Extinction cross section of an arbitrary body in a viscous incompressible fluid

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

doi:10.1103/physreve.52.1857

Cited by 7 publications

(4 citation statements)

References 9 publications

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“…The particular flow studied here satisfies the time-dependent Stokes equation, the time-dependent nature of the flow being handled by assuming a harmonic time-dependence and continuing the solution in frequency space. This is in consonance with our continuing efforts to apply electromagnetic and acoustic scattering techniques to fluid flow problems (Wymer et al, 1995).…”

Section: Introductionsupporting

confidence: 69%

“…The flow studied here satisfies the time-dependent Stokes equation. Assuming that the fluid is viscous and incompressible, and ignoring the convective acceleration, we obtain the linearized equations of the Stokesian flow as (Wymer et al, 1995) Ot:( r, t)…”

Section: Phasor Representation Of Stokesian Flowmentioning

confidence: 99%

“…This incident flow is modified in the region V by the addition of the scattered velocity phasor when the scattering body is immersed in the flow. Thus, the developments of the previous section are ready for setting up scattering problems of the kind attacked by Felderhof and Jones (1986) and Wymer et al (1995).…”

Section: The Scattered Flowmentioning

confidence: 99%

See 2 more Smart Citations

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

Wymer¹,

Lakhtakia²,

Engel³

1996

Fluid Dyn. Res.

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The consequences of immersing a body in a Stokesian flow can be studied in the language employed in scattering research. After implementing the description of Stokesian flow in terms of velocity and pressure phasors, we formulate mathematical expressions delineating the Huygens principle for both phasors. Application is then made to scattering problems with special emphasis on impenetrable bodies.

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Section: Introductionsupporting

confidence: 69%

Section: Phasor Representation Of Stokesian Flowmentioning

confidence: 99%

See 1 more Smart Citation

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

Wymer¹,

Lakhtakia²,

Engel³

1996

Fluid Dyn. Res.

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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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Extinction cross section of an arbitrary body in a viscous incompressible fluid

Cited by 7 publications

References 9 publications

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

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

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

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