Capillary Forces in Immiscible liquid Mixtures and Other Systems

7 Capillary Forces in Immiscible liquid Mixtures and Other Systems 1153 

Q is a constant with the dimension of pressure and Voo is the volume of the final meniscus for t oo. For typical situations such as a head on a magnetic storage disk with film thicknesses of the order of 1 nm and low viscosity, typical time constants are of the order of 1 min to hours [501, 573]. 

Let us turn to the general case of meniscus formation. We consider two surfaces that approach each other in an A-rich phase with a little dissolved B. We further assume that the surfaces attract B more than A. As a result, the contact angle of B on the surfaces in A, B(A). is lower than 90°. In this case, B will tend to form a meniscus of a B-rich phase between the two surfaces. To derive volume equation, we equate the chemical potential of molecules B in the A-rich phase to the chemical potential of molecules B in the meniscus. The chemical potential of molecules B in the A-rich phase is gg + J rin(cB/cg). Here, Cb is the concentration of molecules B in the A-rich phase and gg is the standard chemical potential of B at saturation concentration Cg. The saturation concentration is the concentration of molecules B in the A-rich phase in contact and in equilibrium with a B-rich phase with a planar interface. The chemical potential of molecules Bin the B-rich phase is pg + + V 2) where Yab i  

---