Diffusional boundary‐layer resistance for membranes with low porosity

Abstract

Diffusional mass transfer across membranes with uniform but low pore densities was studied experimentally as a function of stirring rate and pore area fraction. The results were analyzed in terms of a stagnant film boundary-layer model specially formulated for a heterogeneous membrane containing discrete pores. The overall membrane diffusional resistance is linearly related to the inverse of the pore area fraction of the membranes for a constant stirring rate. An equivalent boundary-layer thickness can be defined which is independent of membrane properties but a unique function of stirrer speed. These experimental boundary-layer thicknesses are greater by a factor of 3 than those predicted by a published Sherwood number correlation determined for homogeneous surfaces, but the stirring rate dependence is in excellent agreement with this same correlation.

Electrochemical measurements of mass transfer at surfaces with discrete reactive areas

“…Malone and Anderson (1977) found that Eqs. 3 and 4 correlated their data very well, in that a single value of 6 could be chosen which fit results for membranes covering a range of E .…”

“…One approach has been to measure diffusion through track-etch membranes of known pore size and pore number density (Beck and Schultz, 1972;Malone and Anderson, 1977;Bohrer, 1983). A difficulty with this approach is that the boundary-layer masstransfer resistance must be determined by subtracting from the measured overall resistance the calculated resistance of the membrane pores.…”

Immobilization of enzymes in porous solids under restricted diffusion conditions

“…Hydrodynamic theories of mass transfer have been applied to the transport processes across synthetic and biological membranes (Beck and Schultz, 1972;Malone and Anderson, 1977;Deen et al, 1981;Bohrer et al, 1984), diffusion in pores of silica-alumina (Satterfield et al, 1973), and diffusion in porous glass (Colton et al, 1975). Useful statistical and hydrodynamic principles of the development of these theories are discussed by Bean (1972), Anderson and Quinn (1974), Brenner and Gaydos (1 977), Malone and Anderson (1978), and Klein et al (1979).…”

Effect of the formation of EDTA complexes on the diffusion of metal ions in water

“…1), while the membrane area in the cell is 7.07 cm 2 (circle with radius 1.5 cm). Ideally speaking, the membrane must have pores that have a uniform size with a straight cylindrical shape (Malone and Anderson, 1977;Deen et al, 1981). The polycarbonate membrane generally has uniform and cylindrical pores, which is suitable to this experiment.…”

“…The diffusion model used in this study was described by Malone and Anderson (1977), Deen et al (1981), and Wang et al (2001). Particularly, Malone and Anderson (1977) studied mass transfer in a similar diffusion cell and constructed a model considering the total mass transfer resistance as the sum of resistance from the membrane itself, the boundary layers, and the end effects.…”