The jump condition at a possibly non-material interface for geometricallynecessary dislocation density in field dislocation mechanics (FDM) and its averaged approximation, phenomenological mesoscopic FDM (PMFDM), is derived. In the context of grain boundaries, the condition implies a tensorial constraint on all five grain boundary parameters, slip transmission at the boundary, possible grain bo...

We establish the well-posedness of the infinite Prandtl number model for convection with temperature-dependent viscosity, free-slip boundary condition and zero horizontal fluxes.

Abstract—This paper presents a study on the effect of second-order slip and jump on forced convection through a long isothermally heated or cooled planar microchannel. The fully developed solutions of thermal flow fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and Smoluchowski jump boundary conditions. Results reveal that the second-order term in the Karn...

Dynamic force measurements have been made between an oil drop and a silica particle in surfactant and sucrose solutions with viscosities that range up to 50 times that of water. These conditions provide variations in the shear rate and the relative time scales of droplet deformation and hydrodynamic drainage in a soft matter system. The results obtained indicate that soft deformable boundaries ...

This paper presents a unified theory of phoretic phenomena in single-component fluids. Simple formulas are given for the phoretic velocities of small inert force-free non-Brownian particles migrating through otherwise quiescent single-component gases and liquids and animated by a gradient in the fluid's temperature (thermophoresis), pressure (barophoresis), density (pycnophoresis), or any combi...

A polynomial expansion procedure and an analytical discrete-ordinates method are used to evaluate the viscous-slip coefficient, the thermal-slip coefficient, and the temperature-jump coefficient as defined by a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions and the Cercignani–Lampis boundary condition. © 2003 American Institute of Physics. @DOI: 10.1063/1.15...

for linear partial differential equations in cylinders, which was applied to solve some nonlinear problems. In this paper the numerical simulation of the steady incompressible viscous flow in a no-slip channel is considered. A sequence The purpose of this paper is to design nonlocal artificial of approximate nonlocal artificial boundary conditions on a given boundary conditions for steady incom...

In this article we consider circularly symmetric incompressible viscous flow in a disk. The boundary condition is no-slip with respect to a 4 prescribed time-dependent rotation of the boundary about the center of the disk. We prove that, if the prescribed angular velocity of the boundary 5 has finite total variation, then the Navier–Stokes solutions converge strongly in L2 to the corresponding ...