Breakthrough pressure

Following the intrusion branch with increasing pressure (Fig. 1.16A), the steep initial rise at low pressures is caused by the filling of interparticle spaces. The breakthrough pressure, i.e. the pressure when the voids between the particles are filled, follows in principle the theory of Mayer and Stowe [94], and is inversely proportional to the particle size [95]. The demarcation between interparticle spaces and actual intraparticle pores may be unclear for microparticles, but in the case of polymer beads from suspension polymerization having particle sizes between 50-500 pm, usually no interference occurs. The second rise of the intrusion branch is caused by pores inside the particles. Shown in Fig. 1.16A is a porous material of rather narrow pore size distribution. 

Using low-pressure porosimetry, Winslow measured contact angles by determining the breakthrough pressure required to force mercury into numerous holes drilled into the surface of solid discs. 

Galle, C. (2000) Gas breakthrough pressure in compacted Fo-Ca clay and interfacial gas overpressure in waste disposal context. Applied Clay Science 17, 85-97... 

Big pore size Higher flux (+) and lower breakthrough pressure value (—)... 

If a dry microporous hydrophobic hollow fiber membrane with air-filled pores was surrounded by water there would not be any penetration by water into the pores until the water pressure exceeds a certain critical breakthrough pressure. The magnitude... 

The same principle of operation as described above is applicable also to liquid-liquid extraction where an aqueous liquid and an organic liquid contact each other inside the contactor for extraction of a solute selectively from one phase to another [6-8]. The critical breakthrough pressure for liquid-liquid system could be calculated by Equation 2.1, except that the term A would now be the interfacial tension between the two liquids. Further variation of membrane contacting technology is called gas membrane or gas-gap membrane where two different liquid phases flow on either side of the membrane, but the membrane pores remain gas filled [9-10]. In this situation two separate gas-hquid contact interfaces are supported on each side of a single membrane. 

R,P. Mayer R.A. Stowe, Mercury porosimetry breakthrough pressure for penetration between packed spheres, J. Colloid Interface Sci., 20, 893-911(1965). 

The manner in which mercury penetrates a bed of uniform spherical particles was examined in detail by Mayer and Stowe [2] who postulated that the breakthrough pressure Pb required to force mercury to penetrate the void spaces between packed uniform non porous spheres of diameter D is given by equation (3) ... 

Sample Mayer and Stowe estimated Breakthrough pressure (MPa) Experimental Breakthrough pressure (MPa) estimated intraparticular diameter (pm) (Washburn) experimental intraparticular diameter (pm) (Washburn)... 

Using the breakthrough pressure of intrusion into interparticular voids, one can also evaluate the granulometry of a powder assuming close-packed spherical particles [9]. A more complete information on granulometry is obtained by PSD measured by laser light scattering... 

Vaidya AM, Bell G, Hailing PJ. Aqueous-organic membrane bioreactors. Part II. Breakthrough pressure measurement. J Membr Sci 97 1994 13-26. 

For a water-based drilling fluid, the front of the filtrate which penetrated into the pores of the rock would gradually mix with the pore fluid. As a consequence, the threshold breakthrough pressure will decrease with time as a result of the reduction in interfacial tension between the two fluids. 

The breakthrough pressure ( b) through a pore of cylindrical cross-section can be related to the membrane pore size and to the interfadal tension at the liquid-liquid interface, according to the Laplace-Young law,Eq. (1) [127],... 

The use of UP membranes is therefore advised, as compared to MF membranes, since the smaller pores of the former led to higher breakthrough pressures [ 157,184]. However, microporous polypropylene membranes have been effectively used in several bioconversion systems [ 112,113,155,184,185], probably due to a high interfadal liquid-liquid tension in the reaction systems studied. A detailed theoretical discussion on the effects of pore geometry and the placement of the liquid phases in the breakthrough pressure can be found in an article by Vaidya et al. [127]. 

The presence of a biocatalyst, either whole cells [ 126] or enzymes [ 157], or any other biological surface-active materials either produced or present as substrates in the bioconversion system, such as fatty acids or long chain alcohols [ 127,184], were expected to lower interfacial tension and hence breakthrough pressure [126, 157,184]. A threefold decrease in the interfacial tension was observed in an aque-ous-tetradecane system when either Pseudomonas putida or bakers yeast cells were used, as compared to the cell-free system [126]. A decrease in the breakthrough pressure due to the presence of a surface-active agent, lauric acid, was also cited [184]. 

To have a clearer understanding of the effect of surface-active agents on the breakthrough pressiu e,it should be recalled that,besides a liquid-Uquid interface, two other interfaces are formed one between the wetting liquid and the membrane, the other between the non-wetting liquid and the membrane [127,184]. Equation (2), yielding the effect of the two liquid-membrane interfaces and the breakthrough pressure was proposed by Vaidya and co-workers [127,184],... 

The effect of the wetting characteristics of membrane bioreactors on the operation of organic-aqueous two-liquid phase systems was discussed by Vaidya and co-workers [127, 157, 184]. A similar discussion, but considering the use of membranes for separation of liquid/liquid mixtures downstream of a bioreactor, was carried out by Schroen and Woodley [126]. Some trends for the use of membranes in organic-aqueous two-liquid phase systems can be summarized from these works. The use of UF hydrophilic or amphiphilic membranes was usually advised for two-phase bioreactors [127], although fluo-ropolymer-based membranes could present an exception [126]. PTFE membranes, on the other hand, led to low breakthrough pressures, and therefore their use was limited. 

Swelling of the membrane, resulting from its contact the organic solvent [186], also led to a decrease in the breakthrough pressure [126]. 

---