nucleate pool boiling of aqueous polymer solutions on a cylindrical heater

J. Non-Newtonian Fluid Mech. 125 (2005) 185–196

Nucleate pool boiling of aqueous polymer solutions on a cylindrical heater

Juntao Zhanga, Raj M. Manglikb, ∗a Department of Surgery, School of Medicine, University of Maryland, Baltimore, MD 21201, USA

b Department of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, Cincinnati, OH 45221-0072, USA

Received 5 November 2003; received in revised form 30 November 2004; accepted 23 December 2004

Abstract

Heat transfer and ebullience behavior in saturated, nucleate pool boiling in aqueous dilute to semi-dilute solutions of a surface-active(hydroxyethyl cellulose or HEC-QP300) and a shear-thinning (polyacrylic acid or Carbopol 934) polymer on a horizontal, cylindrical heaterare experimentally characterized. The influence of fluid rheology and interfacial properties (dynamic surface tension and wettability) onthe heat transfer coefficient is delineated. In HEC solutions, nucleate boiling is enhanced with increasing concentrationc till an optimumnear the critical polymer concentration (c* ∼600 wppm); at higher concentrations, the enhancement decreases considerably. Contrarily, thereis continuous deterioration in the boiling heat transfer, relative to water, in Carbopol solutions with increasing concentrations. Adsorptiono ation sites,t rface-activeH ess them©

K

1

cahiatcAorto

c

-iestter

ions.ith activen ap-

ite

C so-arentmuchHart-,lutepurersbe

0d

f macromolecules, or agglomerates of smaller monomers onto a heating surface that may favor the formation of new nucleogether with a decreased dynamic surface tension, are responsible for the general growth in the number of active bubbles in suEC solutions. In HEC solutions withc>c* as well as in all Carbopol solutions, on the other hand, higher viscosity tends to suppricro-convection near the wall and the bubble growth, thereby weakening the boiling process.2005 Elsevier B.V. All rights reserved.

eywords:Shear thinning; Surface tension; Thermal processing; Interfacial transport; Nucleation

. Introduction

Thermal processing of fluid media to produce biochemi-al, pharmaceutical, personal care, and hygiene products isvery complex heat transfer problem. It typically entails

eating and drying of aqueous polymeric solutions by boil-ng them, in order to thicken them and make pastes. Rathernomalous phase-change behaviors have been observed in

his process[1–4], and the consequent lack of close thermalontrol often leads to product loss and quality degradation.variety of factors play a role, and they include the type

f polymer, its molecular weight and concentration, solutionheology and interfacial properties (surface tension and wet-ability), heated surface geometry, and heat flux levels, amongthers.

Several studies have investigated nucleate pool boilingharacteristics of polymeric dilute to semi-dilute solutions

∗ Corresponding author. Tel.: +1 513 556 5704; fax: +1 513 556 3390.E-mail address:[email protected] (R.M. Manglik).

under atmospheric conditions, andTable 1gives a chronological listing of the available literature. In one of the earlwork on the effects of polymer additives on boiling of waon a plate heater, Kotchaphakdee and Williams[2] found theheat transfer to be enhanced in HEC-H and PA-10 solutWhile both additives make the solution more viscous wshear-thinning flow behavior, HEC-H also has surface-aproperties (i.e., it reduces surface tension of the solutiopreciably) and a lower molecular weight (M= 2× 105 Da);for PA-10,M= 106. The combined effects of nucleation sdensity and solution concentration are reported by Ulicny[8].Appreciable enhancement was observed in aqueous HElution on a 600 grit roughened surface, whereas no appenhancement was observed for the same solution on asmoother surface. The experimental data of Wang andnett [4], Paul and Abdel-Khalik[7], and Hu[9], howeverindicate a deterioration in boiling heat transfer for very diaqueous polymeric solutions when compared to that ofwater. All of these studies[4,7,9]used platinum wire heateinstead of a plate heater[2,8] and geometry effects may

377-0257/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.jnnfm.2004.12.001

186 J. Zhang, R.M. Manglik / J. Non-Newtonian Fluid Mech. 125 (2005) 185–196

Table 1Chronological listing of nucleate pool boiling studies of aqueous polymeric solutions

