scattering ka�1 f4 �

Inertial NRe�1 f1/2 �1/2

Viscous NRe�1 f2 �−1

FIG. 16. Velocity profiles for 2% MCC gel obtained at a volumetric flowrate of 15 ml /s acquired using two different velocity resolutions: �vz

=0.41 cm /s �� and �vz=0.026 cm /s ��. The dashed line shows the ve-locity prediction for a power-law model with flow and consistency indicesmeasured by Couette viscometry.



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that as the velocity resolution decreases, the data correspondmuch more closely to the calculation, which is expected. It isalso worth noting again that since velocities are at discretepoints, each data point corresponds to a volume element cen-tered at the represented location.64

As with all of the techniques discussed here, UPDV isnoninvasive in that the transmitter/receiver transducer is notdirectly inserted in the flow. For the data shown in Fig. 16,the transducer is mounted in the wall of the pipe and comesinto direct contact with the fluid. This does lead to possibleerrors close to the wall, which are not present with the othertechniques discussed in this review.

One of the most fundamental and exhaustive applica-tions of UPDV was by Xu and Aidun65 who studied the flowof paper pulp suspensions, which have been the subject ofmany studies over the past 50 years. The issues of dealingwith them by traditional experimental means cover nearlyevery point that makes measurements of velocity difficult.The fibrous nature of the suspension causes Pitot tubes toplug and fibers to attach to hot film anemometers and evenbreak them. Even at relatively dilute concentrations, the sus-pensions are opaque, greatly limiting the usefulness of LDA.One of the early motivations of the development of MRI forflow measurements was to study pulp suspensions, as dis-cussed in Sec. II. The work by Xu and Aidun is unique inthat it covers the range of fiber concentrations of industrialinterest in papermaking: 0.05%–1.0% by weight. For a fiberlength of 2.3 mm, these correspond to values of ncl

3 between0.33 and 6.7. Note that ncl

3�1 corresponds to a dilute sus-pension. The systems studied by Xu and Aidun are semicon-centrated and particularly at the higher concentrations, un-sheared suspensions in this regime are highly entangled andform flocs. To simplify the experiment, rather than studyflow in a pipe, Xu and Aidun used a pressure driven flow ina rectangular channel with depth 2b. They determined themean of the velocity component along the channel overReynolds numbers �based on the viscosity of water� from2000 to 92 000. In the turbulent regime, they were able tosynthesize their results into universal velocity profiles, asshown in Fig. 17. Here, the parameter V�= ��w /��1/2 is usedto nondimensionalize both the distance across the channeland the velocity, where �w is the wall shear stress as deter-mined by pressure drop measurements. Specifically,vx

+=vx /V� and y+=yV� /� where � is the kinematic viscosityof water. The curves in Fig. 17 can be obtained from a cor-relation that depends on ncl

3 and the Reynolds number:

vx+ = 4.69 +

1

0.41�ln�y+� + � sin2 �y

0.9b� ,

�24�� = 0.98 exp�0.14ncl

3 − 1.9 � 10−5NRe� .

Equation �24� represents a significant advancement in theknowledge related to the flow of pulp suspensions. Obtainingthe data needed to make these correlations requires that atechnique such as UPDV or MRI be used.

Xu and Aidun65 also determined the root mean square ofthe velocity fluctuation along the channel. For pulp suspen-sions, this constitutes the first set of comprehensive measure-

ments of this parameter, which is related to the Reynoldsstress, that can be considered as being minimally influencedby the measurement technology. When plotted as vx

2 /vx

versus y /2b �where the overbar denotes the mean value�,they found at low Reynolds numbers, about 12 000, therewas a wide variation among the data for different values ofncl

3. At high NRe, 92 000, the data collapsed to a single mas-ter curve. Although these data are consistent with those fromearlier studies and are arguably less influenced by measure-ments obtained using an intrusive device, there remain issuesto be resolved when measuring unsteady flows with UPDV.In the context of the study by Xu and Aidun, it is importantto recognize that a velocity measurement is not instanta-neous. As described above, data are collected at points acrossa pipe or channel from every pulse. For a pulse consisting offive 5 MHz waves, the total signal duration is only 1 �s.However, building the data set from which the velocity iscalculated requires a number of such signals, typically 128,separated by the pulse repetition time. These two parametersdetermine the frequency response of the experiment. For Xuand Aidun’s work, this ranges from 10 to 100 Hz. Hence, therms values of velocity capture the low frequency fluctuationsbut not the higher ones.

