Do liquid drops roll or slide on inclined surfaces?

Physics – Condensed Matter – Soft Condensed Matter

Scientific paper

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Scientific paper

A solid sphere is likely to roll, while a rectangular box is likely to slide, on an inclined surface. In contrast, a liquid drop moving on an inclined surface can exhibit a variety of shapes and hence complex but interesting dynamics. Combining lattice Boltzmann method for hydrodynamics with a diffuse interface model, a hybrid numerical scheme is used to study the dynamics of binary fluids on an inclined plate under the action of gravity. Using a triple decomposition of the velocity gradient tensor inside a drop, the vorticity associated with the rolling motion is distinguished from that of shearing motion. The average angular velocity based on this residual vorticity becomes significant when the external fluid viscosity is reduced and the shape of the drop approaches a circle. For a given slip length and viscosity ratio with the outer fluid, irrespective of the equilibrium contact angle, plate inclination or Bond number, a universal curve is observed for the amount of rotation as a function of the drop shape characterized by the isoperimetric quotient. Results from a large number of simulations over a wide range of parameters are shown to lie on this curve. The rolling motion is also found to be strongly dependent on the slip length at the contact line.

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