Chapter 6 Principles of Diffusion and Mass Transfer Between Phases
1 Chapter 6 Principles of Diffusion and Mass Transfer Between Phases
1.THEORY OF DIFFUSION Diffusion is the movement,under the influence of a physical stimulus,of an individual component through a mixture The 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
2 1.THEORY OF DIFFUSION • Diffusion is the movement, under the influence of a physical stimulus, of an individual component through a mixture • The 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(分子扩散)and eddy diffusion(涡流扩散)_.Ieg,diffusion process of ink in the stagnant or agitated water...]
3 • 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（分子扩散） and eddy diffusion（涡流扩散）. [e.g., diffusion process of ink in the stagnant or agitated water…]
Mass transfer driving forces 。 E.g.,absorption or stripping process:Gas-liquid phases are not in equilibrium with each other. Xa Equilibrium A curve Driving force Driving 2 .x force X X Vo-yo Lp!xp Driving forces: (Y-y Absorption column (x-x)
4 • Mass transfer driving forces • E.g., absorption or stripping process: Gas-liquid phases are not in equilibrium with each other. Absorption column L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , Equilibrium curve Driving force x x y y A x x y y A x x y y A x x y y A x x y y A Driving force Driving forces: ( ) ( ) x x y y − −
La? amin =mx a Absorption column m
5 Absorption column L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , m y x y mx b b a a = = max min m y x y mx b b a a = = max min
Equilibrium curve ivin Drivin g forcel C '6y6 Lnxp Driving forces: (p-p) Absorption column (c-c) .Question:Can we use (p-c)or (y-x)as mass transfer driving force?Compare mass transfer driving forces with heat transfer driving force?
6 Absorption column L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , L x V y L x V y L x V y b b b b a a a a , , , , , , L x V p L x V y L x V y b b b b a a a a , , , , , , L c V y L x V y L x V y b b b b a a a a , , , , , , Equilibrium curve Drivin g force x x y y A x x y p A x x p y A x c y y A c x y y A Drivin g force Driving forces: ( ) ( ) c c p p − − •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 du Momentum transfer t=-u dy T Heat transfer 9=-k dy Mass transfer dc Ja=-DAwdb g=h(Ti-T) JA=ke(CAi-Ca)=kg(PA-PAi)
7 (1)Comparison of diffusion and heat transfer db dc J D dy dT q k dy du A A = − AB = − Momentum transfer = − Heat transfer Mass transfer ( ) ( ) ( ) A c Ai A g A Ai h w J k c c k P P q h T T = − = − = −
(2)Diffusion quantities(扩散通量) 1.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 PM,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
8 (2)Diffusion quantities（扩散通量） 1.Velocity u, length/time. 2.Flux across a plane N, mol/area•time. 3.Flux relative to a plane of zero velocity J, mol/area•time. 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 diffusion(扩散速率) .Velocity 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
9 (3)Velocities in diffusion（扩散速率） •Velocity 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 N=Puuo (17.1) Where Pm=molar density of the mixture N=total molar flux in a direction perpendicular to a stationary plane u=volumetric average velocity 10
10 (4)Molal flow rate, velocity , and flux •Where M=molar density of the mixture N= total molar flux in a direction perpendicular to a stationary plane u0= volumetric average velocity (17.1) N = M u0