Porous critical thickness

For dense (non-porous) membranes used for oxygen separation the flux becomes insensitive for a decrease of the layer thickness for a critical thickness which is of the order of 0.1-0.3 mm depending on the permeant-membrane... 

Suppose now that we deposit a thick film, the thickness of which we gradually reduce by suction with a pipette (or with a pump if we are dealing with a porous material). A hole created in the film will close up when e > e - When < c < a hole will remain stable since the angle 9 associated with e via equation (7.1) is between On and 6a and the contact line can neither advance nor recede. When e < en, a hole will open up spontaneously since 6 < 6n- It therefore follows that the critical thickness for dewetting on a dirty or rough surface is en-... 

Beyond some critical concentration in solid, aggregation of tactoids occurs undoubtedly. The critical concentration depends, obviously, on many factors, but at the present time we are not aware of any experimental studies on this matter, nor on the factors controlling the critical concentration. This further aggregation process yields larger objects with complicated texture and porous structure. Upon drying thick pastes, some kind of cards house structure has been reported (3). However, irregular stacks composed of tactoids with face to face aggregation have been commonly observed (9). 

The basic mechanism of foam degradation in porous medium is film coalescence. It depends on film thickness and capillary pressure. In the process of advancement the film thickness changes considerably thickens in the narrow parts (pore throats) and thins in the wider parts (pore bodies). Visual observations of such a stretching-squeezing mechanism are reported by Huh et al. [178]. Therefore, the film thickness would depend on the liquid/gas ratio, the rate of movement and the ratio of pore-body to pore-throat. When the critical capillary (disjoining) pressure is reached, the film will rupture. 

In contrast to bulk foam, in a porous medium the majority of films move separately so their rupture under certain critical pressure does not occur simultaneously, i.e. the films are not affected by the rupture of other films (there is no collective effect). On the other hand, moving films are subjected to the oscillation of thickness as well as to other mechanical effects. Hence, their critical pressure should be lower than that of the static foam and should depend also on the rate of movement due to the dynamic effects. Analogous reduction in the critical pressure is observed when a bulk foam advances [47] and when a foam is placed in a centrifugal field [183]. The influence of the dynamic effects on the critical pressure has been explained by the model of Jimenez and Radke [175]. 

The size of pores only enter indirectly into the equation in their combination, they comprise L, the thickness of the liquid layer, the membrane being some 80% porous. The critical measurement of a flaw is the... 

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