1、高等化工传递过程原理全册高等化工传递过程原理全册 配套最完整精品课件配套最完整精品课件2 Basic Concepts Flux Driving Force Constitutive Equation Transport Property Flux Bulk Movement Convective transport Convective Flux Small scale molecular displacement Molecular(or Diffusive) transport Molecular (or Diffusive) Flux Flux= Convective Flux + M
2、olecular Flux Flux=(“concentration”) (“transport velocity”) a bv aa t bbFvfv a f t bvF aa t bfvv i i i i i C nN v the molar flux of species i relative to fixed coordinates the mass flux of species i relative to fixed coordinates the velocity of species i relative to fixed coordinates the mole concen
3、tration of species i the mass concentration of species i 1 ii in t i i CC x C C Transport of Chemical Species mass fraction mole fraction 1 ii in t i i Bulk velocity or reference velocity of a mixture Species velocity relative to the mixture: diffusive velocity 111 nnn aM iiiiii iii ax vvvvvv a i v
4、- v i v - v M i v - v aa iii CJv - v aa iii CNvJ aa iii nvj aa iii jv - v 1 1 n i i a Species Flux Reference velocity Molar units Mass units 0 Ni ni v Ji ji vM JiM jiM 11 11 ,0 ,0 nn MMMM iiiiiiiiti ii nn MM iiiiiiiiti ii CCCC NvJvJvNvJ nvjvjvnvj Flux relationships 1 v n a i it i i a n 1 0 n a i i i
5、 i a j 1 J0 n a i i i i a x 1 v n a i it i i a C x N Transformations between Species Fluxes ( )()MnN()() aa MjJ ,1,2,1i kn ,1,2,1i kn aabb A jj ab knk ikiki knk aa b A b aabb B JJ ab knk ikiki knk aa b Bx xb x GradientEnergy flux Flux of species i Temperature Concentration of specie i Concentration
6、of species j Electrical potential Pressure Other external forces Conduction (Fourier) Diffusion-thermo effect (Dufour) Thermal diffusion(Soret) Binary Diffusion (Fick) Multicomponent diffusion (Maxwell-Stefan) Ion migration (M-S) Pressure diffusion (M-S) M-S Molecular Flux = f (Transport Properties,
7、 Driving forces) Driving forces = Gradients Dominant gradient : Primary transport property Other gradients : Secondary transport properties Constitutive Equations for Molecular Transport Linear Flux-Gradient Laws (Classic Constitutive Equations) : Molecular Flux = -Transport PropertyGradient Heat Tr
8、ansport-Fouriers Law of Conduction Momentum Transport- Newtons Law of Viscosity Mass TransportFicks Law of Diffusion Ficks law for binary mixtures of A and B tAB tABAAA A MM AtA D D M C M A Reference Velocity Mass units Molar units vj- J- vj- M ABAAtABA DxC Dx J- Diffusion of Chemical Species Magnit
9、udes of Transport Coefficients Binary Diffusivity (Ficks ) 10-1410-1210-1010-810-610-410-2 Gases Liquids Binary Diffusivity (m2 s-1) Solids y T kq Tkq yy y n qe en nqn if )( n q x y z n=ey q Tkq Heat Conduction T q For isotropic materials For anisotropic materials Magnitudes of Transport Coefficient
10、s Thermal conductivity 10-310-210-1100101102103 Gases Nonmetallic Liquids Thermal Conductivity (W m-1 K -1) Liquid Metals Nonmetallic Solids Solid Metals Stress and Momentum Flux x yx dv dy t vv n s(n) x y z n=ey sn s1 s2 s(n) yz yx yy ( ) ( )() xxxyxz yxyyyz zxzyzz yyxxyyyyzz s nn s ns eeee xx yvev