Author(s) Heater geometry Polymers

Kotchaphakdee and Williams[2] Plate Acrylamide, PA-10, PA-20, HEC-L, HEC-H, HEC-MMiaw [5] Plate HEC-H, PA-10, PA-30Yang and Maa[6] Plate and wire HEC-250HR, 300HR, 250GRPaul and Abdel-Khalik[7] Wire Separan AP-30, NP-10P, MGL; PEO; HEC 250MR, 250HR, 250HHRUlicny [8] Plate PA-10Hu [9] Wire Separan AP-30, HEC 250HHRWang and Hartnett[4] Wire SLS and Separan AP-30Shul’man et al.[3] Plate PAA, HEC-H, PEOShul’man and Levitskiy[10] Plate PAA, HEC-H, PEOLevitskiy et al.[11] Plate PAA, HEC-H, PEOBang et al.[12] Sphere PEO

present. The results of Yang and Maa[6] are even more con-trary, and the same boiling heat transfer performance for di-lute aqueous HEC solutions with both a plate and platinumwire heater has been reported. More recently, Shul’man et al.[3], and Levitskiy et al.[11] have shown that even with thesame kind of polymers of the same molecular mass, the boil-ing performance can substantially change with concentration,temperature, and external conditions. They report enhancedboiling heat transfer in dilute solutions (c= 15–500 wppm),but a decreased heat transfer in highly concentrated aqueoussolutions (c= 1%) of HEC-H on a plate heater, which has acharacteristic size that is much larger than the mean size ofthe bubbles.

The altered boiling heat transfer in polymer solutions isalso displayed in a markedly different bubbling behavior(shape and size of bubbles, their growth rate, foaming, andnucleation frequency, etc.) compared to that of pure water[3,9,11,12]. Bubbles of smaller sizes and regular shapes arereleased from the heater with higher frequencies than seenin pure water, and they rise in a more orderly fashion. Adja-cent bubbles tend to coalesce less due to the effects of normalstresses and elongational viscosity in thin films formed be-tween them. Levitskiy et al.[11] suggest that the change inthe wetting angle along with a reduction in surface tensionfor HEC-H solutions account for the observed decrease inbubble sizes. The changes in the interfacial characteristicsa rptiond

Polymers are typically large molecules, macromolecules,or agglomerates of smaller chemical units called monomers,and are broadly classified as biological or non-biologicalmacromolecules. Their addition in water primarily increasesthe solution viscosity, which tends to increase with concen-tration as well as the molecular weight of the polymer, and of-ten display a shear-rate dependent rheology[13,14]. With theexception of some surface-active polymers (or polymeric sur-factants) such as hydroxyethyl cellulose (HEC) and polyethy-lene oxide (PEO), most polymeric solutions do not show anysignificant change in surface tensionσ [15,16]. The viscosityof the polymer solution, however, can influenceσ measure-ments considerably, especially at higher viscosity and bubblefrequency[15,17,18]. The reduced surface tension is largelybrought about by the molecular adsorption of surface-activeadditives to the vapor–liquid interface[19]. The time scalesof this process vary from order of seconds to minutes de-pending upon the polymer chemistry and its concentration insolution, which is possibly due to the slow process of diffu-sion transport of polymer molecules to the interface and theirsubsequent reorientation[20]. This, along with time scales of10–100 ms for boiling bubble dynamics in water[21], thusresults in a rather complex interfacial behavior.

The objective of this study is to determine how nucleatepool boiling heat transfer of water is affected by the additionof polymers that have different degrees of polymerization ands ons.H er,

TP

ditive (t

OSOL 4)

C hyl celIA ght tanMMPSV % solu

re perhaps a direct consequence of the molecular adsoynamics of the additive in water.

able 2hysico-chemical properties of HEC-QP300 and Carbopol 934

Polymer ad

HEC (NATR

hemical name Hydroxyetonic nature Nonionicppearance White to liolecular weight (Da) ∼4–6× 105

anufacturer Amercholurity ∼99%pecific gravity 1.033iscositya (cps) (25◦C) 300–400 (2a Brookfield viscometer.

urface-active properties in dilute and semi-dilute solutiydroxyethyl Cellulose (HEC-QP300), a nonionic polym

rade name)

QP-300) Carbopol (Carbopol 93

lulose Polyacrylic acidCationic

dry powder White dry powder∼3× 106

BF Goodrich∼99%

1.41tion) ∼8–9× 104 (2% solution)

J. Zhang, R.M. Manglik / J. Non-Newtonian Fluid Mech. 125 (2005) 185–196 187

and Carbopol 934, a cationic polymer, are employed. Whileboth produce viscous aqueous solutions, the former displayssignificant surface-active properties and the latter rendersa shear-thinning rheology in the shear-rate range of inter-est (10–1000 s−1). Their chemical composition and relevantphysico-chemical properties are listed inTable 2. Intrinsicviscosity, variations in their shear-rate dependent viscosity,along with temperature-dependent equilibrium and dynamicsurface tension are recorded, in order to characterize the rhe-ological and interfacial behaviors of the polymeric solutions.Pool boiling curves (q′′

w versus�Tsat) for the incipience tofully developed nucleate boiling regimes under atmospheric-pressure saturated conditions are presented, which highlightthe effects of polymer concentration and wall heat flux onboiling and the associated heat transfer coefficients. Photo-graphic documentation of the ebullience activity (bubble nu-cleation, growth, and departure at the heater surface) and itsevolution with concentration and heat flux is also presented,with an assessment of the altered bubble dynamics in theaqueous polymer solutions.

