Slow motion of couple stress fluid past a solid sphere in a virtual cell: slip effect

Madasu, Krishna Prasad; Sarkar, Priya

doi:10.1007/s40430-023-04363-y

Cited by 3 publications

(5 citation statements)

References 43 publications

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“…In the case of axisymmetric steady flow, an incompressible couple stress fluid, Prasad [39] discovered the Brinkman solutions (17), while Happel and Brenner [41] discovered the Stokes solutions (18).…”

Section: Solution Of the Problemmentioning

confidence: 99%

“…In the case of axisymmetric steady flow, an incompressible couple stress fluid, Prasad [39] discovered the Brinkman solutions (), while Happel and Brenner [41] discovered the Stokes solutions ().

\begin{equation} \psi ^{(1)}(r, \zeta ) = \frac{1}{2} {\left[r^2 + \frac{B_1}{r} + C_1 \sqrt {r}\; K_{3/2}(\alpha \, r) + D_1 \sqrt {r} \; K_{3/2}(\beta \, r)\right]}\sin ^2 \theta , \;\;\; 1 \le r \le \infty \end{equation}

\begin{equation} \psi ^{(2)}(r, \zeta ) = \frac{1}{2} {\left[A_2 \,r^{-1} + B_2 \,r^2 + C_2 \,r + D_2 \,r^4\right]} \sin ^2 \theta , \;\;\; \ell \le r \le 1 \end{equation}

where

\ell = a/b

K_{3/2}

is the half‐integral index for Macdonald function, B 1 , C 1 , D 1 , A 2 , B 2 , C 2 and D 2 are constants to be resolved from the boundary constraints.…”

Section: Solution Of the Problemmentioning

confidence: 99%

“…The axisymmetrical steady flow of a couple stress fluid through a porous sphere was studied by Shyamala and Shukla [37,38]. The study of the axially symmetric and uniform flow of couple stress fluid past a rigid core implanted in a permeable region by Madasu and Sarkar [39].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Solution Of the Problemmentioning

confidence: 99%

\begin{equation} \psi ^{(1)}(r, \zeta ) = \frac{1}{2} {\left[r^2 + \frac{B_1}{r} + C_1 \sqrt {r}\; K_{3/2}(\alpha \, r) + D_1 \sqrt {r} \; K_{3/2}(\beta \, r)\right]}\sin ^2 \theta , \;\;\; 1 \le r \le \infty \end{equation}

\begin{equation} \psi ^{(2)}(r, \zeta ) = \frac{1}{2} {\left[A_2 \,r^{-1} + B_2 \,r^2 + C_2 \,r + D_2 \,r^4\right]} \sin ^2 \theta , \;\;\; \ell \le r \le 1 \end{equation}

where

\ell = a/b

K_{3/2}

is the half‐integral index for Macdonald function, B 1 , C 1 , D 1 , A 2 , B 2 , C 2 and D 2 are constants to be resolved from the boundary constraints.…”

Section: Solution Of the Problemmentioning

confidence: 99%

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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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“…An incompressible couple's Stokes flow through a permeable spherical shell was investigated by Sai Lakshmi Radhika and Iyengar [24]. Krishna Prasad and Priya [25] discovered the couple stress fluid by embedding a solid spherical body in a permeable Brinkman medium. They discovered that as the slip parameter increased, the real part of drag increased because the fluid velocity on the sphere's surface decreased.…”

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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“…They utilized a Fourier transform to find the exact solution and compare it with the solution in the literature. Madasu et al [16] studied the flow of a Couple stress fluid through a medium with pores and an encapsulated spherical. The drag experienced by an incompressible couple stress fluid on a sphere within a material with pores is estimated.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamics of Incompressible Creeping Couple Stress Fluid Through a Uniformly Porous Channel in Presence of Darcy Resistance: Exact Solution and Physical Insights Using the Inverse Method Approach

Ishaq,

Fatima,

Afzal

et al. 2023

Preprint

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The current study examines the features of a two-dimensional steady incompressible flow of creeping couple stress fluid across a permeable channel with uniform reabsorption. The mathematical model that governs this flow is composed of linear partial differential equations and homogeneous boundary constraints. The Inverse method approach, an analytical technique, is used to find solutions to the problem. By converting the momentum equations to stream functions, the inverse approach helps derive all the relevant physical quantities, including the longitudinal and transverse velocities, fractional reabsorption, leakage flux, axial pressure, volume flow rate, and mean pressure. Using MATLAB software, the dependent functions such as stream function, pressure, and volume flow are evaluated for different parameter values. The findings indicate that the longitudinal velocity is affected by the initial flow rate, while the transverse velocity shows no change in its profile. The streamlines become more straight and identical as the flow rate increases. Backward flow occurs at the end of the slit due to the porosity parameter. However, the initial flow rate does not impact the transverse velocity of the fluid in the permeable channel. This study fully describes a mathematical foundation for understanding fluid movement across permeable boundaries, which have practical applications in areas such as gaseous diffusion, filtration, and biological mechanisms.

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Slow motion of couple stress fluid past a solid sphere in a virtual cell: slip effect

Cited by 3 publications

References 43 publications

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

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

Hydrodynamics of Incompressible Creeping Couple Stress Fluid Through a Uniformly Porous Channel in Presence of Darcy Resistance: Exact Solution and Physical Insights Using the Inverse Method Approach

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