Effect of slippage on the thermocapillary migration of a small droplet.

We conduct a numerical investigation and analytical analysis of the effect of slippage on the thermocapillary migration of a small liquid droplet on a horizontal solid surface. The finite element method is employed to solve the Navier-Stokes equations coupled with the energy equation. The effect of the slip behavior on the droplet migration is determined by using the Navier slip condition at the solid-liquid boundary. The results indicate that the dynamic contact angles and the contact angle hysteresis of the droplet are strictly correlated to the slip coefficient. The enhancement of the slip length leads to an increase in the droplet migration velocity due to the enhancement of the net momentum of thermocapillary convection vortices inside the droplet. A larger contact angle leads to an increase in the migration velocity which in turn enlarges the rate of the droplet migration velocity to the slip length. There is good agreement between the analytical and the numerical results when the dynamic contact angle utilizes in the analytical approach obtained from the results of the numerical computation, and the static contact angle is smaller than 50°.