Rotary Oscillations of a Permeable Sphere in an Incompressible Couple Stress Fluid

Aparna, P.; Pothanna, N.; Murthy, J. V. Ramana

doi:10.1007/978-981-15-4308-1_10

Cited by 5 publications

(5 citation statements)

References 13 publications

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“…Aparna et al. [33, 34] computed the oscillatory and uniform steady flows, respectively, of a couple stress fluid through a permeable sphere using the Darcy–Brinkman model. Radhika and Iyengar [35] investigated the Stokes flow of a couple stress fluid external to a pair of confocal prolate spheroids, with the innermost shell containing couple stress fluid, surrounded by a porous medium (annular region).…”

Section: Introductionmentioning

confidence: 99%

Mathematical modelling of couple stress fluid flow around a semi‐permeable sphere enclosing a solid core

Selvi,

Bég

2024

Z Angew Math Mech

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The focus of this article is to study theoretically the steady‐axisymmetric creeping flow dynamics of a couple stress fluid external to a semi‐permeable sphere containing a solid core. This problem is motivated by emulsion hydrodynamics in chemical engineering where rheological behaviour often arises in addition to porous media effects. The non‐Newtonian Stokes’ couple stress fluid model features couple stresses and body couples that are absent in the classical Navier–Stokes viscous model. It provides a robust framework for simulating emulsions, complex suspensions and other liquids which possess microstructure. The physical regime is delineated into two zones – the interior of the semi‐permeable zone (region II) which engulfs the solid core and the external couple stress fluid zone (region I). The model is formulated using a spherical polar coordinate system in terms of the stream function ψ. The Brinkman‐extended Darcy model is deployed for the porous medium hydrodynamics and isotropic permeability is considered. Analytical expressions are derived for dimensionless pressure, tangential stress and the couple stress components using the method of separation of variables and Gegenbauer functions of the first kind. The integration constants are evaluated with appropriate boundary conditions on the inner and outer boundary of the semi‐permeable zone with the aid of Mathematica symbolic software. Solutions for the drag force exerted by the couple stress fluid on the semi‐permeable sphere and volumetric flow rate are also derived with corresponding expressions for the drag coefficient and non‐dimensional volumetric flow rate. The influence of permeability (k), separation parameter (l), couple stress viscosity coefficient (η), couple stress inverse length dependent parameter (λ = √(μ/η)) and couple stress viscosity ratio (τ = η/η/) on all key variables is studied graphically. Additionally, streamline contours are computed for a range of parameters including inverse permeability parameter (α = 1/k). The computations show that increasing couple stress inverse length dependent parameter (λ) greatly reduces the dimensionless volumetric flow rate in particular at high values of separation parameter (l). Flow rate is, however, markedly enhanced with permeability (k) and also couple stress viscosity parameter (η). In the presence of the solid core, a much greater drag coefficient is observed at all values of couple stress inverse length dependent parameter (λ) relative to the case without a solid core. A significant distortion in streamlines is computed with increasing separation parameter (l) with a dual vortex structure emanating. With greater couple stress viscosity parameter (τ), no tangible modification is observed in the streamline contours. The present work generalizes the earlier study of Krishnan and Shukla to consider a semi‐permeable (porous medium) outer sphere and furthermore presents detailed streamline visualizations of the creeping flow for a range of emerging parameters of relevance to non‐Newtonian chemical engineering processes including emulsion droplet dynamics in porous materials.

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Section: Introductionmentioning

confidence: 99%

Mathematical modelling of couple stress fluid flow around a semi‐permeable sphere enclosing a solid core

Selvi,

Bég

2024

Z Angew Math Mech

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“…They discovered that as the parameter of couple stress fluid increments, so does the velocity. Aparna et al [25][26][27][28][29] discussed the steady and slow streams of a couple stress fluids past penetrable spherical particles in both oscillatory and uniform flow conditions. They investigated the flow caused by a permeable sphere in a couple stress fluid and discovered that the liquid particles have highly couple and stream in couple stress fluid.…”

Section: Introductionmentioning

confidence: 99%

Motion through a viscous liquid sphere enclosed by a solid core embedded into a Brinkman medium

Shyamala

Shukla

2023

Z Angew Math Mech

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The flow around a solid spherical particle encased in a Newtonian liquid sphere and immersed in a couple stress fluid medium is studied. The problem is expressed by using the Brinkman and Stokes equations, which describe both the flow outside and inside the liquid sphere, respectively. The Gegenbauer polynomials and modified Bessel function are used to express the stream function solution for the internal and external regions. An analytical determination for the flow field in terms of stream function is examined by wielding the method of separation of variables. The drag force on a solid spherical particle placed in a permeable region is calculated. On the drag coefficient, the effects of the permeability 𝜅, the viscosity ratio 𝛾 2 , and the couple stress parameter 𝜆 are investigated.Corresponding dependencies (such as the permeability parameter, couple stress parameter, viscosity ratio, and separation parameter) are graphically represented and discussed. The findings shows when the separation parameter is increased the drag coefficient gradually increases, it refers to a sphere surface with a high level of flow resistance. Passages to the limits are used to describe known specific cases. The present study is essentially significant in the course through a layer developed by penetrable particles and has very important and persuasive applications both in nature and innovation, with various potential outcomes. Thus, the discoveries of this article are comprehensively pertinent to the investigation of the flow of permeable liquids past spherical permeable rocks, aloxite materials, sand beds, earthen soil, petrol supply rocks, and so forth. The present application will support in planning a productive bearing framework.

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“…The study of flow caused by permeable bodies is also given very little attention. Ramana Murthy and Aparna [15, 16] studied the couple stress fluid through a permeable Brinkman sphere. They analysed the drag in the case of Stokes flow and the oscillatory flow.…”

Section: Introductionmentioning

confidence: 99%

Drag on a semipermeable spherical particle covered by a couple stress fluid

Selvi

2023

Math Methods in App Sciences

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This paper focuses on the hydrodynamic interaction between a semipermeable spherical particle and a laminar flow of couple stress fluid. The framework of the flow is divided into two regions, in which the non‐Newtonian characteristics of the couple stress fluid are governed by classical Stokes equations and the permeable region is governed by Darcy's law. The asymptotic series expansion involves the stream functions in terms of modified Bessel's function and Gagenbauer's polynomials for the inner and outer regions. The graphical analysis demonstrating the superior outcomes of numerous parameters such as the couple stress parameter, the permeability parameter, and the couple stress viscosity ratio on the drag coefficient is conducted, and the outcomes are discussed comprehensively. The present study discovered that the drag of a semipermeable sphere is greater than that of a couple stress fluid sphere. A continuous reduction in the pressure distribution is observed with the rising value of the couple stress parameter. However, an increasing value of the couple stress parameter in the semipermeable medium contributes to increasing the tangential stress with respect to the distance from the surface. The current study's findings could be useful in analyzing significant clinical and industrial applications such as the filtration process for wastewater treatment, the design of the digestive system, fluid–solid disperse systems, and the petroleum industry. However, experimental verification is required for the proposed work.

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Rotary Oscillations of a Permeable Sphere in an Incompressible Couple Stress Fluid

Cited by 5 publications

References 13 publications

Mathematical modelling of couple stress fluid flow around a semi‐permeable sphere enclosing a solid core

Mathematical modelling of couple stress fluid flow around a semi‐permeable sphere enclosing a solid core

Motion through a viscous liquid sphere enclosed by a solid core embedded into a Brinkman medium

Drag on a semipermeable spherical particle covered by a couple stress fluid

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