New asymptotic heat transfer model in thin liquid films

In this article, we present a model of heat transfer occurring through a li\-quid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow depth to the characteristic wavelength. A new Nusselt solution should be explained, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms coming from temperature variation effects. Comparisons are made with numerical solutions of the full Fourier equations in a steady state frame. The flow and heat transfer are coupled through Marangoni and temperature dependent viscosity effects. Even if these effects have been considered separately before, here a fully coupled model is proposed. Another novelty consists in the asymptotic approach in contrast to the weighted residual approach which have been formerly applied to these problems.Comment: 28 pages, 6 figures, 39 references. Other author's papers can be downloaded at http://www.denys-dutykh.com

Comment on "low-dimensional models for vertically falling viscous films"

International audienceA Comment on the Letter by Mohan K. R. Panga and Vemuri Balakotaiah, Phys. Rev. Lett. 90, 154501 (2003). The authors of the Letter offer a Repl

On the speed of solitary waves running down a vertical wall

International audienceSolitary-wave solutions to surface equations or two-equation models of film flows are investigated within the framework of dynamical system theory. The limiting behaviour of one-humped solitary waves (homoclinic orbits) at large Reynolds numbers is considered. Their predicted speed is in good agreement with numerical findings. The theory also explains the absence of solitary-wave solutions to the Benney equation in the same limit. © 2005 Cambridge University Press

Further accuracy and convergence results on the modeling of flows down inclined planes by weighted-residual approximations

International audienceWe study the reliability of two-dimensional models of film flows down inclined planes obtained by us [Ruyer-Quil and Manneville, Eur. Phys. J. B 15, 357 (2000)] using weighted-residual methods combined with a standard long-wavelength expansion. Such models typically involve the local thickness h of the film, the local flow rate q, and possibly other local quantities averaged over the thickness, thus eliminating the cross-stream degrees of freedom. At the linear stage, the predicted properties of the wave packets are in excellent agreement with exact results obtained by Brevdo [J. Fluid Mech. 396, 37 (1999)]. The nonlinear development of waves is also satisfactorily recovered as evidenced by comparisons with laboratory experiments by Liu [Phys. Fluids 7, 55 (1995)] and with numerical simulations by Ramaswamy [J. Fluid Mech. 325, 163 (1996)]. Within the modeling strategy based on a polynomial expansion of the velocity field, optimal models have been shown to exist at a given order in the long-wavelength expansion. Convergence towards the optimum is studied as the order of the weighted-residual approximation is increased. Our models accurately and economically predict linear and nonlinear properties of film flows up to relatively high Reynolds numbers, thus offering valuable theoretical and applied study perspectives. (C) 2002 American Institute of Physics