Radiation-driven thermocapillary flows in optically thick liquid films

Abstract

A thin liquid film on a horizontal solid surface undergoing radiative heat transfer with an external heat source and the surrounding environment is considered. Thermal gradients along the free surface give rise to a thermocapillary flow in the liquid that is opposed by a hydrostatic pressure gradient within the film. Transient and steady-state solutions are obtained for the interfacial shape and temperature and the velocity field. These results are compared with those from another model, in which a temperature distribution is imposed on the free surface of the film. At a critical value of the dynamic Bond number, a cusp in the form of a free-surface slope discontinuity appears in this fixed free-surface temperature model, but not in the radiation model. When the Bond number is less than this critical value, the time required to thin the film by a significant fraction of its original thickness is much larger with the radiation model. It is shown how the thermal boundary conditions used in the models directly cause these differences.

Principles of Microfluidic Actuation by Modulation of Surface Stresses

“…The capability of guiding thermocapillary flow by chemical surface patterning provides a powerful method for controlled fluidic delivery. Thermal gradients can be generated by means of substrate embedded microheaters or by radiative heating from above (Hitt & Smith 1993, Schatz et al 2002. Darhuber et al (2003a) examined the horizontal thermocapillary spreading of Newtonian liquids emanating from a small reservoir pad onto a wettable microstripe subject to a linear 442 DARHUBER TROIAN temperature decrease.…”

Influence of thermocapillary flow in a liquid film jet

“…Basic equations (26)-(29) of the zero's order of magnitude are similar to the ones given in [4,5]. Hereafter, only the relationships of zero's order will be analyzed, and superscript (0) will is omitted for simpliÿcation.…”

“…Non-dimensional quantities and the parameters may be introduced based on the lubrication theory as follow [5]:…”

“…A similar method was applied to discuss the steady cases where a smooth condition at the symmetric cross-section was improved [5]. The problem of motionless and inÿnitely extending solid boundary was studied in [4,5]. Furthermore, the solutal-capillary ow induced by the surfactant of the liquid may increase the thickness of the liquid layer [6].…”

Thermocapillary flow in an annular liquid layer painted on a moving fiber

“…By using an approximation of the lubrication theory, a higher order ordinary dierential equation of liquid thickness was demonstrated, and its solution for given temperature distribution at solid boundary was obtained for unsteady cases in a thin liquid layer [5]. A similar method was applied to discuss the steady cases where a smooth condition at the symmetric cross-section was imposed [6]. The Die Swell eect due to the thermocapillary¯ow in a jet of liquid ®lm painted on a moving planar solid boundary was analyzed, and the results show that the thermocapillary¯ow may increase the cross-section of the liquid layer [7].…”