11、 Magnitudes of Transport Coefficients Viscosity 10-610-510-410-310-210-1100 Gases Liquids Viscosity (Pas) Transport coefficients (Diffusivities) Classic constitutive equations: Molecular Flux = -“Diffusivity” “Concentration Gradient” () yp p k qC T yC A AyAB C JD y x yx dv dy Prandtl number Schmidt
12、number Lewis number Pr p C k ABAB Sc DD Pr AB Sc Le D Convection relative to Diffusion or conduction Peclet number Pe A measure of convective transport relative to molecular-based transport AB LL Peor D vv Advanced Transport Phenomena 授课教师：王 涛 化学工程国家重点实验室 工物馆286，电话62784877 助教：许文 工物馆175，电话62787578 In
13、troduction Transport Phenomena: A fundamental to Chemical Engineering and other engineering fields About Chemical Engineering 1. One of Four Big Engineering Fields 2. Universal Engineering Transport Phenomena Mass transfer Energy transfer - Heat transfer - Momentum transfer Motion of molecular parti
14、cles Four dimension space: spatial 3D+ time 1D Length scale: 1m 0.01 m Universal natural phenomena Regardless of your discipline, transport phenomena is fundamental to your filed. Transport Phenomena: 1、理解传递机理 2、明确传递推动力及其数学表述 3、建立传递推动力和传递速率（通量）之间的 数学关系，即，本构方程 4、明确系统内物理量的累积速率、传递速率和 生成速率之间的数学关系，即，守恒方程
15、 5、明确系统与外界之间的联系，也就是边界上 的守恒方程，即，边界条件 6、求解由本构方程、守恒方程和边界条件构成 的传递模型，确定场变量的时空分布 7、由场变量的时空分布确定传递通量（数值和 方向） 传递过程原理的任务传递过程原理的任务 General outline to solve transport problems Object Physical Model Mathematic model Analytic or numerical solution C o n s e r v a t i o n equations (bulk +boundary) Constitutive eq
16、uations Mass Transfer Principles Principles of mass transport provides the features that distinguish chemical engineering from other engineering disciplines Contents 1.Basic Concepts and Classic Constitutive Equations 2.Mechanism of Transport and Transport Property 3.Conservation Equations 4. Analys
17、is of Mass Transfer Problems 5.Mass Transfer with Chemical Reactions 6.Multi-components Mass Transfer with Multi- Driving Forces 7.Mass Transfer in Porous Materials 8.Simultaneous Energy and Mass Transfer 学时：48 （3学分） 主要环节：讲课作业专题报告讨论+考试 成绩评定：作业 报告 期末考试（开卷） 先修课： 化工原理 (化学工程基础） 化工热力学（物理化学） 传递过程原理（本科） 数学
18、基础： 微积分 线性代数 常微分方程和偏微分方程 矢量和张量分析 References 1.W.M. Deen, “Analysis of Transport Phenomena”, 2nd ed., New York, Oxford University Press, 2011 2.R.B. Bird, W.E. Stewart, E.N. Lightfoot, “Transport Phenomena”, 2nd ed., John Wiley 0 (phase 1 is an impermeable) ; (phase 1 is an impermeable) iniIniniInSi
19、ininSiIn inSi ininSiInnn inSi NtCvNtCvRt NtNtRtv NR JJRvvv JR sss sss rrr rrr 12 : partition coefficient iiii CK CK symmetry plane 0 0 in in N J axisymmetric or spherically symmetric 00 00 ir ir Natr Jatr i iVi C R t N 121 ()() iIiiIISi CCRNvNvn Transport of Chemical Species Fluxes of Chemical Speci
20、es Reference velocity Molar units Mass units 0 Ni ni v Ji ji vM JiM jiM 11 11 ,0 ,0 nn MMMM iiiiiii ii nn MM iiiiiii ii CCC NvJvJNvJ nvjvjnvj Flux relationships Diffusion of Chemical Species AB ABAAA A MM AAAB D D M CM D A Reference Velocity Mass units Molar units - vj- J vj- M AAABA xCDx J- Ficks l
