The Huygens principle for flow around an arbitrary body in a viscous incompressible fluid

Wymer, Scott A.; Lakhtakia, Akhlesh; Engel, Renata S.

doi:10.1016/0169-5983(95)00029-1

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…This oscillatory behavior for Qext has been observed previously for spherical scatterers (Wymer et al, 1996) and thus is not an artifact of high Iklb calculations developed as a consequence of using the numerical PMM. The inset plots represent magnifications of the ordinate to show details of Q~xt in the region which shows the transition between the (1/]k]b)-behavior for ]k]b < 1 and the oscillatory behavior observed for Iklb > 5.…”

Section: Extinction Efficiencysupporting

confidence: 80%

“…In previous work, we conceptualized the use of the extinction efficiency -a measure used commonly in scattering research (Bohren and Gilra, 1979;Lakhtakia, 1994; for the distortion of a Stokesian flow by a stationary arbitrary body, and presented numerical results relating to a spherical body . Next, we developed the Huygens principle for flow around a stationary arbitrary body immersed in a viscous incompressible liquid (Wymer et al, 1996). In this paper, we turn our attention to the numerical method known as the point-matching t J method (PMM).…”

Section: Introductionmentioning

confidence: 99%

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Point-matching method for examining time-dependent Stokesian flow around a stationary axisymmetric body

1997

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We recast the time-dependent Stokesian flow about an axisymmetric body as a scattering problem, and solve the resulting boundary value problem using the point-matching method (PMM). The fluid is modeled to be viscous and incompressible. The velocity and pressure fields from the resulting linearized equations are cast as phasors in the frequency domain, and are broken up into incident and scattered components which are expressed in terms of spherical harmonic functions. For the numerical results presented, the incident velocity phasor is assumed to be a transverse plane wave progressing parallel to the symmetry axis of the body, and the PMM is applied to determine the scattered pressure and velocity phasors. 2 3Numerical results are shown for spheroids whose aspect ratios vary between g and 2" Two different boundary condition cases are tackled: pure stick (i.e., no-slip) and pure slip. The extinction efficiency, a measure of the change in energy due to the presence of the scattering body, is also computed.

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Section: Extinction Efficiencysupporting

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Point-matching method for examining time-dependent Stokesian flow around a stationary axisymmetric body

1997

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“…This problem was first solved by Basset [8] and in this circumstance the tangential velocity of the fluid relative to the sphere at a point on its surface is proportional to the tangential stress prevailing at that point. It should be pointed out that similar condition have been used by several authors [9][10][11][12][13][14][15][16][17] to solve exterior and interior flow problems past a surface. Now it is intended to present a solution for flow spheres, one with general boundary condition and another one with shear free condition in viscous fluid flow.…”

Section: Introductionmentioning

confidence: 99%

On the Motion Past a Slip-Stick Sphere and a Shear Free Sphere in a Viscous Fluid

Chowdhury,

Sen,

Chowdhury

et al. 2024

EAS

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The theoretical development of the complex fluid flows such as more than one obstacle with different shapes have great interest for scientists to understand flow phenomena and verify the model or approximate solution. The complex physical properties due to a uniform streaming motion past two fixed spheres is investigated having one with shear stress and another being shear stress-free. This study concerns analytical technique of a steady incompressible viscous fluid past to two fixed spheres. The Gegenbaur function and associated Legendre polynomials is used to derive the solution that simplify the process of the theoretical calculations. The mathematical expression for the flow fields are obtained in terms of stream functions by Gegenbaur function and associated Legendre polynomials. The physical properties of interest such as the Stokes stream function, the stress and its drag are calculated. It is understandable that for the uniform streaming motion around a sphere with the stress and its drag are affected owing to the presence of another stress-free are analyzed. The present result can be considered as a generalized by making other established results as a corollary of this solution. This theoretical study helps to the numerical or computational work for the verification of their approximated results of interest.

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Palaniappan¹,

Daripa²

2002

Z angew Math Phys

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Steady two-dimensional creeping flows induced by line singularities in the presence of an infinitely long circular cylinder with stick-slip boundary conditions are examined. The singularities considered here include a rotlet, a potential source and a stokeslet located outside a cylinder and lying in a plane containing the cylinder axis. The general exterior boundary value problem is formulated and solved in terms of a stream function by making use of the Fourier expansion method. The solutions for various singularity driven flows in the presence of a cylinder are derived from the general results. The stream function representation of the solutions involves a definite integral whose evaluation depends on a non-dimensional slip parameter λ 1 . For extremal values, λ 1 = 0 and λ 1 = 1 , of the slip parameter our results reduce to solutions of boundary value problems with stick (no-slip) and perfect slip conditions, respectively.The slip parameter influences the flow patterns significantly. The plots of streamlines in each case show interesting flow patterns. In particular, in the case of a single rotlet/stokeslet (with axis along y -direction) flows, eddies are observed for various values of λ 1 . The flow fields for a pair of singularities located on either side of the cylinder are also presented. In these flows, eddies of different sizes and shapes exist for various values of λ 1 and the singularity locations. Plots of the fluid velocity on the surface show locations of the stagnation points on the surface of the cylinder and their dependencies on λ 1 and singularity locations.

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The Huygens principle for flow around an arbitrary body in a viscous incompressible fluid

Cited by 7 publications

References 15 publications

Point-matching method for examining time-dependent Stokesian flow around a stationary axisymmetric body

Point-matching method for examining time-dependent Stokesian flow around a stationary axisymmetric body

On the Motion Past a Slip-Stick Sphere and a Shear Free Sphere in a Viscous Fluid

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