Similarity solutions for unsteady shear-stress-driven flow of Newtonian and power-law fluids : slender rivulets and dry patches

Unsteady flow of a thin film of a Newtonian fluid or a non-Newtonian power-law fluid with power-law index N driven by a constant shear stress applied at the free surface, on a plane inclined at an angle α to the horizontal, is considered. Unsteady similarity solutions representing flow of slender rivulets and flow around slender dry patches are obtained. Specifically, solutions are obtained for converging sessile rivulets (0 < α < π/2) and converging dry patches in a pendent film (π/2 < α < π), as well as for diverging pendent rivulets and diverging dry patches in a sessile film. These solutions predict that at any time t, the rivulet and dry patch widen or narrow according to |x|3/2, and the film thickens or thins according to |x|, where x denotes distance down the plane, and that at any station x, the rivulet and dry patch widen or narrow like |t|−1, and the film thickens or thins like |t|−1, independent of N

The effect of gravity and shear stress on a liquid film driven in a horizontal minichannel at local heating

The present study is focused on the investigation of gravity effect on thermocapillary deformations in a film flowing under action of co-current gas flow, which creates the tangential force on the gas-liquid interface. The influence of local heating intensity on the heater at a substrate is also investigated. Effects of surface tension, temperature dependent viscosity and thermocapillarity are taken into account. Investigations have shown that gravity has a significant effect on the film deformations and pattern. Decreasing of gravity level leads to a flow destabilization. 3D liquid film pattern noticeably changes in spanwise direction. Increasing of heat flux leads to increasing of liquid film deformations. Dependence of film thinning on heat flux is strongly nonlinear. The most dangerous deformations (regions of minimum film thickness with possible disruption of liquid) take place behind the downstream edge of the heater at any gravity conditions.En ligne: http://www.springerlink.com/content/j207456083166646/info:eu-repo/semantics/publishe

Interfacial balance equations for diffusion evaporation and exact solution for weightless drop

Introducing of additional terms into the balance equations to specify the conditions at the interface allows to study physical phenomena in the diffusion evaporation (condensation) of the liquid into the neutral gas. We have taken into account the vapour dynamic effects on evaporating liquid, as well as the waste of energy on deformation of the boundary, changing of the interfacial temperature (the interface has an internal energy and therefore heat capacity), to overcome the surface tension etc. This paper presents the balance conditions at the interface with the diffusion evaporation of the liquid into the neutral gas, for the case when the vapour is considered as an impurity in the gas phase. The analysis of the dimensionless criteria is carried out. The areas of parameters for which the effect of some physical factors take a place have been defined. The exact solution of the diffusion evaporation for a spherical drop at zero gravity conditions has been constructed. The explicit expression for the interfacial temperature and evaporation rate were derived. Solution for evaporation rate coincides with the solution obtained by Maxwell (1890). © Springer Science+Business Media B.V. 2011.SCOPUS: ar.jinfo:eu-repo/semantics/publishe