As with MRI, UPDV leads to a technique for measuringthe viscosity of complex fluids that can be applied in actualindustrial settings. Several groups have pursued this line ofresearch.66–69 All of these studies base their analyses on thatof Powell et al.4 for MRI as described through Eqs. �1�–�4�.The only difference is the actual technique used for the ve-locity measurement. UPDV is an ideal technique since it isnoninvasive, it is able to accurately measure unidirectionalflows, and it is easy to implement relative to MRI. At theUniversity of California Davis, this technique has been usedfor studies with xanthan gum, corn syrup, starch gels, starchsuspensions, MCC suspensions, carboxymethylcellulose so-lutions, tomato paste, tomato concentrates, diced tomato sus-pensions, a polymer melt, and paper pulp. In all cases, directcomparisons are made with traditional viscometric tech-

FIG. 17. �Color online� �Xu and Aidun �Ref. 65�; reprinted with permissionfrom Elsevier� The reduced velocity profile for a paper pulp suspension atnl3=5.0. The points represent experimental data �� NRe=37 000; ��NRe=60 000; �� NRe=73 000; �� NRe=92 000� and the solids lines resultfrom the correlation given by Eq. �24�.



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niques. A typical result is shown in Fig. 18, where data aregiven for a 12.75% by weight total solid tomato juice sus-pension. In obtaining these data, three different mean veloci-ties were used. Similar to MRI, this approach serves twopurposes. First, it provides a self-consistency check to deter-mine that the viscosity is independent of the mean velocity,as it should be. Secondly, using different mean velocitiesallows different ranges of shear rates to be accessed �see Sec.II D�. This is clearly seen for the 2.8 and 5.7 cm /s data. Inthe case of the 9.5 cm /s data, there is one point at a very lowshear rate that stretches the range of the measurement morethan might be expected, however, overall, if the mean veloc-ity increases, the range of shear rates is the same but the lowand high shear rates defining the range increase.

The best check that one has for the UPDV-based viscos-ity data is to use a traditional viscometric technique andcompare the results from both methods. The four triangles inFig. 18 are data obtained by turning the entire flow systemused for the UPDV experiments into a large “capillary” vis-cometer. The pressure drop and flow rate were measured andstandard formulas for calculating the viscosity were used.There is excellent agreement between the techniques whichis consistent with other studies that compare UPDV withconventional viscometers. Similar to the findings in Sec.II D, Fig. 18 clearly shows the difference between theamount of information that one obtains from a pointwiseviscosity measuring technique �MRI or UPDV based� and aconventional technique. To obtain the four data points by theconventional method, flow rate and pressure drop measure-ments must be obtained for at least six different values of themean velocity. That is, the pump must be set at six differentspeeds, the flow must come to steady state, and the pressuredrop must be measured at each pump speed. In contrast, forsingle pump speed, the pointwise method spans a largerrange of shear rates than that accessed by all six speeds usedto obtain the four points in Fig. 18.

As with MRI, it is possible to use the velocity profilecombined with a pressure drop measurement to determinethe yield stress. The technique is the same as that describedin Sec. II D. For a material flowing through a pipe that has ahighly blunted velocity profile, the radial position is located

where the sheared region transitions to a pluglike behavior.The shear stress at that point is identified with the yieldstress. As discussed in Sec. II D such a profile might beinterpreted as being a power-law fluid with an exponent thatis much less than 1 �Fig. 18�. In fact, data for systems similarto that used to obtain the data in Fig. 18 were obtained andthe yield stress inferred. Typical data for tomato pastes withdifferent solid contents are given in Table II.69 The yieldstress increases with solid concentration, which is consistentwith previous studies.70

C. Summary comments

As mentioned in the Introduction, MRI and Doppler-based ultrasonic devices have developed with impetus fromthe medical field. There are many more developments thatare not touched upon here, including ultrasonic imaging/tomography. These techniques may be complementary toUPDV but have not found many applications in multiphaseflow measurements at this time.

