Part Ⅲ Mass transfer.ppt

1、Chapter 3 Mass transfer,3.1 control equations for mass transfer of multi component system,What do we mean mass transfer here? Mass of one component in a mixture migrates in a certain phase Where does mass transfer take place? in chemical industry ( reactions, e.g. catalyst reaction, and separation p

2、rocesses In environmental engineering In biotechnology In other area, e.g. air conditioning in a room and in a toilet,The purpose of studying mass transfer: 1) find concentration profile 2) get mass transfer rate,mass transfer,Molecular diffusion Convective mass transfer,1. definition of concentrati

3、on, velocity and mass flux,a). Concentration of a mixture,1) mass concentration:,2) mol concentration:,3) mass ratio:,4) mol ratio:,b). Relative velocities for mixtures,1) Mass average velocity for a mixture,Velocity of i component,2) Mol average velocity for a mixture,3) Diffusive velocity of i com

4、ponent relative to mass average velocity,4) Diffusive velocity of i component relative to mol average velocity,c). Relative fluxes for mixtures,1) Mass flux of i component under a static coordinates,2) Mol flux of i component under a static coordinates,3) Mass diffusive flux of i component relative

5、to mass average velocity,4) Mol diffusive flux of i component relative to mol average velocity,Small letter,Small letter,Capital letter,Capital letter,2 Ficks diffusive law (1855),Diffusivity of A relative to B,(Groot proposed in 1951),3 the relation between diffusivity and t , P,From Hirschfelder a

6、nd Birds formula:,The universal conservation relation: accumulate rate = income rate output rate Transferred quantities into or out of a microelement can result from three ways: convection diffusion or conduction self generation,4 differential mass transfer equation for a component in mixtures,For m

7、ass transfer now, we take a microelement of fixed position inside fluid, i.e. Eular method. Thus, convection and diffusion and self generation exist for the microelement,By convection and diffusion,Income rate,Output rate,is mass flux,Then the income rate output rate of mass of A component by convec

8、tion and diffusion is:,the income rate output rate of mass by self generation (chemical reaction etc) is expressed with:,Self generated mass source of A component, in kg/m3/s,The accumulating mass rate can be expressed by:,Therefore, the differential mass transfer equation is:,For incompressible flu

9、id:,Additionally, if there is no chemical reaction and,Ficks second law,3.2 diffusive mass transfer,Gas B,A + B,Liquid A,=0, y=y0,=1, y=y1,y=0, xAL,y=y, xA0,y,For component A, in gas phase:,1). diffusion through a static gas film,Similarity and difference between diffusive mass transfer and conducti

10、on for conduction, velocity is 0. But for diffusive mass transfer, velocity is not 0. Only when velocity is comparatively small and can be neglected, molecular diffusive mass transfer is similar to conduction.,2. One dimensional steady-state diffusion (velocity is not 0),From Ficks law:,2) diffusion

11、 with heterogeneous chemical reaction,a) area is constant (chemical reaction on solid catalyst),Diffusive area,A, B,C,D,x,Catalytic surface,yAL,yA0,L,CH3 OH H2O CO2 3H2 A B C D,How about mass flux of A?,NBx=NAx NCx=-NAx NDx=-3NAx,The chemical reaction is:,Diffusive area,A, B,C,D,x,Catalytic surface,

12、yAL,yA0,L,yAL depends on the chemical reaction:,Chemical reaction constant,2) diffusion with heterogeneous chemical reaction,CO,O2,b) area changes (combustion of a round coal particle) The chemical reaction is: 2C + O2 = 2CO How about mass flux of O2?,?,The total mass transfer rate of O2 is :,?,a) I

13、f the reaction is very fast,b) Otherwise,3) diffusion with homogeneous chemical reaction,Absorbent B,A + other components,A,How about mass flux of absorbed A?,BC:,?,4) diffusion in falling film: forced convection mass transfer,A,A + other gases,Liquid B,If the velocity of falling film is fast enough

14、, the distance of A penetrating in x direction is very short, then,BC:,Combine variables:,The width of the plate,3.3 Convective mass transfer 1. forced laminar flow mass transfer inside pipes,CA0 base line,For area and constant mass flux,Simplification condition:,BC:,Limited value,Concentration prof

