Steady thermocapillary migration of a droplet in a uniform temperature gradient combined with a radiation energy source at large Marangoni numbers

TL;DR

This paper analytically investigates the steady thermocapillary migration of a droplet in a uniform temperature gradient with an added radiation energy source at large Reynolds and Marangoni numbers, revealing how migration speed depends on Marangoni number.

Contribution

It derives an analytical solution for droplet migration considering radiation energy effects at large flow parameters using matched asymptotic expansions.

Findings

Migration speed increases with Marangoni number.

Radiation energy source with sine square dependence influences migration.

Analytical expression for steady migration derived.

Abstract

The steady thermocapillary droplet migration in a uniform temperature gradient combined with a radiation energy source at large Reynolds and Marangoni numbers is studied. To reach a terminal quasi-steady process, the magnitude of the radiation energy source is required to preserve the conservative integral thermal flux across the surface. Under the quasi-steady state assumption, an analytical result for the steady thermocapillary migration of a droplet at large Reynolds and Marangoni numbers is derived by using the method of matched asymptotic expansions. It is shown that the thermocapillary droplet migration speed increases as Marangoni number increases, while the radiation energy source with the sine square dependence is provided.