Numerical study of a droplet migration induced by combined thermocapillary-buoyancy convection

Abstract

Numerical computations have been performed to study the effects of thermocapillary convection and buoyancy convection, and free surface deformation induced by gravity on the migration behavior of a liquid droplet on a horizontal solid surface subjected to a uniform temperature gradient. Investigations are carried out by solving the Navier-Stokes equations coupled with the energy equation through the finite element method. The combined thermocapillary and buoyancy force driven convection produces complex dynamic behavior of fluid motion inside the droplet. The net momentum generated by a pair of asymmetric thermocapillary convection vortices inside the droplet drives the droplet to move in both small and middle droplet sized regimes. In the small sized regime, the quasisteady migration speed of the droplet is mostly linearly proportional to its size because of the stronger net thermocapillary momentum. When the droplet is in the middle sized regime, its quasisteady migration speed reaches a maximum, but this is gradually reduced as the droplet size increases due to the suppression of the net thermocapillary momentum by the buoyancy force. In the large droplet sized regime, two pairs of convection vortices exist inside the droplet as a result of the appearance of the buoyancy-driven convection accompanying the thermocapillary convection. The quasisteady migration speed quickly diminishes mainly due to the reduction of the net thermocapillary momentum from the stronger buoyancy convection.

Effect of Contact Line Dynamics on the Thermocapillary Motion of a Droplet on an Inclined Plate

“…Ehrhard and Davis 11 used lubrication theory to describe the spreading of a droplet on a uniformely heated plate, and Anderson and Davis 12 took into account the effect of evaporation. The latter effect was also studied recently by Karapetsas et al 13 Chen and co-workers took into account the effect of buoyancy convection 14 and studied the phenomenon of thermocapillary nonwetting. 15 Lubrication theory was also used by Smith 16 in the presence of thermal gradients to derive quasi-steady solutions employing a dynamic boundary condition at the contact line, which relates the velocity of the contact line to the dynamic contact angle, taking into account the effect of contact angle hysteresis.…”

Enhancement of contact line mobility by means of infrared laser illumination. II. Numerical simulations

“…Figure 10 shows a schematic illustration of the laser beam coordinate system ðx b ; y b Þ and its relation to the coordinate system (x, y) expressed by Eqs. (20) and (21).…”

“…14 Other techniques for droplet mobilization include substrate vibrations 15,16 or A.C. electrowetting. 17 Many authors have studied droplet actuation by means of thermocapillary stresses as a consequence of localized heating [18][19][20][21][22][23][24][25][26][27][28] and specifically the effect of thermocapillary stresses on the dynamics of the moving contact lines. [29][30][31][32][33][34][35][36] If either the driving force or the imposed speed exceeds a critical limit, commonly residual liquid is left behind on the substrate.…”

Effect of slippage on the thermocapillary migration of a small droplet

“…[24][25][26][27][28][29][30][31][32][33] The main objective of the theoretical studies has been to predict the steady migration velocity of the droplet. Lubrication approximation has been employed for this purpose in several works.…”