Regular and complex singularities of the generalized thin film equation in two dimensions
| Autor: | Miguel A. Herrada, Michael C. Dallaston, Jose M. Lopez-Herrera, Jens Eggers, Marco A. Fontelos |
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| Přispěvatelé: | Universidad de Sevilla. Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Junta de Andalucía, Ministerio de Economía y Competitividad (MINECO). España, Ministerio de Economía y Competitividad (España) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Mechanical Engineering Thin films 010102 general mathematics Mathematical analysis Pattern formation Equations of motion Condensed Matter Physics Space (mathematics) 01 natural sciences 010305 fluids & plasmas Nonlinear system Singularity Mechanics of Materials 0103 physical sciences Exponent Gravitational singularity 0101 mathematics Scaling |
| Zdroj: | Digital.CSIC. Repositorio Institucional del CSIC instname Dallaston, M, Fontelos, M, Herrada, M A, Lopez-Herrera, J M & Eggers, J G 2021, ' Regular and complex singularities of the generalized thin film equation in two dimensions ', Journal of Fluid Mechanics, vol. 917, 2100286 . https://doi.org/10.1017/jfm.2021.286 |
| DOI: | 10.1017/jfm.2021.286 |
| Popis: | 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. M.A.H. and J.M.L.-H. acknowledge financial support from the Ministerio de Economía y Competitividad and the Junta de Andalucia of the Kingdom of Spain under grants PID2019-108278-RB-C31 and P18-FR-3623, respectively. |
| Databáze: | OpenAIRE |
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