PRINCIPLES OF MIXINGFOR

INDUSTRIAL BIOPROCESSING

Hari Venkitachalam

Purposes of mixing (in industrial bio-processes)

Homogenizephysical properties of a mixture of fluids

Create a dispersion in a liquid of a solid, gas or another immiscible liquid

Improve mass transfer effectivenesse.g. rate of dissolution of a solid or gas into a liquid

Methods of mixing

Air liftLiquid circulation due to the drag effect of a rising

column of air bubbles

Static mixersUsed mainly for mixing one liquid with anotherConsist of a pipe or tube with stationary dividers

(baffles) positioned in the interior

Mechanical agitationNeeded where a high mixing intensity is called for e.g. when the components separate relatively easily (as

in gas/liquid or liquid/solid mixing)

Energy for mixing

Energy transferFrom mixing equipment to the fluid causes fluid circulation

The transferred energyAccelerates the liquid and increases its kinetic energy level (called the velocity head, H) Gets transferred through smaller and smaller scales of turbulent eddiesIs eventually dissipated as heat due to fluid friction

Without continuous energy transferFluid movements will eventually die down

Characterizing mixing equipment

Liquid flow patternsLiquid pumping rate

Rate and intensity of liquid circulationHigher pumping rate means more rapid homogenization

Distribution of shear rate in the vesselFluid velocity differentials and fluctuations (due to fluid friction)Higher shear rates mean higher mass transfer effectiveness

Power absorption (i.e. energy transferred to the fluid)the greater the energy transferred, the greater the mixing effectiveness

Flow patterns of different impellers

Axial flow and hydrofoil produce large flows at low powerProduce a single circulating loope.g. marine propeller, PBT and Prochem-Maxflo

Radial flowFlow radiates out from the impellerTwo circulating loops are generatede.g. Rushton turbine

Close clearancefor highly viscous substancese.g. anchor and helical ribbon impellers

Liquid flow induced by mixing

The primary liquid flowIs liquid flow directly induced by the impeller rotation

Secondary (or entrained) flows Is due to the flowing liquid dragging adjacent liquid and entraining it Secondary flows allow the entire contents of vessel to circulate even when a small impeller is inducing the primary flowSecondary flow component is smaller relative to primary flow for larger impellers

Liquid pumping rate

Depends on impeller typeAxial flow turbines produce high flow rates (but low shear rates) at a given power consumption

Radial flow turbines produce higher shear rates (but lower flow)

For a particular type of impeller,Q = Nq.ND3

where Nq = is an impeller-dependent constantN = rotation speed (s-1)D = impeller diameter (m)Q = induced liquid flow (m3s-1)

The velocity head (H)Is the energy transferred to the liquid in accelerating it to its flow velocityIs proportional to the square of the liquid velocity

Liquid velocity induced by the impeller is proportional to impeller tip speed (ND)

ThereforeH N2D2

Velocity head

Energy transfer from impellersPower (Energy per unit time)

transferred by a mixing impeller to the fluid is given by

P Q.H (ND3).(N2D2)or

P = Np.. N3D5where P = power absorbed (J/s)

Np = power number (an impeller-dependentconstant)

= liquid density (kg/m3)

Power no. (NP) vs Reynolds no. (Re)Re = (.N.D2)/

where = liquid viscosity

Tank baffle and impeller spacing

Power absorption from the turbine to the liquid is maximized when the width of the vertical baffles at the tank wall is one-tenth the tank diameter

The spacing of impellersin multi-impeller vessels also impacts on the power absorption. Normal spacing of multiple impellers is at least one impeller diameter apart

Shear rate and shear stress

Shear rate is the velocity gradient in the liquid at a given

location (variation in liquid velocity with distance)is proportional to both the impeller speed and

diameter Shear stress in the liquid

increases proportionately with shear rate Shear stress is responsible for

causing fluid intermixingshearing and dispersion of solids, liquid droplets and gas bubblesand therefore also for enhancing mass transfer

Distribution of shear rates

Maximum shear rate occurs near the tip of the impeller (proportional to tip speed)

Shear rate within the impeller regionis typically an order of magnitude larger than the average shear rate in the whole vessel

