On identifying the appropriate boundary conditions at a moving contact line: an experimental investigation

Abstract

Over the past decade and a half, analyses of the dynamics of fluids containing moving contact lines have specified hydrodynamic models of the fluids in a rather small region surrounding the contact lines (referred to as the inner region) which necessarily differ from the usual model. If this were not done, a singularity would have arisen, making it impossible to satisfy the contact-angle boundary condition, a condition that can be important for determining the shape of the fluid interface of the entire body of fluid (the outer region). Unfortunately, the nature of the fluids within the inner region under dynamic conditions has not received appreciable experimental attention. Consequently, the validity of these novel models has yet to be tested.The objective of this experimental investigation is to determine the validity of the expression appearing in the literature for the slope of the fluid interface in the region of overlap between the inner and outer regions, for small capillary number. This in part involves the experimental determination of a constant traditionally evaluated by matching the solutions in the inner and outer regions. Establishing the correctness of this expression would justify its use as a boundary condition for the shape of the fluid interface in the outer region, thus eliminating the need to analyse the dynamics of the fluid in the inner region.Our experiments consisted of immersing a glass tube, tilted at an angle to the horizontal, at a constant speed, into a bath of silicone oil. The slope of the air–silicone oil interface was measured at distances from the contact line ranging between O.O13a. and O.17a, where a denotes the capillary length, the lengthscale of the outer region (1511 μm). Experiments were performed at speeds corresponding to capillary numbers ranging between 2.8 × 10-4 and 8.3 × 10-3. Good agreement is achieved between theory and experiment, with a systematic deviation appearing only at the highest speed. The latter may be a consequence of the inadequacy of the theory at that value of the capillary number.