Integral equation solution for the flow due to the motion of a body of arbitrary shape near a plane interface at small Reynolds number
type: Item
instance of: scholarly article
title: Integral equation solution for the flow due to the motion of a body of arbitrary shape near a plane interface at small Reynolds number
zbMATH Open document ID: 0601.76025
DOI: 10.1016/0168-9274(86)90018-8
author: H. Power
author: Reinaldo C. Garcia
author: Guillermo Miranda
published in: Applied Numerical Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The problem of determining the slow viscous flow due to an arbitrary motion of a particle of arbitrary shape near a plane interface is formulated exactly as a system of three linear Fredholm integral equations of the first kind, which is shown to have a unique solution. A numerical method based on these integral equations is proposed. In order to test this method valid for arbitrary particle shape, the problem of arbitrary motion of a sphere is worked out and compared with the available analytical solution. This technique can be also extended to low Reynolds number flow due to the motion of a finite number of bodies of arbitrary shape near a plane interface. As an example the case of two equal sized spheres moving parallel and perpendicular to the interface is solved in the limiting case of infinite viscosity ratio.
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 3970302
zbMATH Keywords: slow viscous flow
zbMATH Keywords: motion of a particle
zbMATH Keywords: plane interface
zbMATH Keywords: linear Fredholm integral equations of the first kind
zbMATH Keywords: unique solution
zbMATH Keywords: analytical solution
zbMATH Keywords: equal sized spheres
zbMATH Keywords: limiting case of infinite viscosity ratio
MaRDI profile type: Publication
full work available at URL: 0168-9274(86)90018-8
OpenAlex ID: W2038725561
cites work: Action of a force near the planar surface between two semi-infinite immiscible liquids at very low Reynolds numbers
cites work: Action of a force near the planar surface between semi-infinite immiscible liquids at very low Reynolds numbers: Addendum
cites work: On the motion of a slender body near an interface between two immiscible liquids at very low Reynolds numbers
cites work: Resistance and stability of a line of particles moving near a wall
cites work: Q5549292
cites work: Q5733282
cites work: Motion of a sphere in the presence of a plane interface. Part 1. An approximate solution by generalization of the method of Lorentz
cites work: Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar co-ordinates
cites work: Particle motion in Stokes flow near a plane fluid-fluid interface. Part 1. Slender body in a quiescent fluid
cites work: Stokes flow past a particle of arbitrary shape: a numerical method of solution
description: scientific article; zbMATH DE number 3970302