2. Experimental setup

2.1. Pool boiling experiment

es iss ch

Fp

contains the polymer solution pool and the cylindrical heater,is encased in an outer glass tank that has circulating mineraloil fed from a constant-temperature re-circulating bath (notshown in the figure) to maintain the test pool at its saturationtemperature. A water-cooled reflux condenser, along with asecond coiled-tube water-cooled condenser, helps condensethe generated vapor and maintain an atmospheric-pressurepool. A precision pressure gage (±0.0025 bar accuracy) ismounted on top of the boiling vessel to monitor the pressure inthe pool throughout the experiments. The heating test sectionshown inFig. 1(b) consists of a horizontal, gold plated, hollowcopper cylinder of 22.2 mm outer diameter; the 12.7�m thickgold plating mitigates any surface degradation and oxidationfrom chemicals in the test fluids. A 240 V, 1500 W cartridgeheater, with insulated lead wires, is press-fitted in the hollowcylinder with conductive grease to fill any remaining air gapsand provide good heat transfer contact with the inside ofthe tube. The cartridge heater is centrally located inside thecopper tube, and the gaps at each end are filled with siliconerubber to prevent water contact. Also, because the heater sur-face roughness significantly influences the boiling behavior,it was examined using an optical microscope as well as anatomic force microscope (AFM). The optical microscope im-ages of the heated surface inFig. 2show a random distributionof pits, cavities, and machining grooves of varying shapes andsizes along the heater surface. The overall r.m.s. values for the

The experimental setup used for the pool boiling studihown schematically inFig. 1(a). The inner glass tank, whi

ig. 1. Schematic description of experimental facility: (a) pool boiling ap-aratus and (b) cross-sectional view of cylindrical heater assembly.
Fig. 2. Optical microscope images of heater surface.


surface roughness obtained from the AFM scans, and mea-sured at four different locations, range from 0.076 to0.347�m.

The heater-wall and pool-bulk temperature measurementswere recorded using precision (±0.5◦C) copper-constantanthermocouples, interfaced with a computerized data acquisi-tion system that has an in-built ice junction and calibrationcurve. A variac-controlled ac power supply, a current shunt(0.15� with 1% accuracy), and two high-precision digitalmultimeters for current (within±1%) and voltage (within±0.1%) provided the controls and measurements of the in-put electric power and thus the heat load. At each incrementalvalue of power input or heat load, the dissipated wall heat fluxq′′

w was computed from the measured voltageV, currentI, andheater surface areaA (=2πr0L; whereL is the heated lengthof heater) as

q′′w = VI

A. (1)

The concomitant wall superheat�Tw was determined fromthe average value of the four wall-temperature thermocouplereadings (Ti,r), and the liquid pool’s saturation temperatureTsat as follows:

Tw ={∑4

i=1[Ti,r − (q′′wr0/k)ln(r0/r)]

4

}, (2)

a

�

wc fh dingsf atfl .T d byta edd intya withb

2

atingc nc-t e en-v torw rivem h them par-a angu-l vice,w Rad.F sd ilute

solutions using a Cannon-Fenske capillary-tube viscometer,and then by taking the limiting value of the reduced viscosi-ties at four different concentrations.

Sample weights of HEC and Carbopol were measuredusing a precision electronic weighing machine of±0.1 mgaccuracy, and then dissolved in distilled deionized water (atslightly elevated temperatures to aid solubility) to obtainthe test samples. The rheometer calibration was validatedusing a standard oil sample, and pure water. The test liquidviscosity was then measured using a concentric cylindergeometry with conical end (DIN geometry) for shear ratesless than 100 s−1, and a double concentric cylinder geometrysystem for higher shear rates. Temperature control wasattained via a Peltier system that allows for rapid andaccurate heating and cooling of the liquid sample. The datareproducibility was further checked using multiple runs for afew fixed-concentration samples. Once again, the maximumsingle-sample, error propagation uncertainty in viscosityand temperature were±1.4% and±0.5%, respectively.

2.3. Surface tension measurement

Surface tension measurements were made by themaximum bubble pressure method using a twin orifice com-puterized surface tensiometer (SensaDyne QC6000; CSCScientific Co.). Dry air at 3.4 bar is slowly bubbled throught mmd in as por-t testflp con-t er toc eouss in-t outhi re ofb rfacet s, bya boths staticm nciest s oft lida-t an bef isc e, andsw ,a

2

tionn UL-N tter

nd

Tw = Tw − Tsat, (3)

herer is the radius of wall thermocouple location,r0 is theylindrical heater radius, andk is the thermal conductivity oeater material. It may be noted that thermocouple rea

or T1,r–T4,r were within±0.7◦C of each other for a heux of 100 kW/m2, thus ensuring a near constantTw heaterhe maximum experimental uncertainties, determine

he single-sample propagation of error method[22] in q′′w

nd∆Tw, were±1.44% and±0.5%, respectively. Extendetails of the experimental procedure and uncertanalysis, along with the validation of test measurementsoiling data for distilled water are given in Refs.[23,24].

