Related papers: An integral equation method for closely interactin…
Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method…
The presence of surfactants alters the dynamics of viscous drops immersed in an ambient viscous fluid. This is specifically true at small scales, such as in applications of droplet based microfluidics, where the interface dynamics become of…
We present a highly accurate numerical method based on a boundary integral formulation and the leaky dielectric model to study the dynamics of surfactant-covered drops in the presence of an applied electric field. The method can simulate…
A fast and spectrally accurate Ewald summation method for the evaluation of stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow is presented. This work extends the previously developed Spectral Ewald method for…
Boundary integral numerical methods are among the most accurate methods for interfacial Stokes flow, and are widely applied. They have the advantage that only the boundary of the domain must be discretized, which reduces the number of…
Boundary 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 paper presents a…
A weakly conducting liquid droplet immersed in another leaky dielectric liquid can exhibit rich dynamical behaviors under the effect of an applied electric field. Depending on material properties and field strength, the nonlinear coupling…
Two-dimensional Stokes flow through a periodic channel is considered. The channel walls need only be Lipschitz continuous, in other words they are allowed to have corners. Boundary integral methods are an attractive tool for numerically…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
An accelerated boundary integral method for Stokes flow of a suspension of deformable particles is presented for an arbitrary domain and implemented for the important case of a planar slit geometry. The computational complexity of the…
We introduce a numerical method based on an integral equation formulation for simulating drops in viscous fluids in the plane. It builds upon the method introduced by Kropinski in 2001, but improves on it by adding an interpolatory…
Stokes flows with near-touching rigid particles induce near-singular lubrication forces under relative motion, making their accurate numerical treatment challenging. With the aim of controlling the accuracy with a computationally cheap…
We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…
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…
Boundary integral methods are advantageous when simulating viscous flow around rigid particles, due to the reduction in number of unknowns and straightforward handling of the geometry. In this work we present a fast and accurate framework…
A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method is based on a Dirichlet-Neumann type splitting of the interface conditions…
We present a numerical method for computing the single layer (Stokeslet) and double layer (stresslet) integrals in Stokes flow. The method applies to smooth, closed surfaces in three dimensions, and achieves high accuracy both on and near…
We present an accurate and efficient boundary integral (BI) method for simulating the deformation of drops and bubbles in Stokes flow with soluble surfactant. Soluble surfactant advects and diffuses in bulk fluids while adsorbing and…
We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…
We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…