Two-Dimensional Slow Stagnation Flow near a Slit

Ko, Hyung–Jong; Jeong, Jae–Tack

doi:10.1143/jpsj.63.3288

Cited by 4 publications

(12 citation statements)

References 6 publications

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“…Smith (1987) finds analytical solutions for a uniform shear flow in the region above a wall with a gap (with no flow far beneath the wall) with a view to understanding how the effects of flow along the wall can be transmitted across the gap. Ko & Jeong (1994) find solutions in the same geometry but driven by a stagnation point flow in the region above the wall (again with the assumption that there is no flow far beneath it). Ko and Jeong also allow for a possible pressure difference between the two sides of the wall.…”

Section: Introductionmentioning

confidence: 78%

“…When there is no central plate, the streamlines pass downwards through the single gap as in fig. 5a of the paper by Ko & Jeong (1994). When the central plate is introduced, but is small in length, small (Moffatt-type) recirculating eddies are found to form underneath it as shown in figure 6.…”

Section: Stagnation Flow Past a Wall With Two Gapsmentioning

confidence: 94%

“…After some algebraic manipulation, it can be shown explicitly (details are omitted here but can be found in Samson (2010)) that the solution just derived is exactly the same as that found by Smith (1987) using transform methods. Ko & Jeong (1994) studied the problem of stagnation point flow in exactly the same geometry as Smith (1987). Although their work appeared later, Ko and Jeong do not seem to be aware of Smith's paper and adopt a different approach to him.…”

Section: Shear Flow Past a Wall With A Gapmentioning

confidence: 99%

“…First, we fix the strength of the stagnation point flow and the viscosity by setting k = 1 and m = 1, and vary the pressure difference across the wall. Following Ko & Jeong (1994), we define the number (10.12) When N is positive, the pressure gradient promotes flow downwards through the gap; when N = 0 the flow is driven by the stagnation point flow only; finally, when N is negative, the pressure gradient promotes flow upwards through the gap. First, we set N = 1.…”

Section: Stagnation Flow Past a Wall With Two Gapsmentioning

confidence: 99%

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Stokes flows past gaps in a wall

Crowdy

Samson

2010

Proc. R. Soc. A.

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This paper presents a conformal mapping approach to the study of planar Stokes flows near a wall with either one or two gaps. The technique reproduces, in a unified fashion, analytical solutions for various Stokes flows past a single gap in a wall found by previous authors using different methods. These include purely pressure-driven flows, shear flows and stagnation point flows near a gap in a wall. It is then shown how the conformal mapping method can be generalized to find new analytical solutions for the analogous flows when there are two gaps in the wall. Features of the new two-gap solutions are studied in detail.

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Section: Introductionmentioning

confidence: 78%

Section: Stagnation Flow Past a Wall With Two Gapsmentioning

confidence: 94%

Section: Shear Flow Past a Wall With A Gapmentioning

confidence: 99%

Section: Stagnation Flow Past a Wall With Two Gapsmentioning

confidence: 99%

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Stokes flows past gaps in a wall

Crowdy

Samson

2010

Proc. R. Soc. A.

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“…Unbounded two-dimensional shear flow over a wall with a gap was studied analytically by Smith (1987). In addition, Ko & Jeong (1994) found a solution in the same geometry but driven by a stagnation point flow. More recently, Crowdy & Samson (2010) extended the solutions using complex variable techniques to flow past a wall with two gaps.…”

Section: Introductionmentioning

confidence: 99%

Low-Reynolds-number flow through two-dimensional shunts

et al. 2013

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Motivated by numerous biological and industrial applications relating to bypasses, mixing and leakage, we consider low-Reynolds-number flow through a shunt between two channels. An analytical solution for the streamfunction is found by matching biorthogonal expansions of Papkovich-Fadle eigenfunctions in rectangular subregions.The general solution can be adapted to model a variety of interesting problems of flow through two-dimensional shunts by imposing different inlet and outlet flux distributions. We present several such flow profiles but the majority of results relate to the particular problem of a side-to-side anastomosis in the small intestine. We consider different flux fractions through the shunt with particular emphasis on the pressure and shear stress distributions, which are important factors in estimating health risks pertaining to this surgical procedure.

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Hydrodynamic bound states of a low-Reynolds-number swimmer near a gap in a wall

Crowdy

Samson

2010

J. Fluid Mech.

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The motion of an organism swimming at low Reynolds number near an infinite straight wall with a finite-length gap is studied theoretically within the framework of a two-dimensional model. The swimmer is modelled as a point singularity of the Stokes equations dependent on a single real parameter. A dynamical system governing the position and orientation of the model swimmer is derived in analytical form. The dynamical system is studied in detail and a bifurcation analysis performed. The analysis reveals,inter alia, the presence of stable equilibrium points in the gap region as well as Hopf bifurcations to periodic bound states. The reduced-model system also exhibits a global gluing bifurcation in which two symmetric periodic orbits merge at a saddle point into symmetric ‘figure-of-eight’ bound states having more complex spatiotemporal structure. The additional effect of a background shear is also studied and is found to introduce new types of bound state. The analysis allows us to make theoretical predictions as to the possible behaviour of a low-Reynolds-number swimmer near a gap in a wall. It offers insights into the use of gaps or orifices as possible control devices for such swimmers in confined environments.

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Two-Dimensional Slow Stagnation Flow near a Slit

Cited by 4 publications

References 6 publications

Stokes flows past gaps in a wall

Stokes flows past gaps in a wall

Low-Reynolds-number flow through two-dimensional shunts

Hydrodynamic bound states of a low-Reynolds-number swimmer near a gap in a wall

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