Morphological Stability and Nonlinear Evolution of Capillary Ridges

In this project, we conduct a series of analytical, numerical and experimental studies of capillary ridges, that is, of long, narrow strips of liquid partially wetting a flat or curved substrate. The sketch on the right shows such solid/liquid configuration.

Such thin film geometries possess both free boundaries and moving contact lines, and are known to display a large variety of instability phenomena. They provide an excellent example of the mechanism of dewetting due to capillary instability. Here, the possibility of dewetting and subsequent breaking of the continuous liquid strip into a sequence of droplets is essentially the result of flow induced by an excess of interfacial energies of the liquid/vapor, liquid/solid, and solid/vapor interfaces.

As a first stage of this project, we have determined analytical criteria for the stability of such liquid configurations to transverse sinuous perturbations in the absence of gravity. These results are based on a variational approach using the system interfacial energy functional. It does not require the small slope assumption of the liquid interface, and was applied to various substrate/liquid configurations, demonstrating the sensitive dependence of wall curvature and liquid contact angle upon stability. We have also generalized this static analysis to include the effect of gravity.

As a second stage of this project, we consider the dynamical aspects of dewetting and breakup of liquid ridges. Flow in the bulk of the fluid is dominated by gradient of capillary and hydrostatic presure, while contact line motion is controlled by gradients of both capillary and disjoining pressure. We derive a mathematical model governing the film thickness, which includes the effects of viscous forces, capillary, hydrostatic and disjoining pressure gradients, as well as the effects of substrate curvature, and generalized Newtonian rheology. This model is then analyzed to identify which mechanism governs ridge breakup. In particular, we seek to predict maximum growth rate, yielding information on how fast a ridge breaks up.

The full spatiotemporal evolution of a liquid ridge from an initial cylindrical shape to final equilibrium is then obtained by full nonlinear unsteady simulations. Such dynamic simulation can show the entire pathway of dewetting and breakup. We are developing a numerical package which can assess the effect of

We are also conducting experimental observations and measurements to assess the range of validity of our predictions.

This study is of interest in various applications where liquid stripes are created, and whose morphologies must remain stable, such as in various wet printing technologies. Stripes of differing wettability can be created on substrates by using a number of techniques, such as micro-contact printing, vapor deposition and photolithography. This work is also relevant to applications involving capillary flow in micro-grooves.