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We study the time evolution of a thin liquid film coating the outer surfaceof a sphere in the presence of gravity, surface tension and thermal gradients.We derive the fourth-order nonlinear partial differential equation that modelsthe thin film dynamics, including Marangoni terms arising from the dependenceof surface tension on temperature. We consider two different imposedtemperature distributions with axial or radial thermal gradients. We analyzethe stability of a uniform coating under small perturbations and carry outnumerical simulations in COMSOL for a range of parameter values. In the case ofan axial temperature gradient, we find steady states with either uniform filmthickness, or with the fluid accumulating at the bottom or near the top of thesphere, depending on the total volume of liquid in the film, dictating whethergravity or Marangoni effects dominate. In the case of a radial temperaturegradient, a stability analysis reveals the most unstable non-axisymmetric modeson an initially uniform coating film.

Marangoni effects on a thin liquid film coating a sphere with axial or radial thermal gradients