.2. Viscosity measurement

Viscosity measurements were carried out using a rotylinder rheometer (AR-2000; TA Instruments) that can fuion in both a controlled-stress and controlled-shear-ratironment. It has an electronically controlled induction moith an air bearing support for all rotating parts. The dotor has a detachable draw rod arrangement to whiceasuring geometry (rotating cylinder, cup and cylinder,llel plate, and cone and plate) can be attached. The

ar displacement is measured by an optical encoder dehich can detect very small movements down to 40 nurthermore, intrinsic viscosity [η] of the two polymers waetermined from the viscosity measurements of their d

he small and large glass orifice probes (0.5 and 4.0iameter, respectively) immersed in the test fluid poolmall beaker to produce a differential pressure signal proional to the fluid surface tension. The temperature of theuid is measured using a well-calibrated thermistor (±0.1◦Crecision) attached to the orifice probes. The test-fluid

ainer is immersed in a constant temperature bath in ordontrol and maintain the desired temperature of the aquolutions. The time interval between the newly formederface and the point of bubble break-off at the orifice ms referred to as “surface age,” and it gives the measuubble growth time that corresponds to the dynamic suension value at a given operating bubble frequency. Thultering the air-bubble frequencies through the probes,tatic and dynamic surface tension can be measured;easurement are obtained with very low bubble freque

hat lead to equilibrium conditions. Detailed descriptionhe solution preparation, instrument calibration, and vaion procedures along with measurement uncertainties cound in Refs.[15,24]. The maximum uncertainties, in thase, in the measurement of concentration, temperatururface tension, based on a propagation of error analysis[22],ere found to be±0.4%,±0.5%, and±0.7%, respectivelynd further calculation details are given in Ref.[24].

.4. Photographic observations

The growth of nucleating vapor bubbles and their moear the cylindrical heater surface were recorded with a PiX TMC-7 high-speed color CCD camera that has shu


speeds of up to 1/10,000 s, with a 768 (horizontal)× 494(vertical) pixel resolution. The CCD camera is interfacedwith a PC via a FLASHBUS MV pro image capture kit thathas high-speed PCI-based bus-mastering capabilities (up to132 Mbytes/s); it delivers consecutive frames of video in realtime into system memory while keeping the CPU free to oper-ate on other applications. Furthermore, a FUJI 12.5–75 mmmicro lens was used on the CCD camera to facilitate highquality close-up photography.

3. Results and discussion

The intrinsic viscosity [η] or limiting viscosity numberfor the two polymers was determined by measuring the vis-cosityη at several different concentrations using a capillaryviscometer, and then extrapolating the reduced and/or rela-tive viscosity to zero concentration[25]. The Huggins plot(ηred versusc; ηred=ηsp/c, ηsp= (η − η0)/η0) and the Krae-mer plot (ln(η/η0)/c versusc) are graphed inFig. 3, and theestimated values of [η] for HEC QP-300 and Carbopol 934 inaqueous solutions are found to be 5.4 and 10.8 dl/g, respec-tively. It may be noted that the variation of viscosity withconcentration in dilute aqueous solution depends on the typeof polymer, and its ability to enhance the viscosity of thesolution is reflected in its intrinsic viscosity [η]; the biggert thev r isr tion[

teγ ance

F HECQ osity[

Fig. 4. Variation of apparent viscosity with shear rate for aqueous HECQP-300 solutions.

of aqueous polymeric solutions, and is perhaps one of thekey factors in determining the bubble dynamics and vaporremoval behavior. The apparent viscosity–shear rate (η–γ)data for aqueous HEC QP-300 and Carbopol 934 solutionsare graphed inFigs. 4 and 5, respectively. These were ob-tained in a rate-controlled mode, where the shear rate wasramped and allowed to equilibrate to a steady-state valuebefore the next successive increase. It is seen inFig. 4 thatHEC solutions are significantly more viscous than water, their

F bopol9

he number, the more capable a polymer of increasingiscosity in the solution. In general, the viscosity numbeelated to the molecular weight or degree of polymeriza25].

The apparent viscosityη and its variation with shear ra˙ has a direct bearing on the nucleate boiling perform

ig. 3. Huggins and Kraemer Plots for dilute aqueous solutions ofP-300 and Carbopol 934 to determine their respective intrinsic visc

η].
ig. 5. Variation of apparent viscosity with shear rate for aqueous Car34 solutions.


