Oscillatory Stokes flow due to motions of a circular disk parallel to an infinite plane wall

2004 ◽  
Vol 34 (2) ◽  
pp. 77-97 ◽  
Author(s):  
Jeong Ho Chu ◽  
Moon-Uhn Kim
Keyword(s):  
Stokes Flow ◽  
Circular Disk ◽  
Plane Wall ◽  
Infinite Plane

Stokes flow through periodic orifices in a channel

1994 ◽  
Vol 263 ◽  
pp. 207-226 ◽  
Author(s):  
Y. Zeng ◽  
S. Weinbaum
Keyword(s):  
Aspect Ratio ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Plane Wall ◽  
Channel Height ◽  
Infinite Plane ◽  
Electron Microscopic ◽  
Dimensional Solution ◽  
Aspect Ratios ◽  
Flow Through

This paper develops a three-dimensional infinite series solution for the Stokes flow through a parallel walled channel which is obstructed by a thin planar barrier with periodically spaced rectangular orifices of arbitrary aspect ratio B’/d’ and spacing D’. Here B’ is the half-height of the channel and d’ is the half-width of the orifice. The problem is motivated by recent electron microscopic studies of the intercellular channel between vascular endothelial cells which show a thin junction strand barrier with discontinuities or breaks whose spacing and width vary with the tissue. The solution for this flow is constructed as a superposition of Hasimoto's (1958) general solution for the two-dimensional flow through a periodic slit array in an infinite plane wall and a new three-dimensional solution which corrects for the top and bottom boundaries. In contrast to the well-known solutions of Sampson (1891) and Hasimoto (1958) for the flow through zero-thickness orifices of circular or elliptic cross-section or periodic slits in an infinite plane wall, which exhibit characteristic viscous velocity profiles, the present bounded solutions undergo a fascinating change in behaviour as the aspect ratio B’/d’ of the orifice opening is increased. For B’/d’ [Lt ] 1 and (D’ –- d’)/B’ of O(1) or greater, which represents a narrow channel, the velocity has a minimum at the orifice centreline, rises sharply near the orifice edges and then experiences a boundary-layer-like correction over a thickness of O(B’) to satisfy no-slip conditions. For B’/d’ of O(1) the profiles are similar to those in a rectangular duct with a maximum on the centreline, whereas for B’/d’ [Gt ] 1, which describes widely separated channel walls, the solution approaches Hasimoto's solution for the periodic infinite-slit array. In the limit (D’ –- d’)/B’ [Lt ] 1, where the width of the intervening barriers is small compared with the channel height, the solutions exhibit the same behaviour as Lee & Fung's (1969) solution for the flow past a single cylinder. The drag on the zero-thickness barriers in this case is nearly the same as for the cylinder for all aspect ratios.

On the slow motion of a sphere parallel to a nearby plane wall

1967 ◽  
Vol 27 (4) ◽  
pp. 705-724 ◽  
Author(s):  
M. E. O'Neill ◽  
K. Stewartson
Keyword(s):  
Stokes Flow ◽  
Slow Motion ◽  
Plane Wall ◽  
Rigid Sphere ◽  
Infinite Plane ◽  
Direction Parallel ◽  
Outer Solution ◽  
Velocity Gradients ◽  
Leading Term ◽  
Nearest Points

A new method using a matched asymptotic expansions technique is presented for obtaining the Stokes flow solution for a rigid sphere of radius a moving uniformly in a direction parallel to a fixed infinite plane wall when the minimum clearance ea between the sphere and the plane is very much less than a. An ‘inner’ solution is constructed valid for the region in the neighbourhood of the nearest points of the sphere and the plane where the velocity gradients and pressure are large; in this region the leading term of the asymptotic expansion of the solution satisfies the equations of lubrication theory. A matching ‘outer’ solution is constructed which is valid in the remainder of the fluid where velocity gradients are moderate but it is possible to assume that ε = 0. The forces and couples acting on the sphere and the plane are shown to be of the form (α0+α1ε) log ε + β0 + O(ε) where α0, α1 and β0 are constants which have been determined explicitly.

Three-dimensional flow of Jeffrey fluid along an infinite plane wall with periodic suction

Meccanica ◽  
2017 ◽  
Vol 52 (11-12) ◽  
pp. 2705-2714 ◽  
Author(s):  
A. M. Siddiqui ◽  
M. Shoaib ◽  
M. A. Rana
Keyword(s):  
Three Dimensional ◽  
Plane Wall ◽  
Jeffrey Fluid ◽  
Infinite Plane ◽  
Three Dimensional Flow ◽  
Dimensional Flow

The Involution Correspondence in Plane Elastostatics for Regions Bounded by a Circle

1988 ◽  
Vol 55 (3) ◽  
pp. 566-573 ◽  
Author(s):  
T. Honein ◽  
G. Herrmann
Keyword(s):  
Outer Region ◽  
Elastic Field ◽  
Circular Disk ◽  
Infinite Plane ◽  
Infinite Domain ◽  
Circular Boundary ◽  
Inner Region ◽  
Plane Elastostatics

It is shown that the elastic field induced by prescribed displacements or surface tractions acting on a circular disk (inner region) can be expressed in terms of the elastic field induced by the same quantities acting on the circular boundary (hole) of an infinite plane (outer region), and vice versa. It is shown further that this correspondence is an involution. This novel representation permits one to express the elastic field in a disk with either vanishing displacements or tractions along the boundary in terms of the elastic field of an infinite domain, provided all singularities are in the inner region. Similarly, the elastic field in the outer region can be expressed in terms of the elastic field of the infinite domain, provided all singularities reside in the outer region. The expressions so-derived possess simple algebraic character and are universal in the sense of being independent of the applied loads (singularities) in the two problems.

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