Ramamohan, TR and Shivakumara, IS and Madhukar, K (2011) *The dynamics and rheology of a dilute suspension of periodically forced neutrally buoyant spherical particles in a quiescent Newtonian fluid at low Reynolds numbers.* Fluid Dynamics Research, 43 (4). 045502. ISSN 0169-5983

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## Abstract

We study the effects of both convective and unsteady inertia on the dynamics and rheology of a dilute suspension of periodically forced neutrally buoyant spherical particles, at low Reynolds numbers, in a quiescent Newtonian fluid. The inclusion of inertia results in additional terms in the equation governing the dynamics of the particle that represent a fading memory of the entire history of the particle motion. The inclusion of convective inertia in the low Reynolds number limit makes the memory term nonlinear. Several tests were performed to show that the results presented in this paper are physically reasonable and correct. A perturbation analysis of the problem yields strong evidence that the results of our simulations are correct. It is observed that there is a preferred direction in this system which manifests itself in the properties of the solution. This preferred direction is identified as the direction of the initial motion of the particle. We present here results on the behavior of various parameters with respect to Reynolds numbers and the amplitude of the periodic force. These include phase-space plots between particle displacement and particle velocity and the variation of a rheological parameter, namely a ‘normal stress’ with respect to Reynolds number and the amplitude of the periodic force. We believe that our results may be technologically important since the rheological parameter depends strongly on controllable parameters such as the Reynolds number and the amplitude of the periodic force. Further, this system is one of the simplest systems whose rheology shows non-Newtonian behavior, such as the presence of a normal stress. In addition, this system represents a physically realizable system for experimentally testing the frameworks developed to calculate the collective behavior of systems of oscillators with memory.

Item Type: | Journal Article |
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Subjects: | ENGINEERING > Fluid Mechanics and Thermodynamics |

Division/Department: | CSIR Centre for Mathematical Modelling and Computer Simulation, Other, CSIR Centre for Mathematical Modelling and Computer Simulation |

Depositing User: | Dr. TR Ramamohan |

Date Deposited: | 02 Aug 2011 10:28 |

Last Modified: | 02 Aug 2011 10:28 |

URI: | http://nal-ir.nal.res.in/id/eprint/9257 |

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