Couple on a rotating permeable sphere in a couple stress fluid

Aparna, P.; Murthy, J. V. Ramana; Nagaraju, G.

doi:10.1016/j.asej.2016.03.012

Cited by 23 publications

(10 citation statements)

References 14 publications

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“…The (wherein the entire medium is rotating) and entropy generation aspects. In this regard important benchmarks for future simulation would be the works of [62]- [65] and efforts in these directions are currently being considered.…”

Section: Discussionmentioning

confidence: 99%

Swimming Dynamics of a Micro-Organism in a Couple Stress Fluid: A Rheological Model of Embryological Hydrodynamic Propulsion

Ali

Sajid

Abbas

et al. 2017

J. Mech. Med. Biol.

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Mathematical simulations of embryological fluid dynamics are fundamental to improving clinical understanding of the intricate mechanisms underlying sperm locomotion. The strongly rheological nature of reproductive fluids has been established for a number of decades. Complimentary to clinical studies, mathematical models of reproductive hydrodynamics provide a deeper understanding of the intricate mechanisms involved in spermatozoa locomotion which can be of immense benefit in clarifying fertilization processes. Although numerous non-Newtonian studies of spermatozoa swimming dynamics in non-Newtonian media have been communicated, very few have addressed the micro-structural characteristics of embryological media. This family of micro-continuum models include Eringen’s micro-stretch theory, Eringen’s microfluid and micropolar constructs and V. K. Stokes’ couple stress fluid model, all developed in the 1960s. In the present paper we implement the last of these models to examine the problem of micro-organism (spermatozoa) swimming at low Reynolds number in a homogenous embryological fluid medium with couple stress effects. The micro-organism is modeled as with Taylor’s classical approach, as an infinite flexible sheet on whose surface waves of lateral displacement are propagated. The swimming speed of the sheet and rate of work done by it are determined as function of the parameters of orbit and the couple stress fluid parameter ([Formula: see text]). The perturbation solutions are validated with a Nakamura finite difference algorithm. The perturbation solutions reveal that the normal beat pattern is effective for both couple stress and Newtonian fluids only when the amplitude of stretching wave is small. The swimming speed is observed to decrease with couple stress fluid parameter tending to its Newtonian limit as alpha tends to infinity. However the rate of work done by the sheet decreases with [Formula: see text] and approaches asymptotically to its Newtonian value. The present solutions also provide a good benchmark for more advanced numerical simulations of micro-organism swimming in couple-stress rheological biofluids.

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Section: Discussionmentioning

confidence: 99%

Swimming Dynamics of a Micro-Organism in a Couple Stress Fluid: A Rheological Model of Embryological Hydrodynamic Propulsion

Ali

Sajid

Abbas

et al. 2017

J. Mech. Med. Biol.

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“…[2] and [3] investigated the slow and steady flow of a couple stress fluid through a permeable sphere for both the uniform and oscillatory flow. [4] have studied the flow generated due to a permeable sphere in a couple stress fluid and found that the fluid particles have more swirl and more couple in couple stress fluid. [5] have discussed the problem of creeping flow of couple stress fluid generated by the slow steady rotation of a permeable sphere within surface about its symmetry axis and noticed that the couple acting on the sphere due to internal flow is zero.…”

Section: Introductionmentioning

confidence: 99%

Creeping flow of couple stress fluid past a fluid sphere with a solid core

Krishnan

Shukla

2021

Z Angew Math Mech

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The steady axisymmetric uniform flow of an incompressible couple stress fluid past a fluid sphere with a solid core has been studied analytically. No-slip boundary condition and vanishing couple stress condition are applied on the surface of the sphere. The problem is formulated using the V. K. Stokes equation describing the flow outside the fluid sphere as well as the flow inside the fluid sphere. The stream function solution for the axisymmetric motion and pressure distribution for both regions are solved explicitly. The stresses acting on the fluid sphere are estimated and the drag force experienced by a fluid sphere is determined.Numerical study is undertaken to study the effect of couple stress parameter and viscosity coefficients on the drag and the results are presented in graphical forms.The results reveal that drag force, pressure and velocity of the fluid decreases in the presence of couple stresses. Some special cases of flow past a fluid sphere have been validated with earlier well-known cases.

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“…Couple stress uid ow past a porous spheroidal shell with solid core under Stokesian assumption was studied and analyzed by Iyengar and Radhika [7]. A study of a Couple acting on a couple-stress uid for rotary ows across a permeable sphere was carried out [8]. Vandana Mishra and Ram Gupta [9] studied the concept of analytically uniform ow of steady axi-symmetric creeping ow of an incompressible micro-polar uid around the permeable sphere.…”

Section: Introductionmentioning

confidence: 99%

Couple stress fluid flow due to slow steady oscillations of a permeable sphere

Aparna

Padmaja

Pothanna

et al. 2020

Nonlinear Engineering

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The study of oscillating flow of a Couple Stress fluid past a permeable sphere is considered. Analytical solution for the flow field in terms of stream function is obtained using modified Bessel functions. The formula for Drag acting on the sphere due external flow is evaluated. Pressure field for the flow region past and inside the sphere is obtained. Effects of physical parameters like couple stress parameter, permeability, frequency and geometric parameters on the drag due to internal and external flows are represented graphically. It is observed that the drag for viscous fluid flow will be less than the case of couple-stress fluid flow and hence couple stress fluids offer resistance for flow.

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Couple on a rotating permeable sphere in a couple stress fluid

Cited by 23 publications

References 14 publications

Swimming Dynamics of a Micro-Organism in a Couple Stress Fluid: A Rheological Model of Embryological Hydrodynamic Propulsion

Swimming Dynamics of a Micro-Organism in a Couple Stress Fluid: A Rheological Model of Embryological Hydrodynamic Propulsion

Creeping flow of couple stress fluid past a fluid sphere with a solid core

Couple stress fluid flow due to slow steady oscillations of a permeable sphere

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