Steady recirculating flow near static contact lines

Abstract

Recirculating flow near a static contact line, encountered in the production and deposition of thin liquid coatings, is undesirable since it constitutes a means by which process defects can arise. Here an idealised model for the steady flow near a static contact line in the slide coating process is considered in which the local free surface shape is assumed to be planar, prompted by experimental observations, and the flow is driven by a moving lid/boundary. The resulting nonlinear boundary value problem is solved numerically for Reynolds numbers, Re∈[0, 100] using a finite element formulation of the governing Navier–Stokes equations, enabling the influence of both the value of the static contact angle, θ s , and the inertia of the flow close to the static contact line to be explored. Computational results show that the flow field is characterised by a sequence of distinct eddies, the relative sizes and strengths of which depend strongly upon θ s , while inertia effects have only a minor influence. Moreover, the predictions are in close accord with Moffatt’s classical theory for the Stokes flow regime and, in particular, show that for θ s⪆35° the sequence of secondary eddies adjacent to the contact line diminish in size rapidly and eventually disappear for θ s⪆80° . On the basis of these results it is postulated that increasing θ s in slide coating systems, by some means, could reduce the frequency of defects usually associated with recirculating flow near the static contact line. In addition, although the model is motivated by the slide coating process, it is expected that the results will also be relevant for other coating flows, such as in slot and curtain coating systems.