The point of departure for much of the work in thearea of fluid mechanics was the development of instrumentsthat are specifically aimed at those applications. This led toa commercial instrument called an “ultrasonic profiler”�Met-Flow S. A., Lausanne Switzerland� and an independentpatent by a group at Pacific Northwest National Laboratory.71

At this stage, UPDV is an emerging technique that isreceiving increasing attention. As described in Sec. V, thetechnology is evolving as a result of needs in the medicalfield and these developments promise to increase the useful-ness in the research laboratory.

IV. OTHER TECHNIQUES

A. Electrical impedance tomography

This section deals with some techniques for measure-ments with multiphase flows that have met with success butare not widely applied. The first to be discussed is EIT,which has been developed by Bonnecaze and co-workers.1–3

This technique has been used for measurement of concentra-tion distributions of suspensions undergoing pipe flow. It isimplemented by placing electrodes at regular angular posi-tions around a pipe, typically 32 electrodes are used.2 A cur-rent is applied across the pipe by using two of the electrodes.The voltage difference is measured at adjacent electrodes.This process is repeated until data have been collected as aresult of applying the current across all possible pairs ofelectrodes which are opposite one another and sampling allthe remaining electrodes. These values of voltage are thenused to solve the inverse problem—mapping the conductiv-

FIG. 18. �Dogan et al. �Ref. 69�� Comparison of UPDV viscosity measure-ment technique with a conventional capillary method ��. All data weretaken using a tomato suspension with a total solids concentration of 12.75%.The different symbols represent different average velocities for the flow:�� 9.5 cm /s, �� 5.7 cm /s, and �� 2.8 cm /s.

TABLE II. Yield stress of tomato paste suspensions at different solid con-centrations.

Total weight percent solids Yield stress �Pa�

9 2.0

13 3.2

17 5.0



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ity variations in the pipe from a knowledge of the surfacepotential. This step poses the greatest difficulty for EIT.Bonnecaze and co-workers have developed methods to de-termine the precision of the calculated conductivity field,which is related to the concentration distribution of the dis-persed phase.3 This work has lead to the ability to map thedistribution of particles in a spherical particle suspension.The work of Butler and Bonnecaze2 produced results thatclearly showed the effect of shear-induced particle migration,Fig. 19�a�. The EIT data are indicated by the solid line withdiscrete steps. These clearly show that the concentration isreduced near the pipe wall and is higher than the mean con-centration near the pipe center. Also shown are data obtainedby Hampton et al.26 using MRI and the predictions of themodel of Phillips et al.72

More recently, Norman et al.3 used EIT to study the flowof buoyant suspensions in a pipe. They found that the distri-bution of spheres is governed by a buoyancy number:

Nb =2��p − ��gR2

9�v̄z

. �25�

Typical results are shown in Fig. 19�b� for a suspension withan overall �=0.25 with the particles being heavier than thefluid. A highly concentrated layer is observed near the bot-tom with �0.49. Near the top, the fluid is nearly depletedof particles with �0.04. Data such as these were used to

calculate the first and second moments of the concentrationfield representing the vertical and horizontal distributions,respectively. A plot of the moments versus Nb yielded goodagreement with the results for the suspension balance modelof Nott and Brady39 which includes effects of shear-inducedmigration.

