Oscillations of a periodically forced slightly eccentric spheroid in an unsteady viscous flow at low Reynolds numbers

Singh, Jogender; Kumar, C. V. Anil

doi:10.1007/s00162-020-00547-7

Theor. Comput. Fluid Dyn.

2020

DOI: 10.1007/s00162-020-00547-7

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Oscillations of a periodically forced slightly eccentric spheroid in an unsteady viscous flow at low Reynolds numbers

Jogender Singh

C. V. Anil Kumar

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2024

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Cited by 2 publications

References 17 publications

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Periodically driven spheroid in a viscous fluid at low Reynolds numbers

Singh

Kumar

2022

AIP Advances

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In this paper, we study the motion of a spheroid of a moderate aspect ratio in a viscous fluid under the action of an external harmonic force. We first derive the dynamics equation of the particle oscillating along one of its axes and subject to damping, Basset memory, and second history integral forces at small Reynolds numbers, and then, we proceed to obtain an analytical solution of this equation at resonance. With graphical representation, we observe that for a prolate spheroid, the conventional Q-curves show a greater variation with respect to the particle aspect ratio, particle–fluid density ratio, and natural frequency; the variation is significantly larger for the curve corresponding to the second history force. Furthermore, we find that all three forces affect the amplitude of motion: the amplitude increases with the strength of damping as well as the second history integral forces, whereas the presence of Basset memory decreases it. Remarkably, Basset memory causes a phase-shift in the oscillations, while the other two forces have no effect on the phase. Since our solutions are analytical, they may have valuable application in experiments involving more complex systems, in particular, to understand the effect of external force on the transport of micro-particles.

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Periodically driven spheroid in a viscous fluid at low Reynolds numbers

Singh

Kumar

2022

AIP Advances

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Dynamics of a driven spheroid in a slow oscillating creeping shear flow

Kurian,

Ramamohan,

Anil Kumar

2024

Physics of Fluids

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We report the orientation dynamics of a sinusoidally driven spheroid suspended in a slow and weak/strong oscillatory shear flow without Brownian and inertial forces, derive the governing equations, find the classical Jeffery orbits, and then solve them numerically. These equations describe Jeffery's orbits for no external force and no flow oscillations. When the external forces are small, and there are no oscillations, they can be seen as perturbations of the equations that result in Jeffery's orbits. The small perturbations disturb the Jeffery orbits. We also analyze the chaotic and regular dynamics regimes in nearly quiescent, simple shear, and weak/strong and slow oscillating shear flows. We observe quantitative and qualitative differences in the particle dynamics for an oscillating shear flow compared to simple shear flow, as seen from the Poincaré sections, attractors, phase diagrams, time series, and Lyapunov exponents. The analysis indicates that the slow oscillations reduce the complexity of the dynamics of the particle compared to simple shear flow. The steady-state solutions for both prolate and oblate spheroids remain in the flow gradient plane in the case of strong oscillatory shear. At the same time, there is some disturbance from the flow gradient plane for weak oscillations due to the external force instead of inertial forces reported earlier in the literature. In addition, we propose a mechanism to improve particle separation based on shape using a combination of simple and oscillating shear flows, offering significant advantages in separating particles from a colloidal mixture that would otherwise be impossible.

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Oscillations of a periodically forced slightly eccentric spheroid in an unsteady viscous flow at low Reynolds numbers

Cited by 2 publications

References 17 publications

Periodically driven spheroid in a viscous fluid at low Reynolds numbers

Periodically driven spheroid in a viscous fluid at low Reynolds numbers

Dynamics of a driven spheroid in a slow oscillating creeping shear flow

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