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Correlations for mass transfer coefficients Sc DAB ;......Sh kc L D AB ;.... Re u L Sc: Schmidt number= momentum diffusivity (/) /mass diffusivity (DAB) Sh: Sherwood number= Molecular mass transport resistance (L/DAB) / Convective mass transfer resistance (1/kc) L: characteristic length or diameter kc: mass transfer coefficient u∞: bulk fluid velocity Flow past single sphere Suspended particles; flow of gas past single sphere Froessling Eq. (WWWR 30.9): Sh 2 0.552 Re1/ 2 Sc1/ 3 for 2<Re<800; 0.6<Sc<2.7 If stagnant fluid: Sh=2 (exact solution) Use physical properties of fluid e.g. evaporation of water from falling water droplet into air; Suspended particles; flow of liquid past single sphere Brian and Hales Eq. (WWWR 30.7): 2 / 3 1/ 2 Sh ( 4 1.21PeAB ) ; PeAB Re Sc for PeAB<10,000 e.g. Dissolution of drug from tablet into flowing liquid Flow past a flat plate Laminar flow on flat plate, (Re uses L=total length of plate): eq. 28.21 • ReL< 2E5 Sh 0.664 Re L 1/ 2 1/ 3 Sc Turbulent flow on flat plate, eq. 28-26: ReL>2E5 Sh 0.0365 Re L Sc DAB ;......Sh kc L D AB 0.8 Sc u L ;.... Re e.g. chemical vapor deposition reactor; 1/ 3 Flow inside tubes Laminar flow in tubes, mass transfer to inside wall of pipe )(eq. 30-19 WWWR), 10<Re<2000: 1/ 3 D Sh 1.86 Re Sc L Turbulent flow in tubes, liquid (eq. 30-18 WWWR), 2000<Re<35,000 1000<Sc<2260 Sh 0.023 Re 0.83 Sc1/ 3 e.g. absorption/stripping columns Sc DAB ;......Sh kc L D AB u L ;.... Re Flow normal to single cylinder Eq. (30-16) 400<ReD<25,000 0.6<Sc<2.6 0.56 kc Sc u 0.281Re 0.4 D e.g. humidification process—water drips vertically down Outside walls of vertical cylinders and air flows horizontally Across outside of cylinders; mass transfer of water into air stream Many more correlations available in McCabe and Smith And WWWR