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In this article, the Green function for the Stokes flow in the interior, exterior, and annular regions bounded by cylindrical walls is derived as a function of the pole position and expressed invariantly both at the field and pole points.…
Singular solutions of the Stokes equations play important roles in a variety of fluid dynamics problems. They allow the calculation of exact flows, are the basis of the boundary integral methods used in numerical computations, and can be…
We study the steady state motion of incompressible and viscous fluid flow in a rotating reference frame where vortices may take place. An approximated analytic solution of the Stokes flow problem is proposed for situations where the…
Since their development in 2001, regularised stokeslets have become a popular numerical tool for low-Reynolds number flows since the replacement of a point force by a smoothed blob overcomes many computational difficulties associated with…
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…
The method of regularized Stokeslets, based on the divergence-free exact solution to the equations of highly viscous flow due to a spatially-smoothed concentrated force, is widely employed in biological fluid mechanics. Many problems of…
The method of regularised stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard…
We solve the Stokes equations for the flow around two parallel translating and rotating cylinders using tools from complex analysis and conformal mapping. By considering cylinders of arbitrary size and separation, we generalise the…
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…
Fluid and solute transfer in X-junctions between straight channels is shown to depend critically on the junction angle in the Stokes flow regime. Experimentally, water and a water-dye solution are injected at equal flow rates in two facing…
In this paper, we consider a stationary, constant viscosity, incompressible Stokes flow with singular forces along one or several interfaces. Assuming only the jumps of the pressure are present along the interface, we develop a new…
A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving $p$-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper…
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 unsteady Stokes system in the half-space with zero initial data and nonzero, space-time localized boundary data. We show that there exist boundary influxes for which the induced flow exhibits flow reversal, in the sense that…
New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from…
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…
Non-linear effects of the Navier-Stokes equations disappear under the Stokes regime of Newtonian fluid flows disallowing the fluid flow rectification. Here we show mathematically and experimentally that passive flow rectification of…
We investigate theoretically on the basis of the steady Stokes equations for a viscous incompressible fluid the flow induced by a Stokeslet located on the centre axis of two coaxially positioned rigid disks. The Stokeslet is directed along…
T. Borrvall and J. Petersson [Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107] developed the first model for topology optimization of fluids in Stokes flow. They…
For many biological systems that involve elastic structures immersed in fluid, small length scales mean that inertial effects are also small, and the fluid obeys the Stokes equations. One way to solve the model equations representing such…