21、aw for binary mixtures of A and B One-Dimensional Steady Problems Example 1: Directional Solidification of a Dilute Binary Alloy 0 2 2 dy dC U dy Cd D ii i (1) (0)(0) () ii i i iii dCUK C dyD CC (1)exp() ( ) (1)exp() iii ii iiii i i i y KKPe C y CKKPe U Pe D (1)exp() iSi iiii CK CKKPe 00 iSiSii CyCK
22、 C Example 2: Diffusion in a binary gas with a heterogeneous reaction y=0 y=L A, B CA=CA0 AmB Gas Catalytic surface n AsnSA CkR dy dN dy dN ByAy 0 AyBy mNN () (1) A AyAAyBytAB A AyAAytAB dx NxNNC D dy dx Nx NmC D dy 1(/)(1) Ay A At AB N dC CCm dyD ( ) n AySAsnA NRk C L 0 0 AA CC 1 1 1 )1 (1 )1 (1 ln
23、 )1 ( 1 0 0 0 m m mx mx mxDa A A A n 0 1(1) (0)1 n A d Daxm d 1 0 00 n A AsnA AABA CLCyk CL Da CLDC 0 ( ) 1(/)(1) (0) n Asn AAtAA AB dCk CLCCmCC dyD Example 3: Diffusion in a dilute liquid solution with a reversible homogeneous reaction y=0 y=L CA=CA0,CB=CB0 AB Liquid Inert surface 11111 ()/ VABABAV
24、B Rk Ck Ck KCCRKkk 2 1 2 2 1 2 ()0 ()0 A ASBA B BSBA d C Dk KCC dy d C Dk KCC dy 00 ,at 0 0 at AABB AB CCCCy dCdC yL dydy 22 22 1 0 AB ASBS AB ASBS d Cd C DD dydy dCdC DDa dydy 1 0, at ayL 2ASABSB D CD Ca 200 at 0 ASABSB aD CD Cy 00 () AS BAAB BS D CCCC D 00 AB AB AA yCKC LCC 2 2 22 110 0 ()() A A B
25、 ASBSA d d k Lk LKC DDC )sinh()tanh()cosh( )1 ( )sinh()tanh()cosh( )1 ( B A 1 010 A A d d (1) (1) 1 A B AB e e e 0e 00 / 1/1/ BAAB AB AB CCDD K KDD 0 11 AB Example 4: Transient diffusion in a solid from a surface fixed concentration Doping of semiconductors 2 2 CC D ty I.C. C=0 , y 0, t=0 B.C. C=Cs,
26、 y=0 C=0, y Transient Problems 2 2 ff D ty ,00 0,1 ,0 fy ft ft / S fCC y t ff Similarity method (combination of variables) 2 2 0 d fdf dDd c D 2 2cD 00 1/2 2tcD t 2 y cDt 2 2 0 d fdf c dd 01;0ff 22 cy s Dt 2 2 20 d fdf s dsds The Error Function 2 0 2 (0)0()1 z n erfzedn erferf ,1 2 s y Cy tCerf Dt 2
27、 0 2 11 s n fsednerfs 2 2 0 0 1 s n n edn fs edn Doping of semiconductors A 2mm thick silicon wafer is to be doped with antimony (Sb) in order to create a p-type region. This can be done by passing a SbCl3/H2 gas mixture over the surface of the wafer at 1200 oC, which fixes the surface Sb concentrat
28、ion at 1023 atoms /m3. Suppose that the donor density (which is just another term for the Sb concentration) is hoped to be greater than or equal to 31022 /m3, over a depth of 1m below the surface. Determine how long the wafer should be exposed to this atmosphere in order to achieve this. 1 2 10.7 2
29、0.73 2 s s y CCerf Dt yC erf CDt y Dt 0 -3 172 2 6 4 exp() 383.000 1.3 10 exp() 8.314 1473.2 3.4 10/ 110 1.38 103.8 20.73 Q DD RT ms tsh D Example 5: Transient diffusion in a Symmetric Slab CA* CA* 2L z=0 z CA=CA0 at t=0 2 2 AA A CC D tz 0 0, AA CzC * ,00, A AA C tCt LC z *0 * AA AA CC CC 2 2 z D t
30、0,1z ,00,0tt z z )()(zZtT TZ DTZ 0 ZZ 0 (0)0 Z L Z 0 )cos()sin(zBzAZ 2 (21) 2 n n L )cos(zBZ nnn 0 DTT )exp(DtAT nnn 000 cos()exp() nnnnnn nnn T ZCzDt 4( 1) (21) n n C n ) 2 ) 12( exp() 2 ) 12( cos( ) 12( ) 1(4 2 0 Dt L n z L n n n n ) 2 ) 12( exp() 2 ) 12( cos( ) 12( ) 1(4 )( 2 0 *0* Dt L n z L n n
