Wall Sherwood number

Mass transfer rates attainable In menbrane separation devices, such as gas permeators or dlalyzers, can be limited by solute transport through the menbrane. The addition Into the menbrane of a mobile carrier species, which reacts rapidly and reversibly with the solute of Interest, can Increase the membrane s solute permeability and selectivity by carrier-facilitated transport. Mass separation is analyzed for the case of fully developed, one-dimensional, laminar flow of a Newtonian fluid in a parallel-plate separation device with reactive menbranes. The effect of the diffusion and reaction parameters on the separation is investigated. The advantage of using a carrier-facilitated membrane process is shown to depend on the wall Sherwood number, tfrien the wall Sherwood nunber Is below ten, the presence of a carrier-facilitated membrane system is desirable to Improve solute separation. 

In many cases of practical interest, the membrane s mass transfer resistance is significant, i.e., the wall Sherwood number is small, leading to relatively low mass transfer rates of the solute. The diffusive flux of the permeate through the membrane can be increased by introducing a carrier species into the membrane. The augmentation of the flux of a solute by a mobile carrier species, which reacts reversibly with the solute, is known as carrier-facilitated transport (25). The use of carrier-facilitated transport in industrial membrane separation processes is of considerable interest because of the increased mass transfer rates for the solute of interest and the improved selectivity over other solutes (26). 

The parameters Sh, a, and 0 are the wall Sherwood number, the maximum facilitation factor and the dimensionless equilibrium constant. The equilibrium facilitation factor is given as... 

M = confluent hypergeometric function Sh = wall Sherwood number... 

With typical membrane and liquid diffusivities of l(h and l(h cm /s, respectively, membrane thickness of l(h mm, and tubular diameter of 1 mm, a typical wall Sherwood number becomes... 

Effect of Membrane Resistance The Wall Sherwood Number... 

For the hemodialyzer of Practice Problem 8.10, calculate the percent resistance in the membrane wall, using the wall Sherwood number defined in Illustration 5.1. 

A dimensionless group not listed in Table 5.1 is the so-called Wall Sherwood Number that represents the resistance to mass transfer through a fluid in laminar flow divided by the resistance within the tubular wall. It is used to gauge the relative importance of these resistances in industrial membrane processes as well as those occurring in living organisms (see Chapter 8). 

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