B. Neutron and x-ray radiographies

Neutron and x-ray radiographies are used to image ob-jects using, respectively, neutrons and x rays. In the lattercase, this is essentially the technique widely used in themedical industry, the difference being that a sequence of im-ages can be made that show the dynamics of particlemotion.73,74 In both cases, the equipment is expensive andrequires highly specialized facilities. For example, neutronradiography requires access to a nuclear reactor. However,there are examples where each technique may have inherentbenefits. In both cases, the images that are obtained representthe projection of a three-dimensional object onto a plane.

Of particular interest recently has been the use of neu-tron radiography dynamic imaging to study multiphase flowsinvolving a liquid metal and a gas phase. Such experimentsrequire75 �1� a high flux research reactor, �2� a high speedvideo system, �3� an image intensifier or a high sensitivitycamera; and �4� a high sensitivity converter. Figure 20�a�

FIG. 19. �Color online� �a� �Butler and Bonnecaze �Ref.2�; reprinted with permission from American Instituteof Physics� Volume fraction vs radial position for theflow of a �=0.4 suspension in a pipe. The EIT data arerepresented by the solid curve that has steps. The dottedline is the prediction of Phillips et al. �Ref. 72�. Thecircles are from Hampton et al. �Ref. 26�. �b� �Normanet al. �Ref. 3�; reprinted with permission from Cam-bridge University Press� Volume fraction contours for a�=0.25 suspension flowing through a pipe. The higherconcentration at the bottom of the pipe results from thespherical particles being heavier than the suspendingliquid.

FIG. 20. �Saito et al. �Ref. 76�; reprinted with permission from Elsevier� �a� Schematic of a neutron radiography experiment. �b� Nitrogen bubbles rising ina liquid metal �lead/bismuth�. Gas flow goes from 1 cm /s �left� to 35 cm /s �right�; framing rate is 250 frames /s.



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shows a typical experiment. A collimator is used to provide aneutron beam that is passed through a cell containing a liquidmetal, a lead/bismuth alloy, through which nitrogen flows.The converter transforms the neutrons into visible light thatis then directed to a high sensitivity camera. The recent in-terest in this technique stems from studies of heat transfer inbreeder reactors, which use liquid metal for cooling. Theneutron beam is able to pass through the liquid metal and isattenuated by the gas. A typical image is shown in Fig.20�b�.76 These images of nitrogen bubbles were obtained at arate of 250 frames /s. The image on the left is characteristicof the lower gas flow regimes, roughly 1 cm /s, while theimage on the right has an average gas velocity of approxi-mately 35 cm /s. The spatial resolution is about 0.2 mm. Thiscombination of the temporal and spatial resolutions clearlyallows the outline of the gas bubbles to be seen, keeping inmind that the image is the projection of the three-dimensional phase distribution onto a plane.

C. X-ray tomography

The radiographic techniques described in Sec. IV B donot allow for complex three-dimensional structures to bemapped. The image that is obtained is a projection of a three-dimensional object onto a plane. Tomographic techniquesseek to overcome this limitation by obtaining true three-dimensional images. MRI is one such technique. Anotherthat also owes much of its development to the medical fieldis x-ray computed tomography �CT�. The development ofparticular interest for multiphase flow studies involves dy-namic CT. Jenneson and co-workers77–79 have demonstratedthat it is possible to obtain both high image acquisitionspeeds and good spatial resolution with this technique.Figure 21 shows dynamic CT images obtained for a4�40 mm2 by 300 mm3 high fluidized bed. These images

were obtained for a bed consisting of ZnO nanoparticles withaverage diameters of 50 nm. Each voxel used to constructthe images is 400 nm on a side. Each image took 40 ms toacquire, which can be reduced to 1 ms.79 These imagesclearly show the benefit of having the dynamic capability.The image at the top left is the first of the sequence. Timeincreases, in 40 ms increments, moving from left to right onthe top row and then from the top right image to the leftimage in the second row, and so forth. The letter “a” pointsto an aggregate that breaks down with successive time stepsand then re-forms in the final image, “b.” Results such asthese clearly show that improvements in both the instrumen-tation as well as the computational speed have led to signifi-cant advances in this area over the past decade.80

V. COMPARISONS AND FUTURE DIRECTIONS

One goal of this review has been to provide an overviewof techniques that are used to measure concentration, veloc-ity, and other fields for multiphase fluids with a particularemphasis on the ability to work with systems of practicalinterest. Two other goals are �1� to look ahead to upcomingdevelopments that may impact the versatility or usefulness ofa technique and �2� to provide some guidance as to whichtechniques might be best suited to particular circumstances.