31、 CCCC n n AAAA i iVi C R t N 121 ()() iIiiIISi CCRNvNvn i iiVi C CR t vJ（） 21 ) iiIiiIISi CCRJ(v- vJv- vn（ Transport of Chemical Species Characteristic time for diffusion Characteristic time for heat conduction Infinite or semi-infinite dimension approximation Pseudo-steady Approximation 2 / d tLD 2
32、 / h tL pd tt ph tt 0 C t 0 T t Pseudo-steady Problems pdh ttort ,CCtr ,TTtr Example 6: Pseudo-steady Diffusion in a Membrane 2 2 CC D tx 1 0,CtKC t 2 ,C L tKCt ,00C x 10 0CC 0 x 20 0CC Pseudo-steady approximation 2 / pd ttLD 2 2 0 C x 1 0,CtKC t 2 ,C L tKCt 121 , x C x tKC tK CtC t L 12 0, xx DK C
33、tCt NtNL t L 1 0, x dC VANt dt 2 , x dC VANL t dt 10 0CC 2 00C 1 12 dCADK CC dtVL 2 12 dCADK CC dtVL / 0 1 1 2 p t tC C te / 0 2 1 2 p t tC Cte 2 VL pADK t 2 1 d p tALK tV Example 7: Pseudo-steady Evaporation of a Column of Liquid i iVi C R t N 00h p h tH 0 0, B xtx ,0 B xh t 0 i C t iz Nconst 0 Vi
34、R B BzBAzBztAB x NxNNC D z 0,0,0 L AzAz NtNt 0z 0 Iz v 0,0, LL BzBzB dh t NtNtC dt 0 L dh v dt ,0 Az Nz t 1 tABB Bz B C Dx Nt xz 0 ln 1 tAB Bz C D Ntx h t 0 ln 1 L tAB B dh tC D Cx dth t 20 2ln 1 tAB L B C Dx htt C 2 0 2ln 1 L B p tAB CH t CxD 2 d AB H t D 0 1 2ln 1 L p B dt t C tCx 00h Concentratio
35、n profile in liquid 0 A A D k Film Model Concentration profile at time t in a surface element Unsteady Models 0 0 A A tD kdt t 0 * 2 A A D k t Surface age distribution function for penetration model Penetration Model ( )1/ 0 tt t t t t t Distribution function of age of surface elements for random su
36、rface renewal model 0 AA kD s st tse ( )1/ 0 tt t t t t t Surface Renewal Model Mass transfer in a laminar flow In this case, a pure solvent flowing laminarly in a cylindrical tube suddenly enters a section where the tubes walls are dissolving. The problem is to calculates how the mass transfer coef
37、ficient varies with the fluids flow and the solutes diffusion. In other words, it finds the mass transfer as a function of quantities like Reynolds and Schmidt numbers. 2 0 ( )21 z r v rv R 22 222 11 () iiiiiii rziVi CCvCCCCC vvDrR trrzrrrrz i iiVi C CR t vJ 2 2 0 2 1 21() AAA A rCCC vDr Rzr rrz 0 2
38、 1 A AiA Crv Rz Pe CRDRPe 22 2 222 11 2 1Pe For forced flows in short tubes(small ) , solute transfer occurs mainly near the wall. The thinness of the region of interest makes the curvature term in Lapalcian negligible. 1,1Pe 2 2 1 2 1 2 2 2 ,000,1 The fluid far away the tubes wall (near the tubes a
39、xis) is pure solvent. ,0 Leveque approximation: the neglect of surface curvature and linearization of the velocity profile 2 2 g gc 3 3 2 gc 00g 1/3 3 2 gc 1 3 1 3 2 3 s c 2 2 2 0 dd cs dsds 01;0 1 31 3 1 3 2 39 c s 2 2 2 30 dd dd 2 22 2 20 dd sg g dsds s g s 3 3 0 1 x x edx edx 3 0 1 32.67894 33 x
40、edx 33 1 3 x edx 33 1 3 t AAi CCedt 1 31 3 1 3321 1 39 A AAAAi r R CR NzDD CPe rzR 0 AAAi NzkzC 1 31 3 1 3262 1 39 A A kzRR Sh zPe Dz 0 1n x n edx n gamma function 1 3 1 31 31 3 2/3 1 31 3 0 9222 1.615 Re 1 3 A RvRR ShSc DLL 1 31 3 1 3 0 192 1 39 L R ShSh z dzPe LL 1 3 1 31 3 2 2 1.640 Re Aavg A kR
