Differential mass transfer

This section concerns the modelling of countercurrent flow, differential mass transfer applications, for both steady-state and non-steady-state design or simulation purposes. For simplicity, the treatment is restricted to the case of a single solute, transferring between two inert phases, as in the standard treatments of liquid-liquid extraction or gas absorption column design. 

Vary the guess and iterate between Z = 0 and Z = 1 until convergence is obtained. 

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Chapter 4 eoncerns differential applications, which take place with respect to both time and position and which are normally formulated as partial differential equations. Applications include diffusion and conduction, tubular chemical reactors, differential mass transfer and shell and tube heat exchange. It is shown that such problems can be solved with relative ease, by utilising a finite-differencing solution technique in the simulation approach. 

In the case of chromatographic columns packed with spherical nonporous adsorbent particles the differential mass transfer balance can be described by... 

For large values of the Thiele modulus, the differential mass transfer equation has an asymptotic solution ... 

Referring to one fiber alone, the scheme of the reacting system is similar to those examined so far. However, the reaction does not occur in either regions 1, 2 or 3. The set of differential mass transfer and continuity equations defining substrate and product concentration in these regions are equal to those previously examined. The description of mass transport in the shell-side region is somewhat more complicated. Differences in the environment surrounding each fiber, the position of fibers in the bundle, and the ultrafiltration fluxes make both the analytical and the numerical approach quite difficult. 

What important dimensionless number(s) appear in the dimensionless partial differential mass transfer equation for laminar flow through a blood capillary when the important rate processes are axial convection and radial diffusion ... 

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