Article
Regular and complex singularities of the generalized thin film equation in two dimensions
Author/s | Dallaston, M. C.
Fontelos López, Marco Antonio Herrada Gutiérrez, Miguel Ángel López Herrera, J. M. Eggers, Jens |
Department | Universidad de Sevilla. Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos |
Publication Date | 2021 |
Deposit Date | 2022-10-03 |
Published in |
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Abstract | We use a generalized version of the equation of motion for a thin film of liquid on a solid,
horizontal substrate as a model system to study the formation of singularities in space
dimensions greater than one. Varying ... We use a generalized version of the equation of motion for a thin film of liquid on a solid, horizontal substrate as a model system to study the formation of singularities in space dimensions greater than one. Varying both the exponent controlling long-ranged forces, as well as the exponent of the nonlinear mobility, we predict the structure of the singularity as the film thickness goes to zero. The spatial structure of rupture may be either ‘pointlike’ (approaching axisymmetry) or ‘quasi-one-dimensional’, in which case a one-dimensional singularity is unfolded into two or higher space dimensions. The scaling of the profile with time may be either strictly self-similar (the ‘regular’ case) or discretely self-similar and perhaps chaotic (the ‘irregular’ case). We calculate the phase boundaries between these regimes, and confirm our results by detailed comparisons with time-dependent simulations of the nonlinear thin film equation in two space dimensions. |
Funding agencies | Junta de Andalucía Ministerio de Economía y Competitividad (MINECO). España |
Project ID. | P18-FR-3623
108278-RB-C31 |
Citation | Dallaston, M.C., Fontelos López, M.A., Herrada Gutiérrez, M.Á., López Herrera, J.M. y Eggers, J. (2021). Regular and complex singularities of the generalized thin film equation in two dimensions. Journal of Fluid Mechanics, 917, A20. https://doi.org/10.1017/jfm.2021.286. |
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