Periodically driven spheroid in a viscous fluid at low Reynolds numbers

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Why is it important?

The novelties of the problem are: (1) This study confirms the significance of the second history integral in the transport of geometrically different bodies. (2) In view of the nature of the solution, the conventional Q-curves for a prolate spheroid are modified with respect to the particle aspect ratio, particle-fluid density ratio, and natural frequency. (3) The Q-curves show a greater variation with respect to the parameters; the variation is significantly larger for the curve corresponding to the second history force. (4) The Q-values representing Basset memory vary more rapidly than the other two Q-values in response to the parameter changes. (5) 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. (6) Basset memory causes a phase shift in the oscillations, while the other two forces have no effect on the phase. (7) Since our solutions are analytical, they may have valuable applications to experiments involving more complex systems, in particular, to understand the effect of acoustic waves on micro-particle transport and the problem strikes a reasonably good balance between complication and tractability.