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 $$\delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> </mml:math> , which selects the preferred static equilibrium via surface energy, and on the applied thermal forcing $$\Delta T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> , interesting dynamics are found. Simulations show that the steady, thermally-driven position of the interface — perpendicular to $$\Delta T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> — undergoes a pitchfork bifurcation at a critical $$\delta _\textrm{cr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>δ</mml:mi> <mml:mtext>cr</mml:mtext> </mml:msub> </mml:math> 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 $$\delta _\textrm{cr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>δ</mml:mi> <mml:mtext>cr</mml:mtext> </mml:msub> </mml:math> on $$\Delta T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> . 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.