Abstract
The thermocapillary migration of a drop placed on a solid plate is examined. The Brochard model using the lubrication approximation provides both Marangoni and Poiseuille flow components. The present 2D model extends Brochard analysis and provides a solution for the dynamics of drop migration using extended boundary conditions at the advancing and receding contact lines to account for both Marangoni and Poiseuille flow components, derived approximate drop profiles, and conservation of mass. The model is analytical, and the results are presented in a dimensionless form. The effects of the temperature gradient, surface tension coefficient to surface tension ratio, liquid viscosity, and static advancing and receding contact angles on migration dynamics are analyzed.
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