Abstract
This work examines the orientation profile of a rigid body suspended in a time-dependent uniform flow at low Reynolds numbers under the action of an external periodic field. We derive the unsteady equations governing the transport by considering the influence of both fluid and particle inertia. We observe the significance of the acceleration reaction term, which appeared in the governing equation, as the calculated value increases as the aspect ratio increases. In contrast, the lift force exerted by the flow on the spheroid is insignificant since it is negligibly small. We provide phase diagrams of the solutions with functional relations with the particle’s geometry, amplitude and phase of the external field, and Reynolds numbers. The steady-state solutions are orbits controlled by the parameters. In this analysis, we observe a phase shift in position and velocity, a drift of orbits, and dependence of orientation movement on the aspect ratio and amplitude of the external field and the Reynolds number.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andersson, H.I., Jiang, F.: Forces and torques on a prolate spheroid: low-Reynolds-number and attack angle effects. Acta Mechanica. 230(2), 431–447 (2019). https://doi.org/10.1007/s00707-018-2325-x
Asokan, K., Kumar, C.V.A., Dasan, J., Radhakrishnan, K., Kumar, K.S., Ramamohan, T.R.: Review of chaos in the dynamics and rheology of suspensions of orientable particles in simple shear flow subject to an external periodic force. J. Non-Newton. Fluid Mech. 129(3), 128–142 (2005)
Happel, J., Brenner, H.: Low Reynolds number hydrodynamics: with special applications to particulate media (Vol. 1). Springer Science & Business Media (2012)
Kumar, K.S., Savithri, S., Ramamohan, T.R.: Chaotic dynamics and rheology of suspensions of periodically forced slender rods in simple shear flow. Jpn. J. Appl. Phys. 35(11R), 5901 (1996)
Lawrence, C.J., Weinbaum, S.: The force on an axisymmetric body in linearized, time-dependent motion: a new memory term. J. Fluid Mech. 171, 209–218 (1986)
Lovalenti, P.M., Brady, J.F.: The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. J. Fluid Mech. 256, 561–605 (1993)
Madhukar, K., Kumar, P., Ramamohan, T., Shivakumara, I.: Dynamics and"normal stress"evaluation of dilute suspensions of periodically forced prolate spheroids in a quiescent newtonian fluid at low reynolds numbers. Sadhana 35(6), 659–679 (2010)
Pozrikidis, C.: Boundary integral and singularity methods for linearized viscous flow. Cambridge University Press (1992)
Ramamohan, T.R., Savithri, S., Sreenivasan, R., Bhat, C.C.: Chaotic dynamics of a periodically forced slender body in a simple shear flow. Phys. Lett. A 190(3–4), 273–278 (1994)
Ramamohan, T.R., Shivakumara, I.S., Madhukar, K.: Numerical simulation of the dynamics of a periodically forced spherical particle in a quiescent Newtonian fluid at low Reynolds numbers. In: International conference on computational science, pp. 591–600 (2009)
Ramamohan, T.R., Shivakumara, I.S., Madhukar, K.: 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 Dyn. Res. 43(4), 045–502 (2011)
Singh, J., Kumar, C.V.A.: Dynamics of a periodically forced spheroid in a quiescent fluid in the limit of low Reynolds numbers. Rheol. Acta 58, 709–718 (2019). https://doi.org/10.1007/s00397-019-01169-5
Stokes, G.G.: On the effect of the internal friction of fluids on the motion of pendulums (Vol. 9). Pitt Press Cambridge (1851)
Funding
One of the authors (Mr. Jogender Singh) enjoyed a fellowship from the Indian Institute of Space Science and Technology, Thiruvananthapuram, India, during the period of the work.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
No Conflicts of interest among authors.
Consent to participate
Agreed to participate.
Consent for publication
Agreed to publish.
Ethical approval
Nothing is done against the ethics of scientific research.
Author contributions
All the authors equally contributed to the journal.
Data availability
All data for analysis and for generating graphs are numerically computed by the authors using their own codes.
Code availability
All codes are available with the authors and will be provided to anyone based on one’s request to the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Singh, J., Kumar, C.V.A. Transport of a driven spheroid in a uniform flow at low Reynolds numbers. Acta Mech 234, 3649–3664 (2023). https://doi.org/10.1007/s00707-023-03577-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-023-03577-4