15、ile does not change,Bulk concentration,=0,According to BCs,?,?,Find the mass transfer coefficient,Constant flux,Constant wall concentration,If we apply the pipes with very small size in diameter,Sc,K1,K2,n,Number in mass transfer:,2. boundary layer theory for mass transfer,stream u, CA,XC,ux分布,L,x,y

16、, laminar, turbulent,b, buffer layer,L, laminar sublayer,1) Formation and development of mass transfer boundary layer,C, mass transfer boundary layer,For laminar flow,For turbulent flow,2) Mass transfer equation of boundary layer Try to find a equation used to describe the concentration profile insi

17、de mass transfer boundary layer on a plate,Apply scaling and ordering method to analyze the relative order of above terms,Mass transfer equation of boundary layer,3) Approximate integral solution of thermal equation of boundary layer,How to solve them? Assume velocity profile and concentration profi

18、le Substitute them into the equations Find , ,then velocity and concentration etc.,The velocity and concentration inside laminar boundary layer can be assumed as:,BC:,3. Turbulent mass transfer 1) time average of mass transfer equation,Eddy mass flux,2) semi-empirical expressions of eddy mass flux,a

19、) Eddy diffusivity,Eddy diffusivity,b) Prandtl mixing length try to use mixing length to express CA uy,2,1,lM,A,B,2,1,lM,A,B,(a),(b),For particle B,For particle A,3) concentration profile of steady turbulent flow inside a smooth pipe,1) In laminar sublayer,2) In buffer sublayer,3) In turbulent core,

20、?,4. Analogy between convection mass transfer and convection heat transfer,when, the expressions of concentration profile, mass,transfer rate and mass transfer coefficient are similar to those of temperature distribution, heat transfer rate and heat transfer coefficient.,3.4 Mass transfer theories o

21、n interface Purpose: to obtain mass transfer coefficient between fluid and solid surface or between two fluids (interface). 1. Film theory,Phase ,Phase ,There can be fluid flow (laminar or turbulent) in this direction,Suppositional region, within which mass transfer resistance completely results fro

22、m molecular diffusion,From mass transfer equation,The drawback for this model: is difficult to get,Proposed by Higbie in 1935 The mass transfer equation:,Phase ,Phase ,There can be fluid flow (laminar or turbulent) in this direction,2. Solute permeating model (solute permeates within eddies),IC 1,BC

23、 1,BC 2,Within the eddy,Phase ,Phase ,There can be fluid flow (laminar or turbulent) in this direction,The solution is :,Mass transfer flux:,If exp means the retention period of an eddy at the interface, then, the average mass transfer coefficient during exp is:,The drawbacks for this model: 1) exp

24、is difficult to get; 2) exp of all eddies is the same.,Proposed by Danckwerts in 1951 The idea is similar to that of solute permeating model except exp. Now exp is not the same one for different eddies. Instead, a distribution density function () is used to express the exposure time of eddies. () is

25、 a kind of probability.,Phase ,Phase ,There can be fluid flow (laminar or turbulent) in this direction,3. Surface renewal model,Number of eddies with exposure time ,Total number of eddies,Ratio of eddies with exposure time range of d in total number of eddies.,From the solute permeating model, the m

26、ass transfer flux is:,Flux with exposure time ,For all eddies with different exposure time, the mass flux should be:,Let:,Number of eddies being exposed,Number of eddies being renewed per second,Surface renewal ratio, which is supposed to be independent on time,?,So the ratio of eddies being renewed

27、 within d is,At time , number of eddies with exposure time is,The number of eddies with exposure time + dis,Here, N is the total number of eddies with all kinds of exposure time. After d, being renewed number is, and unrenewd number is,S can be determined by experiment,Chapter 4. Analogy models of t

28、ransport processes 4.1 introduction 1. mechanism of transport is the same,Molecular movement,Eddy transport,Purpose: try to find the relations between f and h or kc0,Therefore their mathematic expressions are very similar. 2. There are quantitave relations between the three transfer processes, so we

29、 can use f to predict h and/or kc0 since fluid dynamic experiments are easy to set up.,Reynolds analogy model-one layer model,Exchanged momentum by the eddy:,Inside a pipe,On a plate,Exchanged heat and mass by the eddy:,Inside a pipe,On a plate,Error:,4.2 Reynolds analogy model,Prandtl and Taylor analogy model-two layer model,1) Laminar sublay