Minimum shear rate in the vessel is around 25% of the average shear rateoccurs in regions well away from the impeller zone

Macro-mixing and micro-mixing

Macro-mixingis largely the general circulation of liquid through various zones in the vessel controls effectiveness of homogenization dependent on the pumping capacity of impeller

Micro-mixingrefers to the intensity of turbulence (rapid velocity fluctuations)characterized by the root mean square velocity at a pointThe greater the velocity fluctuations, the greater the shear stressesvery important for enhancing dispersion and mass transfer

For equal power consumption,the relationship between the diameters (D1 and D2) and speeds (N1 and N2) of two geometrically similar impellers is:

Np..N13.D15 = Np..N23.D25i.e., (D1/D2)5 = (N2/N1)3

e.g., when D2/D1 = 0.5, (N2/N1) = 3.2, at equal power;i.e., an impeller half the size of another will need to run at 3.2 times the speedThe larger impeller will give rise to higher flow but the smaller impeller will result in greater shear

Impeller size vs speed trade-off

Impeller application

Large diameter impellers at low speed are best suited for homogenization

Small diameter impellers at higher speed achieve better phase dispersion and mass transfer outcomes (e.g. oxygen mass transfer)

Mixing and oxygen transfer

In bio-processes mechanical agitators (turbines)are often needed to effect high rates of oxygen transfer to the liquid (i.e., high kLa)

Oxygen transfer rate is determined bythe mass transfer resistance at the gas/liquid interfacethe gas-liquid interfacial area, a (e.g., surface area of gas bubbles dispersed in the liquid medium)average gas hold-up in the liquid, (the volume of gas bubbles in a unit volume of the liquid medium)the mean residence time of gas bubbles, R

Effect of shear rate

Increased shear rate in the liquid Tears up large bubbles into smaller onesdecreases the mass transfer resistance at the gas/liquid interface due to increased turbulence intensity and reduced liquid boundary layer thickness around gas bubbles

Bubble generation in impeller zone

Sparged air is drawn into vortex threads and vortex sheets in the wake of the impeller blades

Small bubbles shear off the tips of the the vortex threads/sheets

The sheared bubbles are dispersed radially out from the impeller zone and rise up the liquid column

Some of the bubbles are recycled back through the impeller zone in a downdraught with the liquid drawn down into it.

Effect of bubble size

With smaller bubbles,Gas/liquid interfacial area of a given volume of dispersed air bubbles will increase (e.g. halving the Bubble size will double as/liquid interfacial area)Rise rate of the bubbles will be slower, so

the gas bubbles will remain in the liquid longer, bubbles will be recirculated more frequently by the liquid circulationgas hold up in the medium will increasethe time that individual bubbles are able to transfer oxygen into the liquid is extended

So, O2 transfer is greatly enhanced

For a given power absorption: A smaller impeller will have to run at a much higher

speeed (when D2/D1 = 0.5, (N2/N1) = 3.2)The shear rate in the liquid (both maximum and average)

being proportional to ND, a smaller impeller will give rise to greater shear rate in the liquid (halving the impeller diameter, will increase shear rate by 0.5x3.2 = 1.6 times)

Smaller impellerstherefore better suited to providing high oxygen mass

transfer rates

Impeller selection for O2 transfer

Impeller selection for O2 transfer

Radial flow turbines Transfer more power and generate greater shear in the liquid than the axial flow designs of the same diameter and speed.

They are therefore preferred for oxygen mass transfer applications

The Rushton turbine design is among the most popular for fermenter applications

Aeration rate and oxygen transfer

Increasing air flow rate improves O2 transfer only to a limited extent

Excessive air flow rate will cause flooding of the impeller

At low impeller speeds, flooding will occur at relatively low air flow rates

Increasing mixer speed will allow higher aeration rate without flooding

Recommended Reading:

M. Howe Grant (Editor) Encyclopedia of Chemical Technology (4th Edition) Vol. 16J. I. Kroschwitz (Executive Editor)John Wiley & Sons, N.Y. (1995)pp. 844-857; 866-869R660.03 E56 2 V.16(in the Librarys reserve collection)