Looking ahead, there are some developments for bothMRI and UPDV that will enhance their usefulness for thestudy of multiphase flows. The issue with MRI has been itsinaccessibility. Fifteen years ago, anyone wanting to use suchequipment for fluid mechanics experiments would eitherneed to build the MRI unit from components or use instru-ments that had been designed for humans or small animals.Changes over the past decade have tended to see a mergingof technologies for analytical and imaging applications. Theinstruments have become more energy efficient, requiringless cryogen. The magnets are better shielded, which reducesthe need for large rooms to ensure a safe operation. One nextstep along this path is the use of permanent magnets forimaging. Technology such as that recently developed byAspect Magnet Technologies, Ltd. �Netanya, Isreal� providesthe opportunity to bring imaging to the laboratory muchmore easily. The 1 T magnet used by this company hasan imaging volume of 80�100�10 mm3. Typical resolu-tions for a volume divided into 128�128�64 points is0.5�0.5�1 mm3 with resolutions as small as 20 �m pos-sible. The introduction of equipment such as this promises tosimplify the use of MRI. It may also allow more complexflow experiments to be introduced so that, for example, anapparatus for simultaneous MRI and pressure measurementsmay be easier to construct.

One issue that confounds the use of MRI is the timerequired to acquire data, especially velocity fields. In gen-eral, the time required to acquire two-dimensional images,comprised of NP�NP pixels, scales as the number of pointsNPs. This may be a one-dimensional velocity profile or atwo-dimensional concentration profile. There are various so-lutions that have reduced the time to acquire a one-dimensional velocity profile to about 10 ms.81–83 There aresome newer techniques that open the opportunity to follow

FIG. 21. �Jenneson and Gundogdu �Ref. 79�; reprinted with permission fromAmerican Institute of Physics� Dynamic computer tomographic images of afluidized bed at 40 ms intervals. The sequence of images starts at the topleft, moves right, and returns to the leftmost image on the second row. Thearrow in that image points to an aggregate that breaks down and then re-forms in the final image.



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processes �concentrations, velocities� within a single voxelon time scales of 100 �s or less.84 On the one hand, the timeresolution issue is dramatically reduced but the penalty is theloss of spatial information, which can still be determinedusing this technique more rapidly than by traditional imag-ing. This method also offers the possibility of imaging solidphases which have relaxation times that are two to threeorders of magnitude shorter than those of liquids.84 Gladdenet al.85 used methods adapted from medical imaging such asfast low angle shot imaging �FLASH� or SNAPSHOT imag-ing to capture unsteady-state gas-liquid distributions intrickle-bed reactors. In these techniques, rapid and repeatedexcitation of the sample at low power is used. FLASH hasalso been used in conjunction with tagging velocimetry forrapid velocity data acquisition. For example, flow transitionsand vortex oscillations in a Taylor–Couette flow were ob-served by this method.86

With UPDV, future instrumentation is likely to get morecomplex and provide more versatility. From a fluid mechan-ics standpoint, some of the most interesting results to datewith multiphase systems deal with unidirectional flows. Thereason is straightforward. Figure 15 and Eq. �17� clearlyshow the crucial role played by the angle �. If � is notknown, the velocity cannot be found. Unidirectional flowsare an important but limited subset of flows. More to thepoint, if UPDV is to be used to map unknown velocity fields,the problem of not knowing � a priori must be mitigated.One approach to solving this problem has been to use anarray transducer and essentially perform the measurementdescribed in Sec. III using each element �typically 128 ele-ments� of the array. This is modeled as a lateral oscillationthat is in addition to the ultrasound pulse.87,88 Much of thetechnology that is used for standard medical ultrasound scan-ners can be applied to these measurements.89 The cost comesfrom the computationally intensive algorithm that is used tocompute the velocity from the large data sets that result froma single measurement. In one case, a 100 CPU Linux clusterwas used for postprocessing.90 This technique has beentested for well-defined flows,90 but the best example of itspower is seen in Fig. 22 which shows blood flow through thebifurcation of the carotid artery at two different times during

