Bifurcations and pattern evolutions of thermo-solutocapillary flow in rotating cylinder with a top disk

Abstract

The characteristics of thermosolutocapillary flow bifurcations and pattern evolutions of binary fluid in a rotating cylinder with a top disk on the free surface are investigated through three-dimensional numerical simulations. The mixture of silicon-germanium is employed as the working fluid. For the special case of the capillary ratio equal to minus one, the total thermo and solutocapillary forces are balanced. Once rotation is introduced, the balance among the driving forces is broken, and a wide variety of flow structures are presented as meridional circulations rolling in different directions. When a threshold value of the thermocapillary Reynolds number is exceeded, the stability of capillary flow is destroyed. The two-dimensional steady flow transits to the three-dimensional oscillatory state. The critical conditions for flow bifurcations are explored, and the pattern transitions are mapped. The rotation of the cylinder can suppress the flow instabilities effectively. When the disk counter-rotates with the cylinder, the critical value for the formation of instabilities increases first and then decreases. For the oscillatory flow, various patterns appear with different combinations of the thermocapillary Reynolds number, disk, and/or pool rotation rate. Without rotation, the surface concentration pattern is shown as rosebudlike wave holding still in time but oscillating in space. With the increasing disk rotation rate, the surface pattern transits from hydrosolutal waves to spiral waves, rotating waves, and superimposition of rotating and annular waves propagating in the radial direction. For counter-rotation of the disk and cylinder, a new pattern with coexistence of hydrosolutal and spiral waves traveling in opposite directions is observed.