3D NUMERICAL SIMULATIONS OF THE FLOW OF A DROP UNDER THE EFFECTS OF A RADIAL TEMPERATURE GRADIENT

Abstract

It has been shown experimentally that when a drop is deposited at the center of a substrate with an axial temperature gradient (hotter in the center), thermocapillarity effects makes an outward flow to appear so that the drop evolves towards
a ring whose radius increases with time. Upon reaching a critical radius, the contact line becomes unstable, showing
gentle undulations whose amplitudes grow with time. Using the lubrication approximation and adopting appropriate
dimensionless variables, a parameter-free differential equation is obtained that governs this type of thermocapillary
flow. Numerical solutions of this equation are presented to study the unstable stage. Experimental results are compared
with those obtained from the numerical solutions.