Table 3Increase in viscosity of aqueous polymer solutions with respect to water at 23◦C as a function of concentration at shear rates of∼0 and 500 s−1

HEC Carbopol

c (wppm) η × 103 (Pa s) Percent increase c (wppm) η × 103 (Pa s) Percent increase

≤0.1 s−1 500 s−1 ≤0.1 s−1 500 s−1 ≤0.1 s−1 500 s−1 ≤0.1 s−1 500 s−1

Water 0.935 0.935 – – 100 2.15 1.03 129.9 10.2300 1.65 1.08 76.5 15.5 500 3.05 1.43 226.2 52.9600 2.02 1.25 116.0 33.7 1000 4.18 1.77 347.1 89.3

3000 5.16 3.65 451.9 290.4 3500 12.27 4.39 1212.0 369.5

viscosity increases with concentration, and at low concentra-tions they virtually behave as Newtonian fluids. The Hu et al.[16] data are also included inFig. 4 for comparison, thoughthese are for a different grade of the HEC family of poly-mers (HEC 250HHR) that has a higher molecular weight(M= 1.3× 106 Da) as well as a higher degree of polymeriza-tion [26], and their shear-thinning behavior in higher concen-tration solutions is evident. A similar rheological behavior hasalso been observed by Maestro et al.[27]. Their data for thelower molecular weight HEC9 (M= 9× 104 Da) show nearNewtonian characteristics even at very high concentration(10% by weight), and a non-Newtonian shear-thinning behav-ior in a 0.75% HEC130 (M= 1.3× 106 Da) solution. Theseresults are clearly indicative of the role of molecular weightand degree of polymerization of the additive in characterizingtheir aqueous solution rheology. The data for Carbopol 934solutions inFig. 5, when compared with the respective valuesfor HEC QP-300 inFig. 4, indicate higher viscosity to re-flect the increased degree of polymerization (M= 4–6× 105

and 3× 106 Da, for HEC and Carbopol, respectively) andthe higher intrinsic viscosity seen inFig. 3. Also, the shear-thinning behavior of Carbopol 934 solutions is obvious athigher concentrations. The relative change in the apparentviscosity of different concentration solutions of both HECQP-300 and Carbopol 934 from that of water, at a shear rateof 500 s−1 (atypical of the bubble-fluid motion encountered inn

ies,t e fre-q solu-t iss d de-ca n tot sys-t arc t2 t oft re-q so men-tr iona alli y the

Fig. 6. Dynamic surface tension and its variation with polymer concentrationin aqueous HEC-QP300 solutions.

bubble frequency of 0.33 Hz, which corresponds to a surfaceage of∼3 s.1 As noted by Persson et al.[20] for polymersbelonging to the class of nonionic cellulose derivates thatinclude HEC, time required for the complete relaxation ofσ to an equilibrium value is of the order of minutes, possi-bly due to the slow process of diffusion transport of polymermolecules to the interface and their subsequent reorientation.In concurrence with this, the present results indicate typicalrelaxation times for HEC to be around 1–2 min. The surfacetension measurements for Carbopol 934 solutions displayeda similar behavior with varying bubble frequency and henceare not discussed separately.

1 It may be noted that though the Hu et al.[16] data were also obtained bythe maximum bubble pressure method, the bubbling frequency (or surfaceage) has not been mentioned in their paper.

ucleate boiling) and at “zero” shear rate are given inTable 3.For characterizing the liquid–vapor interfacial propert

he measured surface tension values with different bubbluencies and polymer concentrations for HEC QP-300

ions at 23◦C are graphed inFig. 6. The surface tensioneen to increase with increasing bubble frequency anreasing concentration. A critical polymer concentrationc* ,lso known as the “overlap concentration,” which is aki

he critical micelle concentration (c.m.c.) in surfactantems, is observed, such that theσ relaxation attains a neonstant value at or aroundc* . Thec* for HEC solutions a3◦C, ascertained from the asymptotic intersection poin

he equilibriumσ–c adsorption isotherm (lowest bubble fuency of 0.017 Hz), is estimated to be∼600 wppm, and it ibserved to increase with bubble frequency. The experi

al data of Hu et al.[16], as well as the manufacturer’s[28]eportedσ value for 0.1% (concentration by weight) solutre also graphed inFig. 6. The former data appear to f

n the dynamic conditions represented approximately b


Fig. 7. Equilibrium and dynamic surface tension data for aqueous HEC-QP300 and Carbopol 934 solutions.

