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

Pharmaceutical Technology

It is the size of the smallest diameter of such a largest pore that is measured by the bubble-point test. As more accurately stated by the Aerospace Recommended Practice, "No bubble point test measures actual pore size but only allows correlation of the measured capillary pressure with some dimensional characteristics of the pore structures" (37). Although not an absolute measure of specific pore sizes, the pressure levels designating bubble points bear the pore sizes a strong relationship on the basis of the capillary rise experience and provide an indication of their magnitude (38).

The other means of measuring filter integrity are the equal of the bubble point for that purpose. They all are accepted as being of equal reliability when properly performed. The forward flow method—often if somewhat erroneously, identified as a single-point diffusive airflow procedure—is an example. The "diffused air" that is measured, however, is the product of Fick's Law of Diffusion that reflects porosity, the total volume of all the pores regardless of their sizes, and not the diameters of its largest pores:

in which N is the permeation rate, D is the diffusivity of gas in the liquid, H is the solubility coefficient of gas in the liquid, L is the membrane thickness, (P 1P2) is the differential pressure, and p is the total porosity.

By contrast, the air quantified in the bubble point reflects, albeit inexactly, that which passes only through the set of largest pores in accord with the capillary rise equation. It is the implications to pore size and, therefore, to particle retentions that suit the use of the bubble-point test for this purpose.

The bubble-point equation, based on the capillary rise equation, involves a reciprocal relationship between its value and the size of the "largest pore" diameter. It is the pore diameter that is being sought.

in which P is the bubble-point pressure, d is the pore diameter, λ is the surface tension, and θ is the wetting angle.

As the applied differential pressure rises, the water layers in the largest pores thin. Successively the next smaller pores are likewise affected and so forth. Eventually the water is expelled from them. The affected pores progressively increase in number from a very few. In the process the air that underwent diffusion becomes added to by the bulk airflow occurring through the vacated pores that also increase progressively in amount. The collected air is then, strictly speaking, not composed completely of diffused air. To this extent, the term "diffusive airflow" is a misnomer (39).

The capillary rise situation

Bubble-point measurements are based on the capillary rise phenomenon. When glass capillaries are dipped into water the liquid rises within them. The rise is motivated by hydrogen bonding of water molecules to the capillary's hydrophilic silicate walls. Given capillaries of different radii, the water rises highest in the narrowest capillaries because the ratio of wall area to liquid volume is greatest and the attractive force of the hydrogen bond more directly affects a larger proportion of the water molecules. In the capillaries with wider lumens there is, in effect, a free-standing column of water not in direct contact with the glass walls. Fewer of the water molecules directly experience the intermolecular forces attracting them to the silicate moieties. As a result, the liquid rises to a lesser extent in the wider capillaries and can be expelled by lesser air pressures. The water within the capillaries of the widest diameters is expelled first.


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