Coarse-grained description of thermo-capillary flow

Details Coarse-grained description of thermo-capillary flow Coarse-grained description of thermo-capillary flow

1996-01-29

arxiv.org/abs/patt-sol/9601004v1

Phys. Fluids 8, 660 (1996)

Nonlinear Sciences

Pattern Formation and Solitons

To appear in Phys. Fluids. Also at http://www.scri.fsu.edu/~vinals/dj1.ps

Scientific paper

10.1063/1.868851

A mesoscopic or coarse-grained approach is presented to study thermo-capillary induced flows. An order parameter representation of a two-phase binary fluid is used in which the interfacial region separating the phases naturally occupies a transition zone of small width. The order parameter satisfies the Cahn-Hilliard equation with advective transport. A modified Navier-Stokes equation that incorporates an explicit coupling to the order parameter field governs fluid flow. It reduces, in the limit of an infinitely thin interface, to the Navier-Stokes equation within the bulk phases and to two interfacial forces: a normal capillary force proportional to the surface tension and the mean curvature of the surface, and a tangential force proportional to the tangential derivative of the surface tension. The method is illustrated in two cases: thermo-capillary migration of drops and phase separation via spinodal decomposition, both in an externally imposed temperature gradient.

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