化工传递过程原理课件：第八multicomponet+%28II%29

1、Generalized Maxwell-Stefan Equation MMijjiijjiijjiij ij ij itijtijtijxxxxxxC DC DC DNNJJJJdlniiiiiiiixxRTxVPFZRTRT d10nMiiJ10niiiixJ 1MtC BJd11ijiinijBxDD1nikiikinikk ixxBDD 1xtCBBJdxknikikiknBxxxMulticomponent mass transfer driven by several driving forces IBIAISCCRNvNvn 1tCBNd VCRtN10niiiNwith app

2、licable 1xttCBBCxNdv 1ttC BxNdNCase I: Mole Fraction Gradient without FluxThe system is at steady.The gas is ideal, isothermal and isobaric.Bootstrap equations:SASRR ByAySNNR 0CyNMaxwell-Stefan equations:1CAyACyCByBCyCtACBCx Nx Nx Nx NdxdyCDD1AByBAyACyCAyAtABACx Nx Nx Nx NdxdyCDDMolar fraction and f

3、lux of species C:11CSCtACBCdxR xdyCDD 011expSCCACBCtRxyxyDDC0MCyCyCyNJJ 00CCxxMolar fraction and flux of species A:1ASCCtABACdxRxxdyCDD 00AAxx AysSANRRxLIn the case of ABACDD 0sAAtABRxyxyC D 0ABstAADRCxxL 11sSAStAWhenRk CLk C xL 00111AAASABxxxLkDaD01 1ABAAysDCNRDaDiscrete Maxwell-Stefan EquationFor

4、the one dimension problem in a thin film0iiiiiiiixdxxdRT dyRTRT ln(ln()()xiiiiiiiiiiiidxxxxdxxdyx *PiiiiiiixxxdPPPdVVRTdyRTP *iiRTPV*iiiiiiixxxddFZFZRTdyRT *iiRTFZ *iiiiiiiixxPdxP *1njiiijjiiiiijj ivvxPxxPk*11nijjiiijiiiitiijj ix Nx NxPxPC xkijijDk1,2,itiiNC x vin1njiiijjijj ivvfx xD10niiiNSteady, n

5、o homogeneous reaction and one dimension problems in a rectangular coordinate systemCase II: Gas diffusion with Heterogeneous Reaction511110548SSPPaTKRk C To estimate the overall rate of the reaction of ethanolijijkD1213230.070.230.23kkk1020300.70.150.15xxx10.45skBootstrap equations:23NN21NN 111StNk

6、 C x1231xxxMaxwell-Stefan equations:11221133112131tdxx Nx Nx Nx NdyCDD22112233212231tdxx Nx Nx Nx NdyCDD1231xxx 00iixx1323DDThe solution of the differential equations yields10.996N Discrete Maxwell-Stefan equations:12211331112131tx Nx Nx Nx NxCkk21122332212231tx Nx Nx Nx NxCkk0iiixxx02iiixxx11221121

7、31tNxxxxCkk 112212122321tNxxxxxCkk111StNk C xThe solution of the discrete equations yields10.959N M-S approach for electrolytesKey points:1. Species: ions and solvent molecules2. Electroneutrality relation3. Bootstrap equation4. Electric driving force (important) 0iiiZ x iiiFZIN1ln()nijjiiiij itiijj

8、xxRTRTxFZC xDNNLFor dilute solution of stagnant water lniiitiiwFZxRTC x D NL*iiitiiwxNxC xk For dilute solution of stagnant water*1ijjiiij iiiitiijx Nx NxxC xkFor the one dimension problem inside a thin film: steady and no homogeneous reaction in a rectangular coordinate systemat room temperature40i

9、iiitiiwxNZxC xk Case III: Electroneutrality12xxxZero electric current 12NNNconst13lntFNxRTC xD M-S equations23lntFNxRTC xD 1113231323111122ttxNCxCDDDD 231313230lnRT DDxFDDx 11112()HClH wClwDDD1113231323111122CJNCDDDD 1112()ABAwBwDDDCase IV: Polarization in electrolysisM-S equations:bootstraps:12xxx320NN113lntFNxRTC xD ln0FxRT 0expFxxRT0132txxIFC D Limiting current when:0 x13lim02tDIFCx0 x13021exptDFIFCxRTlim1expIFIRT at room temperature专题报告Maxwell-Stefan 方法方法在传质过程模型化中的应用在传质过程模型化中的应用1.近期国际刊物文献(不能是review) .2.选择自己感兴趣的主题，限于Maxwell-Stefa