A numerical study of thermocapillary migration of a small liquid droplet on a horizontal solid surface

Abstract

In the present study, the transient thermocapillary migration of a small liquid droplet on a horizontal solid surface is numerically investigated. The droplet has a large static contact angle and a high aspect ratio of the maximum height of the droplet to its footprint. The Navier–Stokes and energy equations for both the droplet and surrounding air are solved through the finite element method. The evolution of the isotherms, the flow fields and the contact angle hysteresis are presented. Two asymmetric thermocapillary vortices appear inside the droplet. The variation of the size of the thermocapillary vortex during the migration process causes the speed of the droplet to first increase significantly, and then decrease gradually to approach a constant value. The higher imposed temperature gradient causes the droplet velocity to reach its maximal value earlier and have a higher final speed. If the static contact angle of the droplet is less than (or higher) than 90°, the droplet speed is lower (or higher) since the net thermocapillary momentum in the horizontal direction is diminished (or enhanced) by the presence of capillary force. The present results for the migration velocity and the contact angle hysteresis for a squalane droplet are also in good agreement with the previous experimental results.

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

“…28 In addition, in the theoretical analysis, the predicted speed of a droplet with a large SCA, and the speed predicted for different slip lengths might also be uncounted. 32 It should also be noted that it is somewhat difficult to carry out precise experimental investigations such as the measurement on the millimeter scale of temperature or flow velocity during the migration of a droplet, the fabrication of solid surfaces with different slip lengths on the nanometer scale, or the establishment of an imposed stable, high temperature gradient on a millimeter length. In spite of the long-standing interest in the slip condition at a liquid/solid boundary, there has been very few theoretical, numerical, and experimental studies focused on understand how the migration of a small liquid droplet on a solid surface with a uniform temperature gradient is affected by the slippage.…”

“…[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.…”

Speeding up thermocapillary migration of a confined bubble by wall slip

“…temperature gradients (Brzoska, Brochard-Wyart & Rondelez 1993;Smith 1995;Pratap, Moumen & Subramanian 2008;Gomba & Homsy 2010;Nguyen & Chen 2010;Karapetsas, Sahu & Matar 2013). Such thermocapillary actuation also has potential applications in microfluidics (Darhuber et al 2003; Baroud et al 2007;Selva et al 2010), because it not only provides an efficient means to drive fluids in small scales but also enables flows to be manipulated without moving parts.…”