Related papers: Leading-order Stokes flows near a corner
When two inclusions with high contrast material properties are located close to each other in a homogeneous medium, stress may become arbitrarily large in the narrow region between them. In this paper, we investigate such stress…
New fundamental solutions for micropolar fluids are derived in explicit form for two- and three-dimensional steady unbounded Stokes and Oseen flows due to a point force and a point couple, including the two-dimensional micropolar Stokeslet,…
We derive new formulas for the fundamental solutions of slow, viscous flow, governed by the Stokes equations, in a half-space. They are simpler than the classical representations obtained by Blake and collaborators, and can be efficiently…
We consider the quasistationary Stokes flow that describes the motion of a two-dimensional fluid body under the influence of surface tension effects in an unbounded, infinite-bottom geometry. We reformulate the problem as a fully nonlinear…
We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire…
Motivated by experimental evidence of violations of the no-slip boundary condition for liquid flow in micron-scale geometries, we propose a simple, complementary experimental technique that has certain advantages over previous studies.…
The two-phase horizontally periodic quasistationary Stokes flow in $\mathbb{R}^2$, describing the motion of two immiscible fluids with equal viscosities that are separated by a sharp interface, which is parameterized as the graph of a…
Single-phase Stokes flow problems with prescribed boundary conditions can be formulated in terms of a boundary regularized integral equation that is completely free of singularities that exist in the traditional formulation. The usual…
We establish pointwise decay estimates for the velocity field of a steady two-dimensional Stokes flow around a rotating body via a new approach rather than analysis adopted in the previous literature. The novelty is to analyze the singular…
This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the…
Trapping and manipulation of small particles underlies many scientific and technological applications. Recently, the precise manipulation of multiple small particles was demonstrated using a Stokes trap that relies only on fluid flow…
The Stokes equation describes the motion of fluids when inertial forces are negligible compared to viscous forces. In this article, we explore the consequence of parity-violating and non-dissipative (i.e. odd) viscosities on Stokes flows in…
A number of new closed-form fundamental solutions for the generalized unsteady Oseen and Stokes flows associated with arbitrary time-dependent translational and rotational motions have been developed. These solutions are decomposed into two…
An efficient, accurate, and flexible numerical method is proposed for the solution of the swimming problem of one or more autophoretic particles in the purely-diffusive limit. The method relies on successive boundary element solutions of…
Slender-body approximations have been successfully used to explain many phenomena in low-Reynolds number fluid mechanics. These approximations typically use a line of singularity solutions to represent the flow. These singularities can be…
A complete analysis is presented for the far-field creeping flow produced by a multipolar force distribution in a fluid confined between two parallel planar walls. We show that at distances larger than several wall separations the flow…
Particles whose shapes couple translation to rotation display a rich array of behaviors as they sediment at low Reynolds number. We introduce a unifying perspective in which the possible dynamical regimes and bifurcations between them can…
In this paper, a mathematical model of two adjacent rigid particles immersed into a viscous incompressible fluid is considered. The main feature of the flow is that the Cauchy stress tensor consisting of the strain tensor and the pressure…
In this work we will study the dynamics of a thin layer of a viscous fluid which is embedded in the interior of another viscous fluid. The resulting flow can be approximated by means of the solutions of a free boundary problem for the…
The velocity and trajectory of particle moving along the corrugated (rough) surface under action of gravity is obtained by meshless Boundary Singularity Method (BSM). This physical situation is found often in biological systems and…