Abstract
AbstractBoundary integral methods are highly suited for problems with complicated geometries, but require special quadrature methods to accurately compute the singular and nearly singular layer potentials that appear in them. This article presents a boundary integral method that can be used to study the motion of rigid particles in three‐dimensional periodic Stokes flow with confining walls. A centerpiece of our method is the highly accurate special quadrature method, which is based on a combination of upsampled quadrature and quadrature by expansion, accelerated using a precomputation scheme. The method is demonstrated for rodlike and spheroidal particles, with the confining geometry given by a pipe or a pair of flat walls. A parameter selection strategy for the special quadrature method is presented and tested. Periodic interactions are computed using the spectral Ewald fast summation method, which allows our method to run in time for n grid points in the primary cell, assuming the number of geometrical objects grows while the grid point concentration is kept fixed.
Highlights
Microhydrodynamics is the study of fluid flow at low Reynolds numbers, known as Stokes flow or creeping flow
We present a boundary integral method based on the Stokes double layer potential, which can be used to solve the mobility and resistance problems for a system of rigid particles in incompressible three-dimensional Stokes flow, possibly confined within a container geometry
Our quadrature by expansion (QBX) implementation is based on the work by af Klinteberg and Tornberg,[37] which we have extended to rodlike particles, plane walls and pipes
Summary
Microhydrodynamics is the study of fluid flow at low Reynolds numbers, known as Stokes flow or creeping flow. Applications are found in biology, for example in the swimming of microorganisms[1] and in blood flow,[2] as well as in the field of microfluidics, which concerns the design and construction of miniaturized fluid devices.[3] Suspensions of rigid particles in Stokes flow are important both in various applications and in fundamental fluid mechanics.[4,5,6,7] In this article, we describe a boundary integral method that can be used to study the motion of rigid particles of different shapes in Stokes flow. The particle suspension may be confined in a container geometry, such as a pipe or a pair of flat walls. The flow in the fluid domain (i.e., within the container but outside the particles) is governed by the Stokes equations, which for an incompressible Newtonian fluid take the form
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