We study the Stokes problems in a bounded planar domain Ω with a friction type boundary condition that switches between a slip and no-slip stage. Our main goal is to determine under which conditions concerning smoothness of Ω, solutions to the Stokes system with the slip boundary conditions depend continuously on variations of Ω. Having this result at our disposal, we easily prove the existence...

As an attempt to take into account the mechanical role of oxide films at liquid surface melted or metal flows, a model is proposed based on Boussinesq-Scriven law corrected by non-Newtonian behavior. A characterisation device developed annular open-channel viscometer positioned in chemical reactor and pervaded uniform static magnetic field. The makes it possible monitor oxidation process liquid...

High-frequency radar observations of surface current at 100 m resolution are used to stochastically determine the vorticity variability in the boundary layer between the Florida Current and the Florida coast. Using the empirical data, several formulations of the stochastic boundary condition (SBC) are then developed and evaluated for the parameterization of sub-grid scale variability along the ...

A boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. The present approach is an improvement to the conventional IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately satisfied. As a result, there is flow penetration to the solid boundary. Another drawback of conventional IB-LBM is the use of Dirac delt...

This communication is concerned with the nonlinear flows of an Oldroyd 8-constant fluid when the no-slip condition is not valid. Due to slip effects in terms of shear stress, the arising slip conditions are nonlinear. The resulting mathematical problems involves nonlinear differential equations and nonlinear boundary conditions. To the best of my knowledge, no such analysis for the flows of an ...

Dynamic forces between a 50 microm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accou...

We investigate how the choice of either no-slip or stress-free boundary conditions affects numerical models of rapidly rotating flow in Earth's core by computing solutions of the weakly-viscous magnetostrophic equations within a spherical shell, driven by a prescribed body force. For non-axisymmetric solutions, we show that models with either choice of boundary condition have thin boundary laye...

The aim of the present work is to analyze the accuracy and to extend the capability of lattice Boltzmann method in slip EOF; a phenomenon which was previously studied by molecular dynamics and less considered by LBM. At the present work, a numerical experiment on boundary conditions of slip velocity is performed and the proportionality of slip with shear stress in electroosmotic pump is proved....

this paper addresses the combined effects of couple stresses, thermal radiation, viscous dissipation and slip condition on a free convective flow of a couple stress fluid induced by a vertical stretching sheet. the cogley- vincenti-gilles equilibrium model is employed to include the effects of thermal radiation in the study. the governing boundary layer equations are transformed into a system o...

Incompressible two dimensional lattice Boltzmann method (LBM) is adopted to simulate flow inside a pipe commonly called Poiseuille flow. Instead of D2Q9 lattice Boltzmann model, we used an incompressible two-dimensional model, D2Q9i to simulate the flow conditions. At the inlet, velocity boundary condition, while at outlet, pressure boundary condition and at the surfaces, no slip boundary condi...