We use the lubrication approximation to investigate the steady flow of a thin rivulet of viscous fluid draining down a heated or cooled planar or slowly varying substrate when the surface tension of the fluid varies linearly with temperature. Utilizing the (implicit) solution of the governing ordinary differential equation that emerges, we undertake a comprehensive asymptotic and numerical analysis of the flow. In particular, we find that the variation in surface tension drives a transverse flow that causes fluid particles to spiral down the rivulet in helical vortices. We find that a continuous rivulet can run from the top to the bottom of a large horizontal circular cylinder provided that the cylinder is heated or significantly cooled, but that if it is only slightly cooled then a continuous rivulet is possible only for a sufficiently small volume flux.
|Number of pages||7|
|Publication status||Published - 2001|
|Event||American Physical Society, 53rd Annual Meeting of the Division of Fluid Dynamics - Washington, USA|
Duration: 19 Nov 2000 → 21 Nov 2000
|Conference||American Physical Society, 53rd Annual Meeting of the Division of Fluid Dynamics|
|Period||19/11/00 → 21/11/00|
- fluid dynamics
- numerical analysis
- differential equations
Holland, D. B., Duffy, B. R., Wilson, S. K., King, A. C. (Ed.), & Shikhmurzaev, Y. D. (Ed.) (2001). Thermocapillary effects on a thin rivulet draining down a heated or cooled surface. 129-136. Paper presented at American Physical Society, 53rd Annual Meeting of the Division of Fluid Dynamics, Washington, USA, .