Modelling of Non-coalescing Liquid Drops in the Presence of Thermocapillary Convection

A fluid-dynamic model of two non-coalescing liquid drops of the same liquid, pressed against one another in the presence of thermocapillary convection, is proposed to correlate experimental results on the deformation of the drop surfaces, on the pressure distribution and on the thickness of the air film between the drops. The two-point boundary value problem for the Gauss–Laplace hydrostaticequation, subjected to the constant volume constraint, is solved by a fourth order Runge Kutta method to evaluatethe shapes of the drops for different values of the applied pressure jump across the surface exposed to a constant ambient pressure. The flow fields in the liquid drops and in the air layer are obtained by numerical solutions of the dynamic problem. Thenumerical results qualitatively agree with the experimental ones, explain why an air film could be created between the two drops and show that film thicknesses of some microns exist with excess pressures of the same order of magnitude of the pressure needed to deform the drops.