The effect of an axial temperature gradient on the steady motion of a large droplet in a tube

Abstract

In this paper we analyse the steady motion of a large droplet of fluid with temperature-dependent surface tension in a cylindrical tube subject to a constant axial temperature gradient in the asymptotic limit of small Capillary and Marangoni numbers. The leading order problem obtained is a generalisation of the classical work of Bretherton (J. Fluid Mech. 10 (1961) 166–188) for an inviscid droplet with constant surface tension and leads to a generalised version of the well-known Landau-Levich equation for the shape of the free surface in the transition regions. Numerically calculated values for the leading order thickness of the thin film surrounding the droplet and fractional velocity correction are presented, and both are found to be monotonically increasing functions of the Marangoni number.