We consider the free fall of a sphere above a wall in a viscous incompressible fluid. Weinvestigate the influence of boundary conditions on the finite-time occurrence of contactbetween the sphere and the wall. We prove that slip boundary conditions enable tocircumvent the ”no-collision” paradox associated with no-slip boundary conditions. Wealso examine the case of mixed bou...

The general form of Maxwell’s velocity slip boundary condition for rarefied gas flows depends on both the geometry of the surface and the constitutive relations used to relate the viscous stress to rate of strain. The dependence on geometry is often overlooked in current rarefied flow calculations, and the generality of the constitutive dependence means the condition can also be usefully applie...

On-site boundary conditions are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as those of porous media or microfluidic devices. The possibility of specifying the exact position of the boundary, independently of other simulation parameters, simplifies the analysis of the system. For practical applications it should allow one to freely specify the direct...

Gas  ows throughmicroŽ lters are simulated in the continuumand slip  ow regimes as a functionof theKnudsen, Reynolds, and Mach numbers. The numerical simulations are based on the spectral element formulation of compressible Navier–Stokes equations, which utilize previously developed high-order velocity slip and temperature jump boundary conditions. Both slip and no-slip simulations are used t...

Interfaces in elastic media need not be in welded contact. For instance, fractures allow a small amount of slip to occur along their surfaces during the passage of a seismic wave. By slip, we mean that the displacement across the interface can be discontinuous. Reflection and transmission of plane waves in this case are frequency dependent. Previous numerical studies have chosen the finite-diff...

In this study we develop a gradient theory of small-deformation single-crystal plasticity that accounts for geometrically necessary dislocations (GNDs). The resulting framework is used to discuss grain boundaries. The grains are allowed to slip along the interface, but growth phenomenona and phase transitions are neglected. The bulk theory is based on the introduction of a microforce balance fo...

in this study, nonlocal nonlinear instability and the vibration of a double carbon nanotube (cnt) system have been investigated. the visco-pasternak model is used to simulate the elastic medium between nanotubes, on which the effect of the spring, shear and damping of the elastic medium is considered. both of the cnts convey a viscose fluid and a uniform longitudinal magnetic field is applied t...

We say that the vanishing viscosity limit holds in the classical sense if the velocity for a solution to the Navier-Stokes equations converges in the energy norm uniformly in time to the velocity for a solution to the Euler equations. We prove, for a bounded domain in dimension 2 or higher, that the vanishing viscosity limit holds in the classical sense if and only if a vortex sheet forms on th...

Graphene has attracted considerable attention due to its characteristics as a 2D material and its fascinating properties, providing a potential building block for nanofabrication. In nanochannels the solid-liquid interface plays a non-negligible role in determining the fluid dynamics. Therefore, for an optimal design of nanofluidic devices, a comprehensive understanding of the slippage in a wat...

We present an analysis of the transverse-velocity fluctuations in an isothermal liquid layer with a uniform shear rate between two parallel horizontal boundaries as a function of the wave number and the Reynolds number. The results were obtained by solving a stochastic version of the Orr-Sommerfeld equation subject to no-slip boundary conditions in a second-order Galerkin approximation. We find...