Ultrafilter Membranes and Ultrafiltration.

Statistical Evaluation of Sieve Constants in Ultrafiltration

“…Thus, for membranes of porosity only slightly above the end-point value, the probability for transmission of virus is apparently much lower than that derived from the simple steric considerations of equation (4). This situation may be ascribed to the difficulty of saturating the primary adsorbing capacity of the membrane in dilute virus suspensions (4,5). However, the general agreement of the end-point curve for foot-and-mouth disease with the theoretical curve is sufficient to suggest that the shape of the former may be due to statistical sieving alone, without the necessity of postulating the existence of aggregates held back at high porosities, or of a certain degree of heteroporosity in the filters employed.…”

“…The usual method of calibrating an ultrafilter membrane, by the measurement of the rate of flow of water through it and the application of Poiseuille's law to an assumed structure of cylindrical capillaries of circular cross-section, probably gives a figure for the average pore diameter which is, if anything, too small, especially for a membrane of low porosity; while the sizeof the largest partides retained by the membrane is smaller still (4,15,5).2 The continuous scale of porosity grading provided by rate of flow calibrations, calculated in terms of average pore diameter (j), is the most convenient for comparative purposes (5). For statistical evaluation of the sieve constant, however, the pore size will be at first expressed in terms of the diameter effective in filtration (j'), defined equal to the radius of the largest particulate species which absolutely fails to pass the filter under given experimental conditions.…”

“…It is assumed that the membrane structure consists of parallel cylindrical capillaries of circular cross-section, a model whose plausibility as a working basis is indicated by studies of water content, diffusion, and conductivity (15,5); and that, when the membrane is in adsorption equilibrium with the filtering solution, the pore diameter j' effective in the filtration of the disperse phase is also effectively the diameter of the cylinder through which the dispersion medium flows.…”

“…At the end-point, equation (5) becomes where ¢, is the smallest relative concentration of the disperse phase which can be detected by the analytical methods employed, and f, is the end-point porosity measured on the filtration-effective scale (only very slightly greater than J). The end-point porosity in terms of the calibrated average pore diameter, j~, may be substantially greater than J, and the relationship between the two may be determined for a given type of suspension by filtration of suspensions of known particle size (4,5), to evaluate an experimental correction factor:…”

“…Probably, however, the most serious objection to the calculations outlined above lies in the fact that penetration of a particle into a pore does not assure its emergence at the bottom of the membrane. The ratio of pore length to pore diameter is seldom less than a thousand to one, and, although the tortuosity of pores as pictured by some authors has perhaps been exaggerated (15,5), it is likely that many particles become lodged in the membrane in the course of filtration. From this standpoint, values of the sieve constant calculated from equation (9) may be too large.…”