Mass Transport Described by Ficks law

This section contains a simple introduction to steady state and unsteady species mole (mass) diffusion in dilute binary mixtures. First, the physical interpretations of these diffusion problems are given. Secondly, the physical problem is expressed in mathematical terms relating the concentration profiles to the diffusion fluxes. Emphasis is placed on two diffusion problems that form the basis for the interfacial mass transfer modeling concepts used in reaction engineering. The basic theory is reviewed in many textbooks on chemical reaction engineering [6, 15, 27, 52, 87]. These texts may be recommended for complimentary studies. 

Adolf Fick developed the law of diffusion by means of analogies with Fourier s work on thermal conduction [42]. Mathematically, the mass diffusion flux is thus expressed as  

This equation states that the flux of species is proportional to concentration gradient and occurs in the direction opposite to the direction of the concentration gradient of that species. The proportionality coefficient is the molecular diffusion coefficient. This diffusion coefficient formulation is useful for fundamental studies where we want to know concentration versus position and time. 

Steady Diffusion Across a Thin Fiim with a Fixed Boundary 

Consider a very thin film between two well-mixed fluids. Each of the fluids are dilute binary mixtures, consisting of the same solvent and solute having different concentrations. The solute diffuses from the higher concentrated solution into the less concentrated one. The diffusion across this thin film is considered to be a steady-state problem. There are no concentration changes with time, as indicated in Fig. 5.13. 

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