Journal ArticleDOI
Two-dimensional Stokes flows with cylinders and line singularities
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In contrast to the Stokes paradox for flow past an isolated cylinder, if either type of singularity, with suitably chosen strength and location, is present, there can exist a flow which is uniform at infinity as discussed by the authors.Abstract:
A study is made of Stokes flows in which a line rotlet or stokeslet is in the presence of a circular cylinder in a viscous fluid. In contrast to the Stokes Paradox for flow past an isolated cylinder, it is shown that if either type of singularity, with suitably chosen strength and location, is present, there can exist a flow which is uniform at infinity. A similar phenomenon can occur when two equal cylinders rotate with equal and opposite angular velocities, and the flow pattern is then such that there is a closed streamline enclosing both cylinders.read more
Citations
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Journal ArticleDOI
Stokes flow in a mixer with changing geometry
Matthew D. Finn,Stephen M. Cox +1 more
TL;DR: In this article, a slow-flow mixing device that mimics a natural mixing technique is described, and analytical, numerical and experimental results are presented for the translating, rotating mixer, which illustrate its mixing effectiveness.
Journal ArticleDOI
Stokes flow past slits and holes
TL;DR: In this article, the Stokes flow behavior for such a phenomenon in a number of different geometries, with particular interest in the singular solutions generated when the width of the slit, or size of the hole, is small.
Journal ArticleDOI
Some Stokes flows exterior to a spherical boundary
R. Shail,S. H. Onslow +1 more
TL;DR: In this article, the rotlet and Stokeslet solutions were used to solve asymmetric singularity-driven flows of a fluid exterior to a rigid spherical surface. But the Stokeslets were not used to calculate the forces and couples acting on the sphere and the rotlets were only used to compute an approximation to the drag force experienced by a particle which sediments in the fluid in a direction perpendicular to a sphere radius.
Journal ArticleDOI
No-slip images of certain line singularities in a circular cylinder
A. Avudainayagam,B. Jothiram +1 more
TL;DR: In this paper, it was shown that the far field is either a uniform flow or an eccentric rotational flow, and that the uniform flow past a cylinder or a eccentric flow around a cylinder becomes a well-posed problem if a singularity of a suitably chosen strength is present in the flow field.
References
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Journal ArticleDOI
Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder
Ian Proudman,J. R. A. Pearson +1 more
TL;DR: In this paper, the Navier-Stokes equation is replaced by a set of differential equations for the coefficients ψn and Ψn, but only one set of physical boundary conditions is applicable to each expansion (the no-slip conditions for the Stokes expansion, and the uniform-stream condition for the Oseen expansion).
Journal ArticleDOI
The Rotation of Two Circular Cylinders in a Viscous Fluid
TL;DR: In this paper, the authors employed the solution of the equation ∇4 ψ = 0 in bipolar co-ordinates defined by α + iβ = log x + i ( y + a )/x + i( y - a ) (1) to discuss the problem of the elastic equilibrium of a plate bounded by any two nonconcentric circles.
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Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder
Ian Proudman,J. R. A. Pearson +1 more