a heartbeat.91 Two components of the velocity vector areobtained. The total time for image acquisition and display is3 s. The maximum velocities that can be measured are 3 m /sin the horizontal direction and 0.46 m /s in the vertical. Thecorresponding resolutions are 0.048 and 0.008 m /s. The con-fidence in the quantitative nature of these data stems fromboth the extensive calibrations in a known geometry as wellas comparisons the authors make with existing detailedcalculations.88,92

Recalling the discussion of the experiments of Xu andAidun,65 it would appear to be possible to obtain informationabout the turbulent structure of the flow from UPDV. As Xuand Aidun,65 others have asserted that these measurementsare instantaneous.93 It seems more reasonable to expect thatan approach like that used for MRI �Refs. 37 and 94� mightprovide the best means to analyze UPDV signals.95

Lastly, ultrasonic tomography appears to provide ameans of measuring phase distributions in multiphase flows.The technique has been shown to be capable of visualizinggas holdup in a liquid by imaging the dynamics of the systemat 300 frames /s.96 As with EIT and two-dimensional UPDVvelocity measurements, there is considerable data processingwhich makes the image reconstruction time 10 frames /s.The potential of combining this with techniques such asthose of Jensen and co-workers could lead to a very powerfuland portable instrument for simultaneous velocity and phasedistribution measurements.

The final goal of this review is to provide some perspec-tive on the uses of the various techniques, considering whenone may offer advantages over another. In terms of versatil-ity, MRI has many direct advantages for concentration, ve-locity field, droplet size, and chemical constituent mapping.Indeed, of all the methods surveyed, it is the one that offersall of these capabilities. It can extend beyond what has beenshown here and truly map three-dimensional fields of all ofthese variables. The issues with MRI have resulted from theneed to purchase large magnets that require considerablespace and highly trained technicians. As indicated above,many of these issues are being addressed by a new genera-tion of instruments. Other issues remain. While the newmagnets confine the field to a much smaller space, it is stillthe case that the materials of construction for a flow cellmust be carefully chosen to minimize interference with themeasurement. This may mean using plastic or glass flowloops, or certainly having the section of the test cell overwhich the actual measurement is made be free of a substancethat would distort the applied magnetic fields. This also in-cludes the discrete phases. Although MRI will work withconcentrated, opaque systems, fluids containing magneticparticles cause problems that need to be overcome on a case-by-case basis.

From the standpoint of this article, the principal alterna-tive to MRI for velocity measurements is UPDV. Some ofthe limitations of this technique, particularly those relating tothe determination of two-dimensional velocity profiles, werediscussed above. It appears that this issue will be resolved.The second limitation results from signal attenuation due toabsorption and also scattering. Kytömaa mapped out this be-havior for suspensions and provided an excellent starting

FIG. 22. �Color online� �Udesen et al. �Ref. 91�; reprinted with permissionfrom Elsevier� �a� Two-dimensional velocity field in the bifurcation of thecarotid artery at the time of peak systole; �b� two-dimensional velocity fieldin the bifurcation of the carotid artery shortly after the peak systole. Velocitymagnitude is represented by the vectors and also by the color.



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point for estimating how large these effects will be.8 In someof the work described above and especially that related to themeasurement of viscosity in concentrated systems wherescattering can be significant, a complete velocity profile isnot required. It is usually safe to argue that the profile issymmetric and only results from the wall to the center of thepipe are needed. In cases when there are high attenuationvelocities, data from a portion of the pipe may be acquiredand viscosity data can still be determined.69 An advantagewith multiphase flows is that there is no need to seed theflow with scattering particles. One consistent issue with ul-trasonic techniques is that transducers that are mounted onthe outside of the wall of the pipe do not give a high qualitysignal.97,98 Generally, measurements are made with transduc-ers in contact with the fluid.

