Steady azimuthal flow field induced by a rotating sphere near a rigid disk or inside a gap between two coaxially positioned rigid disks
| Autor: | Alexander R. Sprenger, Andreas M. Menzel, Abdallah Daddi-Moussa-Ider, Thomas Richter, Hartmut Löwen |
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| Rok vydání: | 2021 |
| Předmět: |
Fluid Flow and Transfer Processes
Physics Mechanical Engineering Fluid Dynamics (physics.flu-dyn) Computational Mechanics Rotation around a fixed axis FOS: Physical sciences Reynolds number Physics - Fluid Dynamics Function (mathematics) Radius Mechanics Condensed Matter - Soft Condensed Matter Condensed Matter Physics Integral equation Domain (mathematical analysis) symbols.namesake Flow (mathematics) Mechanics of Materials symbols Soft Condensed Matter (cond-mat.soft) Particle |
| Zdroj: | Physics of Fluids. 33:082011 |
| ISSN: | 1089-7666 1070-6631 |
| DOI: | 10.1063/5.0062688 |
| Popis: | Geometric confinements play an important role in many physical and biological processes and significantly affect the rheology and behavior of colloidal suspensions at low Reynolds numbers. On the basis of the linear Stokes equations, we investigate theoretically and computationally the viscous azimuthal flow induced by the slow rotation of a small spherical particle located in the vicinity of a rigid no-slip disk or inside a gap between two coaxially positioned rigid no-slip disks of the same radius. We formulate the solution of the hydrodynamic problem as a mixed-boundary-value problem in the whole fluid domain, which we subsequently transform into a system of dual integral equations. Near a stationary disk, we show that the resulting integral equation can be reduced into an elementary Abel integral equation that admits a unique analytical solution. Between two coaxially positioned stationary disks, we demonstrate that the flow problem can be transformed into a system of two Fredholm integral equations of the first kind. The latter are solved by means of numerical approaches. Using our solution, we further investigate the effect of the disks on the slow rotational motion of a colloidal particle and provide expressions of the hydrodynamic mobility as a function of the system geometry. We compare our results with corresponding finite-element simulations and observe very good agreement. 14 pages, 9 figures, revised manuscript resubmitted to Phys. Fluids (invited article) |
| Databáze: | OpenAIRE |
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