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- Title
Oscillations of a periodically forced slightly eccentric spheroid in an unsteady viscous flow at low Reynolds numbers.
- Authors
Singh, Jogender; Kumar, C. V. Anil
- Abstract
The equations governing the dynamics of a periodically driven micro-spheroid in an unsteady viscous fluid at low Reynolds number are derived. Its oscillation properties in the presence/absence of memory forces are reported. The core part of the derivation is a perturbation analysis of motion of a sphere. The calculated solutions match with those available in the literature in the limiting case of a sphere. The dependence of the solutions on shape (α ), free oscillation frequency ( ω 0 ) and particle–fluid density ratio ( d r ) is calculated. The maximum amplitude of the oscillations of an oblate spheroid is greater than that of a prolate spheroid, showing that the velocity disturbance for an oblate spheroid is higher in the presence/absence of the memory force. The increase in α leads to the enhancement(reduction) of amplitude peaks in the case of the oblate (prolate) spheroid in the presence and more dominantly in the absence of the force. There is also a reduction in the amplitude of spheroid oscillations of many multiples due to the presence of the memory force. Stronger oscillation variations are observed on changing ω 0 or d r compared to α. The variations of the value of the phase are similar for both the spheroids on varying ω 0 and d r , whereas they are reversed on varying α. The linear scaling of amplitude on α observed for the spheroids may give insight into the physics, especially regarding the quantum of velocity disturbances due to particle size. The slopes are high in the absence of the force, confirming that the presence of the force increases the resistance of spheroid motion, largely. The dependencies of oscillations on the parameters can be utilized for better separation of particles or for characterizing the suspension. The novelty of the problem and its analytical solutions might have value as tests in software for more complicated and realistic systems and hence strikes a good balance between complication and tractability.
- Subjects
VISCOUS flow; UNSTEADY flow; REYNOLDS number; OSCILLATIONS; SPHEROIDAL state; FREQUENCIES of oscillating systems
- Publication
Theoretical & Computational Fluid Dynamics, 2021, Vol 35, Issue 1, p1
- ISSN
0935-4964
- Publication type
Article
- DOI
10.1007/s00162-020-00547-7