41、R ShSc DL From experiments, the Sherwood number in the early part of the entrance region: Mass Transfer Coupled with Chemical Reaction i iVi C R t N 21 ()() iiiiSi CCR II NvNvn i iiVi C CR t vJ（） 21 ) iiiiSi CCR II f(v- vfv- vn（ Transport of Chemical Species Heterogeneous Reaction Homogeneous Reacti
42、on Effect of Transport Phenomena on Reaction Octave Levenspiel, Ind. Eng. Chem. Res. 1999, 38, 4140-4143 Effects of Reaction on Mass Transfer Two distinct effects of chemical reactions on mass transfer: I.To maintain a high concentration difference II.To enhance the rate at given level of concentrat
43、ion difference The mass transfer rate enhancement by homogeneous reaction The rate enhancement factor I: 00 000 0 0 () () A AAiAAx AAiAAA x N kCCk I kCCkN Key points about rate enhancement factor I 1.Ratio of the rates at the same concentration difference 2. or kA0 , depended on the real fluid mecha
44、nics; the analytical expression is unavailable from first principles 3. or kA, more complex, no hope to get the analytical expression from first principles 4.The ratio I turns out to be almost independent of the fluid mechanics involved; can be developed on the basis of very crude models of the flui
45、d mechanics involved 5.I is, in general, a complicated function of the composition of the phases involved; simplified equations emerge from the consideration of the limiting conditions 0 0 A x N 0 A x N Reaction time tr Mass transfer time tm 0 2 0 0 () 2() 2() Ai A AiA AiA rC VAavg VA C CCCC t R RdC
46、 0 0 1Ai A C VAavgVAA C AiA RR dC CC 02 () A m A D t k Dimensionless ratio =tm/tr A measure of the relative rate of reaction to mass transfer I= f() a complex function Slow reaction regime: 1 Instantaneous reaction regime (up limit): II 1II Physical interpretation on rate enhancement effect Case: on
47、ly one reaction may takes place in one phase with the chemical kinetic: Using film theory for the dilute solution, one dimensional and steady case 12 (,) VAVAABBBn RRCCCC 2 2 A AVA d C DR dx 0 jj j AB Steeper concentration gradient at the interface Enhancement factor larger than unity 0 0 AiAA x CCd
48、C dx 0 0 0 0 0 /1 AiAA AAAA x x x CCdC INNDD dx The condition where the enhancement effect is negligible: Average curvature Average gradient/film thickness 0 () / VAavg AiA A R CC D 2 0 2 AiA rm VAavg CC tt RD 1I Slow Reaction 2 rm tt 0 0 0 AAAiA x NkCC 1 0 0 1 jj BB AAiA j D C DICC 0 0 2 0 2() () A
49、i A C AVAAA C A AiA DRCdC k CC A A r D k t m r t I t 0 0 0 2Ai A C A VAAA C xA dC RCdC dxD Instantaneous Reaction With film model and Ficks law 0 jj j AB ()/ j j BA j KCC 0 r t II 0 1 AiA ICC 00 1 j jj jA Ai j ABB v D C CD C 0 jj j A B iBj B D CC D 0 1 AiA I CC 00 1 jj j A B iBjAiA B D CCCCI D 1 11 0 1 1 BB AiA CD I CD 102 103 K 11 0 1 1 BB AiA CD I C D Physical interpretation of mass transfer with instantaneous irreversible reaction 1 1AB NN 1 22 0 20 1 BB AA CD I CD 1 1 2 00 1 1 / jj AAjBB j I D CCD 0K 1 1 0 1 AiA I CC 00 1 j jj jA Ai j ABB v D C CD C II The Slow-Fast Transition The transi
