Quasi-static shape of the steady moving meniscus — comparison of the apparent and extrapolated dynamic contact angles

Abstract

The present investigation compares apparent dynamic contact angles, evaluated from dynamic capillary heights via the corresponding static relationships, and extrapolated contact angles deduced from dynamic meniscus profiles fitted with the Laplace equation. A siliconized glass cylinder and a thin filament vertically withdrawn from glycerol—water mixtures are studied as being representative of the two limiting cases of very low and high azimuthal curvature. Published data for plunging of a hydrophobic tape (flat wall) into similar mixtures are also discussed. It is found that all steady menisci considered are adequately described by the Laplace equation with the exception of the point at the solid wall. Thus, apparent contact angles, which are larger than the extrapolated ones, are found in all cases. This difference is small, but significantly exceeds the experimental error; it indicates a hydrodynamic deformation close to the contact line. The thickness of this deformation is estimated from the deviation between the extrapolated Laplacian fitting curve and the actual dynamic profile of the fluid interface. For the systems and conditions studied (capillary number, Ca < 0.15) the thickness of this deformation is 3–5% of the maximum static capillary height.