Sharp scalar and tensor bounds on the hydrodynamic friction and mobility of arbitrarily shaped bodies in Stokes flow
| Autor: | Eligiusz Wajnryb, Jerzy Blawzdziewicz, J. B. Hubbard, James A. Given |
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| Rok vydání: | 2005 |
| Předmět: |
Fluid Flow and Transfer Processes
Physics Mechanical Engineering Computational Mechanics Particle-laden flows Stokes flow Dissipation Condensed Matter Physics Matrix (mathematics) Classical mechanics Mechanics of Materials Equipotential Calculus of variations Magnetosphere particle motion Brownian motion |
| Zdroj: | Physics of Fluids. 17:033602 |
| ISSN: | 1089-7666 1070-6631 |
| DOI: | 10.1063/1.1852315 |
| Popis: | We prove rigorous inequalities for the hydrodynamic translational friction and mobility matrices ζ and μO of an arbitrarily shaped rigid particle in terms of the electrostatic capacitance C of a conducting particle of identical shape. Specifically, we derive the scalar and matrix inequalities 13trζ−1⩽13trμO⩽C−1 and 23ζ−1⩽C−1I, where all quantities are normalized by the corresponding values for a sphere, and the mobility matrix is evaluated in the center-of-mobility reference frame. These bounds are obtained using a variational approach with the energy dissipation functional expressed in terms of the induced force distribution on the surface of the particle. To relate the hydrodynamic problem to the solution of the corresponding electrostatic problem, the trial force field is expressed in terms of the charge distribution on the equipotential particle surface. This procedure yields the first rigorous bounds on hydrodynamic friction that apply to bodies with translation-rotation coupling. We demonstrate that... |
| Databáze: | OpenAIRE |
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