# 1 chapter 6 principles of diffusion and mass transfer between phases

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Chapter 6 Principles of Diffusion and Mass Transfer Between Phases

1.THEORY OF DIFFUSIONDiffusion is the movement, under the influence of a physical stimulus, of an individual component through a mixtureThe most common cause of diffusion is a concentration gradient of the diffusing component.E.g., The process of dissolution of ammonia into water: (1)A concentration gradient in the gas phase causes ammonia to diffuse to the gas-liquid interface; (2)Ammonia dissolves in the interface; (3)A gradient in the liquid phase causes ammonia to diffuse into the bulk liquid.

A concentration gradient tends to move the component in such a direction as to equalize concentrations and destroy the gradient.If the two phases are in equilibrium with each other, diffusion, or mass transfer fluxes is equal to zero.Other causes of diffusion: activity gradient (reverse osmosis); temperature gradient (thermal diffusion); application of an external force field (forced diffusion, e.g., centrifuge, etc).Two kinds of diffusion caused by concentration gradient : molecular diffusion and eddy diffusion. [e.g., diffusion process of ink in the stagnant or agitated water]

Mass transfer driving forcesE.g., absorption or stripping process: Gas-liquid phases are not in equilibrium with each other.

Question: Can we use (p-c) or (y-x) as mass transfer driving force? Compare mass transfer driving forces with heat transfer driving force?

(1)Comparison of diffusion and heat transfer

(2)Diffusion quantities1.Velocity u, length/time.2.Flux across a plane N, mol/areatime.3.Flux relative to a plane of zero velocity J, mol/areatime.4.Concentration c and molar density M, mol/volume (mole fraction may also be used).5.Concentration gradient dc/db, where b is the length of the path perpendicular to the area across which diffusion is occurring.Appropriate subscripts are used when needed.

(3)Velocities in diffusionVelocity without qualification refers to the velocity relative to the interface between the phases and is that apparent to an observer at rest with respect to the interface.

(4)Molal flow rate, velocity , and flux

(5)Relations between diffusivitiesFor ideal gases, and for diffusion of A and B in a gas at constant temperature and pressure,

(6)Interpretation of diffusion equationsThe vector nature of the fluxes and concentration gradients must be understood, since these quantities are characterized by directions and magnitudes.The sign of the gradient is opposite to the direction of the diffusion flux, since diffusion is in the direction of lower concentrations. A

(7)Equimolal diffusion()Zero convective flow and equimolal counterdiffusion of A and B, as occurs in the diffusive mixing of two gases and in the diffusion of A and B in the vapor phase for distillations that have constant molal overflow.

Fig.17.1(a) Component A and B diffusing at same molal (equimolal) rates in opposite directions [Like the case of diffusion of A and B in the vapor phase for distillations that have constant molal overflow].Note that for equimolal diffusion, NA=JA.

Assuming a constant flux NA and zero total flux (N=0), integrating Eq.(17.17) over a film thickness BT,

(8)One-component mass transfer (one-way diffusion) Fig.17.1(b) Component A diffusing, component B stationary with respect to interface. [Like the case of diffusion of solute A from gas phase into liquid phase in absorption process.]

(8)One-component mass transfer (one-way diffusion) When only component A is being transferred, the total flux to or away from the interface N is the same as NA, and Eq.(17.17) becomes

[Comparing one-way diffusion in the Chinese textbook,

Comparing Eq.(17.26) with Eq.(17.19),the flux of component A for a given concentration difference is therefore greater for one-way diffusion than for equimolal diffusion.[Example17.1.]

2.PREDICTION OF DIFFUSIVITIESDiffusivities are physical properties of fluids. Diffusivities are best estimated by experimental measurements, or from published correlations. The factors influencing diffusivities are temperature, pressure, and compositions for a given fluid.

Assume concentrations of component A in the two layers with distance of the molecular mean free path of a binary mixture are cA1 and cA2, respectively, the diffusion flux is

In general, influence of concentrations for diffusion in gases can be neglected, and

(2)Diffusion in liquidsDiffusivities in liquids are generally 4 to 5 orders of magnitude smaller than in gases at atmospheric pressure.

Other empirical correlations for diffusivities:For dilute aqueous solutions of non-electrolytes, using Eq.(17.32).For dilute solutions of completely ionized univalent electrolytes,using Nernst equation(17.33). (3)Schmidt number ScSc is analogous to the Prandtl number.

For gases, Sc is independent of pressure when the ideal gas law applies, since the viscosity is independent of pressure, and the effects of pressure on and Dv cancel. Temperature has only a slight effect on Sc because and Dv both change with about T0.7~0.8.For liquids, Sc decreases markedly with increasing temperature because of the decreasing viscosity and the increase in the diffusivity.Unlike the case for binary gas mixtures the diffusion coefficient for a dilute solution of A and B is not the same for a dilute solution of B in A. i.e., DABDBA [Comparing with eq.(17.15)?]

EXAMPLE 17.3. [p.522]From eq.(17.31), it is apparent that unlike the case for binary gas mixtures, the diffusion coefficient for a dilute solution of A and B is not the same for a dilute solution of B in A. But, from EXAMPLE 17.3., the diffusivities of benzene in toluene and toluene in benzene have only a slight difference, and in this case the conclusion of Eq.(17.15) DAB=DBA is still effective

(4)Turbulent diffusionIn a turbulent stream the moving eddies transport matter from one location to another, just as they transport momentum and heat energy.

The eddy diffusivity is not a parameter of physical property, it depends on the fluid properties but also on the velocity and position in the flowing stream.