The Relationship among Pore-Size Ratings, Bubble Points, and Porosity - Pharmaceutical Technology

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The Relationship among Pore-Size Ratings, Bubble Points, and Porosity


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Table I: Percent retention of various size latex particles for 0.2 μm-rated membranes.
By particle retention. Pore sizing based on the retention of organisms of presumably known sizes has been widely investigated (14, 16–18). Pore sizing attempts also were made using latex beads of very narrow particle-size distributions (19, 20) (see Table I). These latter methods, in conjunction with the use of surfactant, have the advantage of eliminating adsorptive effects from those ascribed to sieving (21) (see Table II). Various surfactants were found to differ in their influencing the sizing results (22). The assigned pore sizes assumed the particle to be spherical and the area of pore restriction to be circular in shape. Simplifying assumptions were necessitated to finesse the shape factor that is operative in retentions. The exclusivity of sieve retentions also was assumed, ignoring adsorptive arrests, and at best allowed inadequately for pore-size distributions. Reductions in organism sizes resulting from contact with given liquid preparations, shown to be possible by Sundaram et al. (23) were not investigated. Nor have the possible plasticizing effects of the suspending liquids on membrane pore-size alterations reported by Lukaszewicz and Meltzer in 1980 been investigated (24).


Table II: Retention (%) of 0.198-μm spheres by various 0.2 μm-rated membranes.
The results of these trials usually were judged to be of limited value. This is typical of efforts where simplifying assumptions are used to support a hypothesis, and the very conclusions are limited by the inherent arbitrariness of the necessary premises. They are complicated by the fact that the definitions of the particles themselves may depend on the particle-measuring methodologies, on the procedural protocols, and on the measuring devices used (16).

By flow through pores. The engineering principle enabling an orifice's dimensions to be sized using the rates of flow it permits can be applied to determining pore sizes. The rate of flow through a pore at a given differential pressure is essentially inversely proportional to its length and directly so to its width or diameter. Thus, the flow characteristics of single pores are described by the Hagen–Poiseuille Law:












wherein a fluid of viscosity η with an average velocity u of the fluid is related to the tube diameter d and pressure drop, ΔP along a given length z (5).

At the site of the pore's most restricted diameter its retention and flow properties are defined. Nonetheless, flow rate is influenced by more than the pore's area of constriction. It reflects also the length of the pore. Conceivably, a relatively open pore, less constricted and, therefore, less retentive, may be rendered slower-flowing by its extended length. The area of a filter, however, contains numerous pores. Its rate of flow is defined as its flux. It is the total and simultaneous flow through the many pores of the given filter area that is measured. Flux has the dimensions of volume of flow per unit time, under unit pressure differentials, per unit area of filter. Because several pores are involved, the concept of porosity comes into play.


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