Galerkin representations and fundamental solutions for an axisymmetric microstretch fluid flow

Sherief, Hany H.; Faltas, M. S.; Ashmawy, E. A.

doi:10.1017/s0022112008004485

Cited by 25 publications

(17 citation statements)

References 24 publications

(32 reference statements)

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“…Neto et al [39] provided an excellent review of experimental studies regarding the phenomenon of slip of Newtonian fluids at solid interface. In the recent years, there has been an increasing interest in using the slip boundary condition for Newtonian fluids [40--43] and for micropolar and microstreach fluids [44,45]. This paper investigates Stokes flow past an assemblage of slip eccentric spherical particle-in-cell models.…”

Section: Introductionmentioning

confidence: 99%

Stokes flow past an assemblage of slip eccentric spherical particle-in-cell models

Faltas

Saad

2011

Math. Meth. Appl. Sci.

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The quasisteady axisymmetrical flow of an incompressible viscous fluid past an assemblage of slip eccentric spherical particle-in-cell models with Happel and Kuwabara boundary conditions is investigated. A linear slip, Basset type, boundary condition on the surface of the spherical particle is used. Under the Stokesian approximation, a general solution is constructed from the superposition of the basic solutions in the two spherical coordinate systems based on the particle and fictitious spherical envelope. The boundary conditions on the particle's surface and fictitious spherical envelope are satisfied by a collocation technique. Numerical results for the normalized drag force acting on the particle are obtained with good convergence for various values of the volume fraction, the relative distance between the centers of the particle and fictitious envelope and the slip coefficient of the particle. In the limits of the motions of the spherical particle in the concentric position with cell surface and near the cell surface with a small curvature, the numerical values of the normalized drag force are in good agreement with the available values in the literature.

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Section: Introductionmentioning

confidence: 99%

Stokes flow past an assemblage of slip eccentric spherical particle-in-cell models

Faltas

Saad

2011

Math. Meth. Appl. Sci.

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“…Eringen's micropolar model includes the classical Navier-Stokes equations as a special case, but can cover, both in theory and applications, many more phenomena than the classical model. Physically, the mathematical model underlying micropolar fluids may represent the behavior of polymeric additives, animal blood with rigid cells, lubricants, liquid crystals, dirty oils and solutions of colloidal suspensions [2,4,5]. In practice, the theory requires that one must solve an additional transport equation representing the principle of conservation of local angular momentum, as well as the usual transport equations for the conservation of mass and momentum.…”

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confidence: 99%

Exact solution for the unsteady flow of a semi-infinite micropolar fluid

2011

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The unsteady motion of an incompressible micropolar fluid filling a half-space bounded by a horizontal infinite plate that started to move suddenly is considered. Laplace transform techniques are used. The solution in the Laplace transform domain is obtained by using a direct approach. The inverse Laplace transforms are obtained in an exact manner using the complex inversion formula of the transform together with contour integration techniques. The solution in the case of classical viscous fluids is recovered as a special case of this work when the micropolarity coefficient is assumed to be zero. Numerical computations are carried out and represented graphically.

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“…They gave a particular attention to the factors which affect the fluid slippage at the solid boundary, such as surface roughness, wetability and the presence of gaseous layers, might have on the measured interfacial slip. In recent years there has been an increased interest in using the slip boundary condition for Newtonian fluids [6][7][8][9], and for micropolar and microstreach fluids [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…Eringen [1] studied the steady flow of an incompressible microstretch fluid in circular arteries. Sherief et al [13] obtained Galerkin-type representations and fundamental solutions for the rotational motion of an axisymmetric microstretch fluid flow and deduced a general formula to evaluate the resultant couple on a spherical particle. They also applied their result to solve the problem of slow steady rotation of a rigid sphere in a microstretch fluid flow.…”

Section: Introductionmentioning

confidence: 99%

Fundamental solutions for axi-symmetric translational motion of a microstretch fluid

2012

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The fundamental solution for the axi-symmetric translational motion of a microstretch fluid due to a concentrated point body force is obtained. A general formula for the drag force exerted by the fluid on an axi-symmetric rigid particle translating in it is then deduced. As an application to the obtained drag formula, this paper has discussed the problem of creeping translational motion of a rigid sphere in a microstretch fluid. The slip boundary condition on the surface of the spherical particle is applied. The drag force and the other physical quantities are obtained and represented graphically for various values of the micropolarity and slip parameters.

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Galerkin representations and fundamental solutions for an axisymmetric microstretch fluid flow

Cited by 25 publications

References 24 publications

Stokes flow past an assemblage of slip eccentric spherical particle-in-cell models

Stokes flow past an assemblage of slip eccentric spherical particle-in-cell models

Exact solution for the unsteady flow of a semi-infinite micropolar fluid

Fundamental solutions for axi-symmetric translational motion of a microstretch fluid

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