Microgravity Control of a Free Surface in Elliptical Containers Via Thermocapillary Flows

Abstract

We present here an extensive analysis of the free surface dynamics driven by the thermocapillary effect in half-filled elliptical containers in microgravity. Depending on the cell ellipticity \(\delta \), which selects the preferred static equilibrium via surface energy, and on the applied thermal forcing \(\Delta T\), interesting dynamics are found. Simulations show that the steady, thermally-driven position of the interface — perpendicular to \(\Delta T\) — undergoes a pitchfork bifurcation at a critical \(\delta _\textrm{cr}\) that breaks the vertical reflection symmetry of the system. These results are supported by (leading order) estimates of the opposing thermocapillary and surface tension forces, predicting the linear dependence of \(\delta _\textrm{cr}\) on \(\Delta T\). Finally, the free surface relaxation after switching off the thermal control is explored. As a whole, the present analysis indicates that one can combine thermocapillary flows and an adequate cell design to manipulate and control fluids in microgravity, with potential in a wide variety of applications.