Effect of Contact Angle on Capillary Displacement Curvatures in Pore Throats Formed by Spheres

Abstract

The curvature of an interface in a pore depends upon the shape of the pore and the operative contact angle that the interface makes with the solid surface. Even relatively simple pores formed by the surfaces of equal spheres have a complex shape including nonaxisymmetric cross-section and converging-diverging geometry. For such pores, a theory for meniscus behavior has been devised that uses a combination of a theory for meniscus curvature in rods together with the toroidal approximation of Purcell. The results of the theory show that converging-diverging geometry tends to compensate for the effect of contact angle. This is because the position at which the nonzero contact angle meniscus has maximum curvature in a converging-diverging pore is not the narrowest part of the pore throat. Due to this compensation, the effect of contact angle on maximum meniscus curvatures for drainage is approximately proportional to cos 23 θ (rather than the cos θ appropriate for cylindrical tubes). Experiments on pores formed by PTFE spheres using partially wetting liquids confirmed the theoretical prediction. Contact angle measurements on the PTFE spheres also demonstrated that, because of microscopic surface roughness, receding contact angles (these being operative with respect to drainage) on ground surfaces are significantly lower than values for smooth surfaces.