Therefore, the direct comparison between UPDV andMRI results in the conclusion that MRI is much more versa-tile and has many capabilities that are relatively unexplored,especially by the fluid mechanics community. It is currentlyexpensive and difficult to implement but that is changing.UPDV offers a more limited menu of capabilities, but it isinexpensive, portable, and easy to implement. There are alsodevelopments on the horizon that may bring UPDV capabili-ties more into line with those of MRI, at least in terms ofmeasuring velocities in multiphase flows. These points andother comparisons among the techniques are summarized inTable III.

The other three techniques discussed in this review aremuch more specialized. EIT offers a potentially inexpensiveapproach to the measurement of particle concentration atvarious points along a pipe. This could be very valuable inpractical applications where there are long transfer lines in-volving particulate suspensions that would benefit from on-

line monitoring to ensure that particles remain in suspensionand that plugging is not imminent. However, the core issue isthe difficulty that is involved in extracting meaningful infor-mation from EIT measurements in an automated, robust, androutine manner.

The other two techniques discussed in this review, x-rayand neutron radiographies, suffer from similar drawbacks.The equipment used to make the measurements is highlyspecialized and in the case of neutron radiography requiresaccess to a nuclear reactor. This is rarely available. Usually,an experimental apparatus must be assembled at the sitewhere the instrument is. It is possible to make the sameargument for MRI, however, MRI equipment is ubiquitous ina research university, especially those associated with medi-cal schools. Further, with the advent of smaller scale andeasier to use equipment, there is the possibility of “bringingthe �MRI� equipment to the experiment” rather than what isdone today, “bringing the experiment to the �MRI� equip-ment.” Still, the advantages of the radiography techniquesmay, in some specialized cases, weigh in favor of schedulingto do an experiment at a remote location. Neutron radiogra-phy is well suited for looking at gas–molten metal flows.X-ray radiography can be used for highly concentrated sus-pensions of heterogeneous solids. Both might be useful forlooking at multiphase flows in pressure vessels that are madeout of materials which cannot be placed in a MRI unit andwhich may not allow flush mounted transducers that are incontact with the fluid.

In summary, today, there are several techniques that areavailable to study multiphase flows of real and model sys-tems. These techniques are continually being advanced dueto a number of influences outside the community of scholarswho are doing fundamental research on multiphase flows.

TABLE III. Summary of techniques.

Technique Concentration Velocity

Chemicalconstituent/dropletdynamics Diffusivity Comments

MRI Yes Yes Yes Yes Difficult to use; some restrictions on types of materials forboth flow cells and fluids themselves.

Temporal resolutions limit frequency response to about 100 Hzfor a full one-dimensional flow mapping. New equipmentmay make this much more accessible.

UPDV Yes �1� Yes �2� No No �1� Concentration maps not discussed here.

Tomography techniques are available but attenuation is an issue.

�2� New technologies will allow a full mapping oftwo-dimensional flows.

EIT Yes No �1� No No Low cost for hardware. Easily installed at multiple locationsalong a pipe.

Extracting information from data is difficult.

�1� If used to track tracer particles can give velocity data�Ref. 97�.

X-ray andneutronradiographies

Yes No �1� Possible;not widelydone

No Highly specialized and expensive equipment.

Generally would need to take experiments to the site wherethe equipment is located.

New developments show better spatial and temporalresolutions.

�1� Velocity obtained from particle tracking.



129.62.12.156 On: Sun, 01 Jun 2014 16:44:54

This is quite advantageous but at the same time requires thatthe user be knowledgeable about fields that are far from fluiddynamics, making this research truly multidisciplinary.

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experimental techniques for multiphase flows

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