https://doi.org/10.1140/epjst/e2009-00884-0
Film flows down a fiber: Modeling and influence of streamwise viscous diffusion
1
Lab. FAST, UMR 7608, Campus Univeristaire, 91405 Orsay, France
2
Service de Chimie-Phyisque E.P., Université Libre de Bruxelles, CP. 165/62, Brussels, Belgium
3
Department of Chemical Engineering, Imperial College London, London, SW7 2AZ, UK
Corresponding author: ruyer@fast.u-psud.fr
A two-equation model is formulated in terms of two coupled evolution equations for the film thickness h and the local flow rate q within the framework of lubrication theory. Consistency is achieved up to first order in the film parameter ϵ and streamwise diffusion effects are accounted for. The evolution equation obtained by Craster and Matar [1] is recovered in the appropriate limit. Comparisons to the experimental results by [2] and [3] show good agreement in the linear and nonlinear regimes. Second-order viscous diffusion terms are found to potentially enhance the speed and amplitude of nonlinear waves triggered by the Rayleigh-Plateau instability mechanism. Time-dependent computations of the spatial evolution of the film reveal a strong influence of streamwise diffusion on the dynamics of the flow and the wave selection process.
© EDP Sciences, Springer-Verlag, 2009