Liquid-solid contact angle

Bubble Point Large areas of microfiltration membrane can be tested and verified by a bubble test. Pores of the membrane are filled with liquid, then a gas is forced against the face of the membrane. The Young-Laplace equation, AF = (4y cos Q)/d, relates the pressure required to force a bubble through a pore to its radius, and the interfacial surface tension between the penetrating gas and the liquid in the membrane pore, y is the surface tension (N/m), d is the pore diameter (m), and P is transmembrane pressure (Pa). 0 is the liquid-solid contact angle. For a fluid wetting the membrane perfectly, cos 0 = 1. 

A liquid-solid contact angle away from 90° induces the formation of a meniscus on the free surface of the liquid in a vertical tube (the solid phase). In the nonwetting case, the meniscus concaves upwards to the air. The upwards meniscus is the result of a downward surface tension at the liquid-tube interface, causing a capillary depression. In the wetting case, the meniscus has a concave-downward configuration. The downwards meniscus is the result of an upward surface tension at the liquid-tube interface, causing a capillary rise. 

Some experiments very similar to these outlined above were carried out by Ruch and Bartell [31]. Metal surfaces were equilibrated with aqueous decylamine, and the air-liquid-solid contact angles were then measured, using small air bubbles. The degree of adsorption of the decylamine was determined by optical measurements of the thickness of the film, but could be only approximately related to actual amounts adsorbed. While the results correlated well with a semi-empirical analysis, they unfortunately do not allow a verification of Equation 25. As shown in Figure 5, a qualitative calculation of > using the solution adsorption data, then allows calculation of TTgyo, assuming Equation 25 to hold. Clearly this last quantity is far from zero, as opposed to the situation assumed by Fowkes and Harkins for their system. Ruch and Bartell in fact took the adsorbed film to be identical in nature at the SL and the SV interfaces, but without any independent verification of the assumption. 

Several theoretical descriptions have been proposed to describe the electric field-induced change in the macroscopic liquid-solid contact angle in static electrowetting. These are based on thermodynamic, molecular kinetic, electromechanic, and static approaches [2]. Vallet et al. [7] and Kang [9] considered an infinite planar wedge analysis in the three-phase contact line region, as shown in Fig. 4. As the top... 

These methods are independent of liquid/solid contact angle, but require accurate knowledge of liquid density. 

Liquid/solid contact angles were measured by a Wettability Tester ( Lorentzen-Wettre, Sweden) and the method of Mack. ... 

Here S is the saturation of the porous agglomerate with liquid (ratio of liquid volume versus total void volume within the agglomerate), C a constant parameter (C = 6 for monosized spheres), y the stuface tension of the liquid, and 0 the liquid-solid contact angle (cf. Schubert (1975, 1979)). 

If we could take the interface to be a cylinder (i.e., a liquid-solid contact angle of 90 °), then our free surface condition would be On = - P + rrr = 0. This approximation is also inadequate in the present context, however, since if we take the assumed kinematics to be valid right up to r = i we will find that is a function of z and cannot vanish everywhere. The best resolution at this level of approximation is to take the interface to be a cylinder, to take the kinematics in Equations 6.28a-b to be valid at r = R, and to set the average value of Orr at r = R equal to zero. Thus, we determine (P from the equation... 

One current limitation of all existing slip models is that none incorporates the observed strong dependence of slip on surface roughness. This could, however, easily be added to Tolstoi s model, since liquid/solid contact angle is known to be very dependent on roughness [17][18]. 

---