Experimental studies on the parametrization of liquid spreading and dynamic contact angles

Abstract

The dynamics of a spreading liquid are controlled by the details of the fluid motion very near the moving contact line. Modeling this motion is not trivial. The classical hydrodynamic model has a singular stress field at the moving contact line. This singularity prevents the use of the contact angle in dynamic conditions and predicts that an infinite force would be needed to sink a solid into a fluid. A model, valid in the small capillary number ( Ca) limit, describes the fluid motion and viscous interfacial deformation near the moving contact line. The model contains a single free parameter, ω 0, which can be related to material parameters and muust be determined experimentally. Experiments are reported that tested the range of validity of this asymptotic hydrodynamic model. The fluid-vapor interface shape and fluid velocity field produced by a glass tube entering a bath of polydimethylsiloxane at constant speed were measured near and far from the contact line. They were compared with the model using the free parameter ω 0 as a fitting constant. This procedure established the validity of the theory and provided a means of measuring ω 0. The ranges (in capillary number and in space) of validity of the theory were established. The model fails near the contact line at Ca ⩾ 0.1. This failure starts near the contact line, propagates out and increases in magnitude as Ca increases. For Ca ⩽0.1, the model with viscous deformation fails far from the contact line but describes the interface shape within ∼400 μm from the contact line. The model begins to fail at distances where the interface shape ceases to be controlled by geometry-independent viscous forces but responds instead to a competition between viscous and gravitational forces. At even larger distances from the contact line, viscous forces become negligible and the interface looks static-like. The experiments showed that the contact angle formed by the extrapolation to the solid surface of the static-like interface far from the contact line equals ω 0 as predicted by the theory. Comparisons of ω 0 and apparent dynamic contact angles based on meniscus height measurements, θ app, are presented. Small but systematic errors were found which increase with Ca. In contrast to ω 0, θ app cannot be related to material parameters and hence cannot be used to generate archival modeling information for spreading dynamics.