The variation with concentration and temperature of themeasured dynamic and equilibrium surface tension of aque-ous HEC QP-300 and Carbopol 934 solutions are graphed inFig. 7. The values of dynamicσ in this figure are for a bubblesurface age of 50 ms, which is representative of bubble fre-quencies typically encountered in nucleate boiling of water.The dynamicσ at both temperature conditions (23 and 80◦C)and at all concentration levels (c> 0) is seen to be greater thanthe corresponding equilibrium value for both HEC and Car-bopol solutions. Also, the results at 80◦C, when comparedwith the respective values at 23◦C, indicate overall reduc-tion in σ at the higher temperature, which is due to increasedpolymer diffusivity with increased temperature[19]. In com-parison to Carbopol solutions, however, the HEC solutionsshow significantly higherσ relaxation both under dynamicand equilibrium conditions, with a rather sharp change inslope or surface tension gradient nearc* . This is because HECis a surface-active polymer, and thus its adsorption behaviortends to be similar to those of surfactant solutions[15,19]. Itshould be noted that under dynamic conditions, theσ mea-surements by the maximum bubble pressure method in highlyviscous fluids always need a viscosity correction to compen-sate for the viscous resistance offered by the fluid againstthe growing bubble interface. This has been found to be de-pendent upon the fluid viscosity, capillary radius, and surfaceage[15,17,18], and such corrections were made to the presentd

The polymer adsorption process at the bubble vapor–liquid interface is time dependent, which manifests in a dy-namic surface tension behavior that eventually reduces to theequilibrium condition after a long time period. Furthermore,both equilibrium and dynamicσ are seen to decrease withincreasing concentration, and asymptotically attain a nearconstant value beyondc* . This trend inσ relaxation is essen-tially an outcome of the molecular kinetics of the additivesin water. In solutions with lower than overlap concentrationsor c* , the polymer molecules remain as isolated macro-molecules with little intermolecular interactions. At overlapor “semi-dilute” concentrations, the polymer molecules“touch” each other, and, with increasing concentration, thefrequency of collisions between the polymer coils eventuallycauses overlapping and entanglement of their chains.

The experimental pool boiling data for the surface-activeHEC-QP300 solutions of different concentrations as wellas that for water are presented inFig. 8. The heat transferenhancement with increasing surfactant concentration isevident from the leftward shift in the boiling curve (q′′

w–�Twcurve) relative to that for pure water. This boiling processwas further visually observed to have an early incipienceor onset of nucleate boiling (ONB); displayed by theappearance of the first set of bubbles on the heater surface.However, the enhanced heat transfer is seen to “peak” witha 600 wppm concentration (∼c* for HEC-QP300) solution,

Fig. 8. Nucleate pool boiling data for aqueous solutions of HEC-QP300.
ata set as per the procedure described in Ref.[15].


Fig. 9. Nucleate pool boiling data for aqueous solutions of Carbopol 934.

and then decrease with higher concentrations. The results for3000 wppm solutions even show degradation in performancerelative to that of water at lower heat fluxes. The higherconcentration (>600 wppm) boiling curves that exhibit arightward shift were seen to have delayed incipience aswell. A similar performance with HEC-H has been reportedby Shul’man et al.[3], and their results show that the heattransfer coefficient reaches its maximum atc∼500 wppm ona plate heater with a size that is much larger than the meansize of the boiling bubbles. This 500 wppm concentration isprobably thec* for HEC-H, which is a different grade of theHEC family of polymers and has a lower molecular weightthan HEC-QP300. The nucleate boiling data for aqueousCarbopol 934 solutions graphed inFig. 9display a somewhatdifferent behavior. With the rightward shift in the boilingcurve relative to that for pure water, the heat transfer is seento continuously decrease and deteriorate with increasingconcentrations. Boiling was visually also observed to beaccompanied by delayed incipience, low bubble departurefrequency, and some vapor explosions due to higher viscousresistance. Deterioration of boiling heat transfer has alsobeen reported by Paul and Abdel-Khalik[7] in aqueoussolutions of drag-reducing polyacrylamide (Separan AP-30).

The effects of heat flux and surfactant concentration on thenucleate boiling heat transfer in HEC-QP300 solutions arefurther highlighted inFig. 10, where the relative increases in

Fig. 10. Variation of the enhanced boiling heat transfer performance of HEC-QP300 solutions with heat flux and additive concentration.

non-dimensional Nusselt numberNu(=hd/k) from that of wa-ter are graphed for different concentrations and heat fluxes.Hereh is the heat transfer coefficient (= q′′

w/�Tw),k the ther-mal conductivity of the fluid, andd the heater tube outer diam-eter (characteristic length scale). A maximum enhancementof 22.9% in a 600 wppm aqueous solution is seen, and the im-proved performance tends to be somewhat weakly dependentupon the wall heat flux. Enhanced heat transfer in nucleateboiling of dilute (c<c* ∼ 500 wppm) aqueous HEC-H solu-tions on a plate heater is also evident from the Kotchaphakdeeand Williams[2] data. Furthermore,Fig. 10 clearly showsthe decrease in the boiling heat transfer enhancement in HECsolutions withc>c* (700, 1000, and 3000 wppm). In the veryhigh concentration (3000 wppm) solution, up to 7.5% degra-dation in the heat transfer coefficient when compared to thatfor pure water is evident forq′′

w < 70 kW/m2; the degradationalso tends to be strongly dependent upon wall heat flux.

