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By Irving J Dunn
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Additional resources for Biological reaction engineering : principles, applications and modelling with PC simulation
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4). 2 Formulation of Dynamic Models [ Mass rate of component i 1 = - 17 )r [ Diffusivity Concentration Area of graodfient )(perpendicular) component i to transport The concentration gradient can often be approximated by difference quantities, where with units kg s m2 m2 kg ,2=---s ,3 1 m m2 D. Interphase Transport Interphase mass transport also represents a possible input to or output from the system. In Fig. 10, transfer of a soluble component takes place across the interface which separates the two phases.
In Fig. 10, transfer of a soluble component takes place across the interface which separates the two phases. Shown here is the transfer from phase G to phase L, where the separate phases may be gas, liquid or solid. 10. Transfer across an interface of area A from phase G to phase L. When there is transfer from one phase to another, the component balance equations must consider this. Thus taking a balance for component i around the well-mixed phase G, with transfer of i from phase G to phase L, gives [ 1- Rate of accumulation ofi in phase G - [ Rate of interfacial mass transfer of i fromphaseG into phase L ] 18 1 Basic Concepts This form of the transfer rate equation will be examined in more detail in Sec.
Diffusion of Components As shown in Fig. 9, diffusional flow contributions in engineering situations are usually expressed by Fick's Law for molecular diffusion where ji is the flux of any component i flowing across an interface (kmol/m2 s or kg/m2 s) and dCi/dZ (kmol/m3 m) is the concentration gradient and Di is the diffusion coefficient of component i (m2/s) for the material. 9. Diffusion flux ji driven by concentration gradient (Cio - Cil)/AZ through surface area A. In accordance with Fick's Law, diffusive flow always occurs in the direction of decreasing concentration and at a rate, which is proportional to the magnitude of the concentration gradient.