The interaction of thermocapillary convection and low-frequency vibration in nearly-inviscid liquid bridges

Abstract

The combined effect of thermocapillary stress and steady forcing due to vibrations of the disks in a model-half-zone axisymmetric liquid bridge is considered for low-viscosity liquids (i.e., with a large capillary Reynolds number), and low nondimensional vibration frequencies (i.e., small as compared to the capillary Reynolds number). An asymptotic model is derived for the slowly-varying streaming flow in the bulk (outside the oscillatory boundary layers) resulting from both effects that includes also buoyancy and other thermal expansion effects. This model is used to first analyze the steady streaming flow patterns in isothermal conditions and then to show that mechanical vibrations can annihilate almost completely thermocapillary flows of fairly large Reynolds numbers provided that: (i) the Prandtl number is appropriately small, (ii) both disks are vibrated, and (iii) the vibrating amplitudes, frequency and phases are appropriate (the counterbalancing effect depends crucially on the difference of the vibrating phases of both disks).