A theorem for a shear stress-free plane boundary in Stokes flow

2011 ◽  
Vol 38 (7) ◽  
pp. 529-531 ◽  
Author(s):  
N. Akhtar ◽  
S.K. Sen
Keyword(s):  
Shear Stress ◽  
Stokes Flow ◽  
Plane Boundary ◽  
Free Plane

Stokes flow due to fundamental singularities before a plane boundary

2004 ◽  
Vol 25 (7) ◽  
pp. 799-805 ◽  
Author(s):  
N. Aktar ◽  
F. Rahman ◽  
S. K. Sen
Keyword(s):  
Stokes Flow ◽  
Plane Boundary

scholarly journals Converging three-dimensional Stokes flow of two fluids in a T-type bifurcation

1994 ◽  
Vol 270 ◽  
pp. 51-72 ◽  
Author(s):  
Joseph Ong ◽  
Giora Enden ◽  
Aleksander S. Popel
Keyword(s):  
Finite Element Method ◽  
Shear Stress ◽  
Stokes Flow ◽  
Flow Problem ◽  
Viscosity Ratio ◽  
Three Dimensional ◽  
Side Branch ◽  
The Finite Element Method ◽  
Two Fluids ◽  
Flow Through

Studies of three-dimensional Stokes flow of two Newtonian fluids that converge in a T-type bifurcation have important applications in polymer coextrusion, blood flow through the venous microcirculation, and other problems of science and technology. This flow problem is simulated numerically by means of the finite element method, and the solution demonstrates that the viscosity ratio between the two fluids critically affects flow behaviour. For the parameters investigated, we find that as the viscosity ratio between the side branch and the main branch increases, the interface between the merging fluids bulges away from the side branch. The viscosity ratio also affects the velocity distribution: at the outlet branch, the largest radial gradients of axial velocity appear in the less-viscous fluid. The distribution of wall shear stress is non-axisymmetric in the outlet branch and may be discontinuous at the interface between the fluids.

The velocity of a circular disk moving edgewise in quasi-steady Stokes flow toward a plane boundary

1999 ◽  
Vol 11 (9) ◽  
pp. 2463-2470 ◽  
Author(s):  
Jeffrey F. Trahan ◽  
R. G. Hussey ◽  
R. P. Roger
Keyword(s):  
Stokes Flow ◽  
Circular Disk ◽  
Plane Boundary

Modelling the motion of particles around choanoflagellates

2003 ◽  
Vol 475 ◽  
pp. 333-355 ◽  
Author(s):  
B. A. A. ORME ◽  
J. R. BLAKE ◽  
S. R. OTTO
Keyword(s):  
Cell Body ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Plane Boundary ◽  
Good Qualitative Agreement ◽  
Beat Pattern ◽  
A Cell ◽  
Passive Tracers ◽  
Main Components ◽  
Particle Paths

The three-dimensional particle paths due to a helical beat pattern of the flagellum of a sessile choanoflagellate, Salpingoeca Amphoridium (SA), are modelled and compared to the experimental observations of Pettitt (2001). The organism’s main components are a flagellum and a cell body which are situated above a substrate such that the interaction between these entities is crucial in determining the fluid flow around the choanoflagellate. This flow of fluid can be characterized as Stokes flow and a flow field analogous to one created by the flagellum is generated by a distribution of stokeslets and dipoles along a helical curve.The model describing the flow considers interactions between a slender flagellum, an infinite flat plane (modelling the substrate) and a sphere (modelling the cell body). The use of image systems appropriate to Green’s functions for a sphere and plane boundary are described following the method of Higdon (1979a). The computations predict particle paths representing passive tracers from experiments and their motion illustrates overall flow patterns. Figures are presented comparing recorded experimental data with numerically generated results for a number of particle paths. The principal results show good qualitative agreement with the main characteristics of flows observed in the experimental study of Pettitt (2001).

Steady viscous flow near a stationary contact line

1988 ◽  
Vol 187 ◽  
pp. 35-43 ◽  
Author(s):  
Ian Proudman ◽  
Mir Asadullah
Keyword(s):  
Contact Line ◽  
Stokes Flow ◽  
Power Supply ◽  
Plane Boundary ◽  
Immiscible Liquids ◽  
Phase Theory ◽  
Viscous Incompressible Flow ◽  
Global Power ◽  
Complex Eigenvalues ◽  
Stationary Contact

The paper presents the asymptotic solution, near a stationary contact line at a plane boundary, for steady viscous incompressible flow of two immiscible liquids. The eigenvalues which determine this Stokes flow are determined by the contact angle α of the more viscous liquid and the ratio μ of the two viscosities. The dominant eigenvalues are found for all values of α and μ. As μ → 0 the results agree with those of Moffatt's (1964) one-phase theory for the case μ = 0 only when α > 81°. For α < 81° the two sets of results are qualitatively different. In particular, the eddy structure corresponding to complex eigenvalues occurs only in the α-range (34°, 81°). As μ increases from 0 to 1, this range steadily decreases to zero, which is located at 60°. The transport of energy across the liquid interface is almost always from the obtuse-angled sector to the acute-angled sector, irrespective of α, μ, and the location of the global power supply.

Modeling of Stokes Flow in Axisymmetrical Fields Due to Various Boundary Velocity Distributions

Volume 1 ◽  
2004 ◽  
Author(s):  
Mohamed A. Gadalla
Keyword(s):  
Exact Solution ◽  
Stokes Flow ◽  
Hankel Transform ◽  
Incompressible Fluids ◽  
Velocity Variation ◽  
Plane Boundary ◽  
Inverse Transform ◽  
Discontinuous Boundary ◽  
Boundary Velocity ◽  
Velocity Variations

This paper aims at investigating the effect of various boundary velocity distributions on the flow field in Stokes flow of incompressible fluids flow with axisymmetry. It was reported in literature that if the velocity variation at a plane boundary is suitably prescribed, the whole field of Stokes flow in a half-plane can be identified immediately by the artifice of Laplace transform. Similarly, it can be shown that if the boundary velocity distribution is represented for an axisymmetrical half-space, the whole field of Stokes flow can be described by the use of Hankel transform. With suitable given boundary velocity variations, the exact solution can be obtained through the integration of the resulting inverse transform. In this paper several realistic, continuous and discontinuous boundary velocity variations are analyzed following an intuitive derivative of the exact solution in cylindrical coordinates. The variations of the velocities and the pressure in the fluid are obtained for several examples of particular velocity variations at the plane boundary.

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