Capillary pressure, effect dispersions

Capillary pressure effects appear to explain the very important 1964 discovery of Bernard and Holm that dispersions could make the mobility of the nonwetting phase essentially independent of the absolute permeability of the porous medium (52). (See above.) Indeed, the theoretical analysis of Khatib, et al., which was corroborated by experiments, gave dispersed-phase mobilities at the upper limiting capillary pressure (for coalescence) that were nearly constant for absolute permeabilities ranging from 7D to ca. 1,000D (41). 

Thus, it might be assumed that stabilisation of foam films will depend also on the action of other positive components of disjoining pressure. For example, equilibrium films are obtained from concentrated butyric acid solutions and, therefore, in this concentration range the foam lifetime also increases. On the basis of these concepts it should be expected that a foam consisting of films with equilibrium thicknesses at a constant capillary pressure pa = n, should be infinitely stable. In fact, a real foam decays both in bulk and as a disperse system, due to gas diffusion transfer and certain disturbances (shift of films and borders on structural rearrangement as a result of the collective effects , etc.)... 

Larger values of the accumulation ratio can be reached in dry foams [24,25,47,73,74,76-78]. Kruglyakov and Kuznetsova [47,71] have studied the effect of capillary pressure, foam expansion ratio and dispersity on / mjn. The foam was prepared from NaDoBS and NP20 solutions. The accumulation ratio //m,n increased directly proportional to the expansion ratio (at a = const) and inversely proportional to the parameter a (at n = const) (Fig. 10.4). The maximum degree of accumulation in a NaDoBS solution (0.3 g dm 3 + 0.4 mol dm 3 NaCl) which could be achieved was = 1050 at Ap = 102 kPa. Further increase in... 

Effects of Capillary Number, Capillary Pressure, and the Porous Medium. Since the mechanisms of leave-behind, snap-off, lamella division and coalescence have been observed in several types of porous media, it may be supposed that they all play roles in the various combinations of oil-bearing rocks and types of dispersion-based mobility control (35,37,39-41). However, the relative importance of these mechanisms depends on the porous medium and other physico-chemical conditions. Hence, it is important to understand quantitatively how the various mechanisms depend on capillary number, capillary pressure, interfacial properties, and other parameters. 

The fluid-fluid interfacial tension also appears as the controllable design parameter in the capillary pressure and its effects on dispersion-based mobility control. As described by Equation 9, the capillary pressure, P, is directly proportional to the fluid-fluid tension, y ... 

Nevertheless, drying may precede compaction of the film. Dispersions wiiich are dried at 2" < Tg and subsequently annealed at higher temperatures form fully dense films. One interpretation of what Speny et al. [24] have shown is that when the surface tension is sufficiently strong and the compliaiKe sufficiently high, the compaction driven by yp, can occur at the same rate as that driven by capillary pressure. Of course for many latex particles immersed in water, hydroplastic effects can lower Tg, and film formation can occur more easily at lower temperature. A review of s topic by HoU [73] appeared in early 1996. 

Kashid and Agar (2007) investigated the effects of various operating conditions on pressure drop in a PTFE microchannel reactor with a Y-junction as mixing zone. They developed a theoretical prediction for pressure drop based on the capillary pressure and the hydrodynamic pressure drop without the presence of a continuous film and for a constant contact angle between the dispersed plug and the channel wall (Fig. 2.11a). 

As the initially injected sample plug is normally a distance away from the capillary inlet in capDlaiy electrophoresis, the entrance region should have negligible influence on the species transport. In the region of fully developed (denoted by the subscript fd) flow field, the thermally induced pressure-driven flow causes additional hydrodynamic dispersion to the species diffusion. Analogous to Eq. 17, the effective dispersion coefficient is given by... 

Two main types of foams may be distinguished (1) spherical foam ( Kugel Schaum ), consisting of gas bubbles separated by thick films of viscous liquid produced in freshly prepared systems. This may be considered as a temporary dilute dispersion of bubbles in the liquid. (2) Polyhedral gas cells produced on aging thin fiat walls are produced with junction points of the interconnecting channels (plateau borders). Due to the interfacial curvature, the pressure is lower and the film is thicker in the plateau border. A capillary suction effect of the liquid occurs from the centre of the film to its periphery. 

Higuchi and Misra were the first to show that if one of the components of a dispersed phase is completely insoluble in the continuous phase, then even small amounts of such a substance may stop the Ostwald ripening in the system. The reason for this is as follows. In a two-component dispersed phase system, the mass transfer of the more soluble component from small to larger drops caused by the difference in the Laplace pressures changes the composition of the drops. Namely, it increases the concentration of the poorly soluble component in the small drops and decreases it in the larger ones. According to Raoult s law, this results in a compensation of the difference in chemical potentials of the more soluble component caused by the difference in capillary pressures. When the capillary and concentration effects completely compensate, the mass transfer terminates and the drops come to equilibrium . This equilibrium implies the equality of the chemical potentials of the major component in all of the drops of the polydisperse emulsion. Such an equality is unattainable for the second component if its solubility in the continuous phase is truly zero. Kabalnov et have considered two cases as... 

As demonstrated, Eq. (7) gives complete information on how the weight fraction influences the blend viscosity by taking into account the critical stress ratio A, the viscosity ratio 8, and a parameter K, which involves the influences of the phenomenological interface slip factor a or ao, the interlayer number m, and the d/Ro ratio. It was also assumed in introducing this function that (1) the TLCP phase is well dispersed, fibrillated, aligned, and just forms one interlayer (2) there is no elastic effect (3) there is no phase inversion of any kind (4) A < 1.0 and (5) a steady-state capillary flow under a constant pressure or a constant wall shear stress. 

A significant effect of pressure on the rate of foam destruction was not established for coarsely dispersed foams with NBF, formed by blowing air through a single capillary in a NaDoS solution (10 3 mol dm 3 containing 0.4 mol dm 3 NaCl). In these experiments the pressure drop in the Plateau borders changed from 103 to 4.5-104 Pa and the maximum... 

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