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The Study of a Dilute Suspension of Periodically Forced Spherical Particles in an Oscillating Newtonian Fluid at Low Reynolds Numbers


  • Department of Mathematics, St. Joseph’s College (Autonomous), Lalbagh Road, Bangalore – 560027, Karnataka, India


Background/Objective: The dynamics of a dilute suspension of periodically forced spherical particles in an oscillating Newtonian fluid at low Reynolds numbers is discussed. The behavior of the particle(s) due to the periodic force imposed on the spherical particle, the particle Reynolds number and the oscillating fluid has been studied. Methods: The expression for the hydrodynamic force acting on a particle moving in a fluid undergoing uniform time dependent flow, given by Lovalenti and Brady, is used and equations for the particle velocity and particle displacement under these conditions have been formulated. These integro differential equations have been solved numerically and are compared with analytical solutions obtained from a linearized version of the equations. Findings: It is observed that the phase space plots obtained by omitting the nonlinear term are reasonably accurate for most of the parametric regimes considered. It is also shown that the numerical solution can be approximated from the analytical solution of the linearized equations by scaling them suitably. The numerical solution obtained from the full nonlinear equation has also been compared with the solutions obtained by a perturbation method obtained by using Re1/2 (where Re is the particle Reynolds’ number), as the perturbation parameter. The variation of the rheological parameters with the parameters of the system is depicted. The particle motion had a preferred direction and it was seen that the direction of the initial motion was its preferred direction of motion. Hence the reflection of the phase plots was obtained, when the forces were applied in the opposite direction. Applications: The software/ program developed and the study will serve as a test case for the study of periodically forced particles in a fluid at low to moderate Reynolds numbers.


Low Reynolds’ Number, Newtonian Fluids, Normal Stress, Periodic Force, Rheology, Volume Fractions

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