Related papers: Extrapolation theory for Stokes flow past a deform…
There are numerous ways to control objects in the Stokes regime, with microscale examples ranging from the use of optical tweezers to the application of external magnetic fields. In contrast, there are relatively few explorations of…
Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical…
We consider Stokes' conjecture concerning the shape of the extremal two-dimensional water wave. By new geometric methods including a nonlinear frequency formula, we prove Stokes' conjecture in the original variables. Our results do not rely…
Impact of single particle onto a rigid substrate leads to its deformation and fragmentation. The flow associated with the particle spreading on a solid substrate after impact is extremely complicated. In this theoretical study a simplified…
Two dimensional flows on fixed smooth surfaces have been studied in the point of view of vorticity dynamics. Firstly, the related deformation theory including kinematics and kinetics is developed. Secondly, some primary relations in…
We investigate the dynamics of several slender rigid bodies moving in a flow driven by the three-dimensional steady Stokes system in presence of a smooth background flow. More precisely we consider the limit where the thickness of these…
A new highly efficient method is developed for computation of traveling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularites above the free…
Swimming fish and flying insects use the flapping of fins and wings to generate thrust. In contrast, microscopic organisms typically deform their appendages in a wavelike fashion. Since a flapping motion with two degrees of freedom is able,…
The paper reports on the quasi-static steady flow of a dry liquid foam around a fixed spherical bead, few times larger than the typical bubble size. The force exerted on the bead is recorded with a precision and a time resolution large…
Several intrinsic topological ways to encode connections on vector bundles on smooth complex algebraic curves will be described. In particular the notion of {\em Stokes decompositions} will be formalised, as a convenient intermediate…
Rigid particles in a Stokesian fluid can physically not overlap, as a thin layer of fluid always separates a particle pair, exerting increasingly strong repulsive forces on the bodies for decreasing separations. Numerically, resolving these…
We derive an exact solution for Stokes flow in an in a channel with permeable walls. We assume that at the channel walls, the normal component of the fluid velocity is described by Darcy's law and the tangential component of the fluid…
We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface $\Gamma \subset \mathbb{R}^3$ without boundary. This formulation leads to a coupled system of two second order scalar surface partial…
In this dissertation, we seek to expand the scope of work done by Lustri and Chapman (2013) in modelling 3D flow past a point source, in order to account for more general flows, where the strength of such a source, $\delta$, is now $O(1)$.…
Particulate Stokesian flows describe the hydrodynamics of rigid or deformable particles in Stokes flows. Due to highly nonlinear fluid-structure interaction dynamics, moving interfaces, and multiple scales, numerical simulations of such…
The Reynolds equation from lubrication theory and the Stokes equations for zero Reynolds number flows are distinct models for an incompressible fluid with negligible inertia. Here we investigate the sensitivity of the Reynolds equation to…
The vorticity plays an important role in aerodynamics and rotational flow. Usually, they are studied with modified Navier-Stokes equation. This research will deduce the motion equation of vorticity from Navier-Stokes equation. To this…
An inhomogeneous electric field is used to study the deflection of a supersonic beam of water molecules. The deflection profiles show strong broadening accompanied by a small net displacement towards higher electric fields. The profiles are…
Despite the fact that the calculations of drag coefficient and pressure distribution for airfoils can be completed by using Navier-Stoke's equation with help of experimental parameters and advanced computer programming, a simple theoretical…
We study the turbulent flow of the density-stratified fluid around a small translating (either passively or self-propelled) particle. It was found recently [A. M. Ardekani and R. Stocker, Phys. Rev. Lett. vol. 105, 084502 (2010)] that…