The nucleate boiling performance of aqueous HEC-QP300 and Carbopol 934 solutions can be qualitatively re-lated to the ebullient characteristics (or the inception and ges-tation→ growth→ departure behavior of vapor bubble onthe heater surface), and typical photographic records are pre-sented inFig. 11. These photographs depict the boiling his-tory (or heater surface bubbling activity) with increasing heatflux (q′′

w = 20, 50, and 100 kW/m2) for aqueous solutions oftwo different concentrations each (300 and 1000 wppm for


Fig. 11. Ebullient behavior in nucleate boiling of distilled water, and aqueous HEC-QP300 and Carbopol 934 solutions of different concentrationscat differentheat fluxes (q′′

w = 20, 50, and 100 KW/m2).

HEC-QP300; 100 and 300 wppm for Carbopol 9342), alongwith that for deionized distilled water. The bubbling processduring boiling in HEC solutions is seen to be distinctly differ-ent from that in pure water. It is more vigorous, and is charac-terized by smaller-sized and more regularly shaped bubblesthat have a reduced tendency for coalescence whenc<c* .There is an early inception of bubbles with a faster covering ofthe heating surface and a higher bubble departure frequency,which is essentially the outcome of reduced surface tensionat the liquid–vapor interface. Also, molecular adsorption onthe heating surface may contribute to the formation of newsites[11], which in turn would explain the increase in numberof bubbles as there was no change in the surface wettability(as measured by the contact angle[29]). However, at verylarge concentrations (c>c* ), the bubbles that originate at theunderside of the cylindrical heater tend to coalesce and form

2 In Carbopol 934 solutions, the boiling pool became significantly morecloudy with increasing concentration and it was very difficult to get clearphotographs whenc> 300 wppm. Hence, snapshots for a higher concentra-tion solution are not presented.

bigger bubbles as they slide along the cylindrical peripheryof the heater surface at departure. At the same time, there aresome small patches that are covered by liquid, and no bubblesformed underneath these patches. This phenomenon is quitecontrary to that seen in boiling of surfactant solutions, inwhich foaming begins to occur or surface wetting conditionsignificantly changes whenc> c.m.c. [30,31]. Perhaps thesignificantly increased viscosity of higher concentrationpolymer solutions tends to suppress the bubble nucleationprocess and growth of vapor bubbles. As a result, somenuclei do not get activated at all, and this also then leads tothe deterioration of boiling performance in aqueous solutionswith c>c* .

Boiling in Carbopol 934 solutions, on the other hand,shows an entirely different ebullient behavior than thatof water, as well as that of surface-active HEC solutions.Considerable bubble suppression is observed in Carbopol934 solutions, along with dispersed vapor explosions (brightwhite spots captured in the picture;Fig. 11) in some regionsof the heater surface. The same kind of bubbling activity wasalso observed by Bang et al.[12] in dilute polyethylene oxide


(PEO) solutions. Furthermore, the Carbopol additives inwater lead to a delayed inception of bubbles, or ONB, and thesparsely formed bubbles have a slower departure frequency.This is essentially due to the increased viscosity of Carbopolsolutions, which lends to a higher viscous resistance for thenucleating and departing bubbles to overcome. Again, con-trasting the boiling ebullience or bubbling activity with that ofpure water, as well as between HEC and Carbopol solutions,there appear to be more nucleation sites activated in aqueousHEC QP-300 solutions than that with Carbopol 934. Thehigher active nucleation site density would also explain theincreased heat transfer performance in surface-active HECsolutions.

In general, the factors that affect the nucleate boilingperformance of polymeric additives in water include, amongothers, the changes in surface tension of the liquid, adsorp-tion of macromolecules on the heating surface, nucleate sitedensity, heater geometry and its surface characteristics, influ-ence of macromolecules on diffusion heat transfer in solventevaporation, hydrodynamics of convective flows in the boil-ing boundary layer and bubble motion (micro-convection),thermodynamics features of the polymer–solvent solutions,and rheological effects. At high heat fluxes and sufficientlylarge time duration of nucleate boiling, the possibility ofmacromolecular thermo-destruction (degradation) shouldalso be taken into account[11]. For surface-active HECs hichd iling),a rface( tions e twom nt inl erh nsferc ons( arep iquidv theb aporb

leo ont boil-i and6 olu-t tionsa olu-tη ofh r en-h s,w tioni sur-f rizedba

Fig. 12. Effect of dynamic surface tension, represented byDe, on the boilingheat transfer coefficient.

bulk concentrationc∞, andD is the diffusivity of the poly-mer in solution[32]. Those with smallest values forτD tendto equilibrate faster. The characteristic relaxation time scaleτD, along with the typical time scalet of boiling in aque-ous polymeric solutions, can be generalized as theDeborahnumber(De) to delineate the dynamic surface tension effect,and can be defined asDe= τD/t. It would then follow that thesmaller values ofDewould lend to more surface-active ef-fects of the additive on nucleate boiling in aqueous solutions.As seen from the normalized boiling data for the 600 wppmHEC solution inFig. 12, with a τD of 0.16 s the value forDe is 3.2, which represents a much larger dynamic surfacetension reduction compared to that in the largerDe valuesof the other three solutions3 and thereby a higher heat trans-fer performance. Considering that the only drastic physicalproperty change in these four solutions is the dynamic surfacetension relaxation, and that the measured surface wettability(represented by the solid–liquid interface contact angle4) forboth HEC and Carbopol are close to that of water (77◦), theresults inFig. 12clearly suggest that the dynamic surface ten-sion (inherent inDe) is perhaps one of the more significantprediction parameters.

3 The typical flow time scalet in this study was taken as 50 ms, which isr boilingo tionsw

QP-3 od ford ter orw

olutions, the reduction in dynamic surface tension (wecreases the required superheat for the onset of bond the macromolecular adsorption on the heating suwhich could contribute to the formation of new nucleaites and increased bubble frequency) are perhaps thain factors for the boiling heat transfer enhanceme

ower concentration (c<c* ) HEC solutions. On the othand, the decreases in the nucleate boiling heat traoefficients in HEC solutions with higher concentratic>c* ), and pure shear-thinning Carbopol 934 solutionsossibly associated with the substantial increase in the liscosity that tends to suppress micro-convection inubble boundary layer as well as retard the growth of vubbles.

Finally, Fig. 12 provides further insights on the rof dynamic surface tension or surface-active effects

he heat transfer performance. The normalized poolng heat transfer coefficient data for HEC-QP300 (30000 wppm) and Carbopol 934 (100 and 300 wppm) s

ions are graphed. While their respective concentrare different, the apparent viscosity of their dilute s

ions is comparable (ηHEC,300 wppm≈ ηCarbopol,100 wppmandHEC,600 wppm≈ ηCarbopol,300 wppm). In the measured rangeeat fluxes in the nucleate boiling regime, heat transfeancement, (Nupoly–Nuwater) > 0, is seen in HEC solutionhile, contrastingly, there is only heat transfer deteriora

n Carbopol solutions. The ability of a reagent to reduceace tension under dynamic conditions can be charactey a diffusion time scaleτD (=φ2/D), whereφ is defineds the ratio of equilibrium surface concentrationΓ eq to the

epresentative of bubble frequencies usually encountered in nucleatef water. The diffusivities of both HEC and Carbopol in aqueous soluere evaluated by the well-known Stokes–Einstein equation[33].4 Though not presented here, the solid–liquid contact angles for HEC00 and Carbopol 934, which were measured by the sessile drop methifferent concentration solutions, using a Kernco GI contact angle meettability analyzer, showed insignificant change from those for water[29].


4. Conclusions

With the addition of small amounts of polymers (HEC-QP300 and Carbopol 934), the boiling behavior of wateris found to be altered significantly. This is essentiallydue to the changes in solvents rheological and interfacialcharacteristics. While aqueous solutions of both polymersbecome substantially more viscous, with a significantlyhigher intrinsic viscosity the higher molecular weightCarbopol 934 renders aqueous solutions to be much moreviscous; they also exhibit a distinct shear-rate dependentnon-Newtonian shear-thinning rheology. On the other hand,reflecting its surface-active nature and molecular adsorptionat the vapor–liquid interface, HEC-QP300 solutions showmuch greater relaxation of both the dynamic and equilibriumsurface tension in comparison with Carbopol 934. As aconsequence, nucleate boiling in dilute HEC solutions (c<c*

or the critical polymer concentration) is observed to becharacterized by significantly larger number of considerablysmaller bubbles that have much higher departure frequenciesthan that in pure water. The reduced surface tension,along with the molecular adsorption on the heating surface(liquid–solid interface) perhaps also contributes to theformation of new nuclei. The combined mechanisms resultin considerable enhancement, with up to 22.9% higher heattransfer coefficients, relative to water, in the nearc* or overlapc pacto cter-i g iss erl ,h them psd ssiono theh ectsa 934s heatt pres-s alsoo aviorn ltss t vis-c ouldp el forn ions.

A

nceF Re-g ech-n hl ina fullya

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[ lesInt.

[ uter ex-

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[ ocessorth-

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[ ment991)

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This study was supported in part by the National Scieoundation (Grant No. CTS-9502128), Ohio Board ofents, and the University Research Council. Also, the tical assistance of Satish Vishnubhatla and Manish Bacquiring the viscosity and contact angle data is gratecknowledged.

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nucleate pool boiling of aqueous polymer solutions on a cylindrical heater

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