In this paper we analytically solve the velocity of the lattice Boltzmann BGK equation [LBGK) Ibr several simple flows. The analysis provides a framework to theoretically analyze various boundary conditions. In particular, the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition. We find that the slip velocity is zero as long as Z=J~e~ =...

Consider a viscous liquid droplet spreading on a surface. The classical slip condition at the liquid–solid interface is the no–slip condition. However, this condition lead to infinite dissipation of energy for propagating contact lines (“no–slip paradox”). For this reason other slip conditions such as the Navier–slip have been introduced. We prove well–posedness for a reduced 1–d fluid model mo...

The Navier-Stokes equations are solved exactly, assuming the Navier slip boundary condition, for flow between coaxial circular cylinders (with possibly different slip lengths at the inner and outer walls), and flow in an equilateral triangular pipe. The velocity fields and total flow rates are found analytically. A relatively small slip length can lead to a large increase in the total rate of f...

We make an analytical study of the nonsteady flow of Newtonian fluids in microchannels. We consider the slip boundary condition at the solid walls with Navier hypothesis and calculate the dynamic permeability, which gives the system's response to dynamic pressure gradients. We find a scaling relation in the absence of slip that is broken in its presence. We discuss how this might be useful to e...

The steady-state fully-developed laminar flow of non-Newtonian power-law fluids is examined in a circular microchannel with slip boundary condition and under an imposed constant wall heat flux. Effects of slip as well as the hydrodynamic and thermal key parameters on heat transfer and entropy generation are investigated. The results reveal that increasing the Brinkman number and the flow behavi...

A steady mixing (even Bernoulli) smooth volume-preserving vector field in a bounded container in R3 with smooth no-slip boundary is constructed. An interesting feature is that it is structurally stable in the class of C3 volumepreserving vector fields on the given domain of R3 with smooth no-slip boundary, thus if one could think how to drive it then it would be physically realisable. It is poi...

Unsteady pulsatile flow of blood through porous medium in an artery has been studied under the influence of periodic body acceleration and slip condition in the presence of magnetic field considering blood as an incompressible electrically conducting fluid. An analytical solution of the equation of motion is obtained by applying the Laplace transform. With a view to illustrating the applicabili...

Two differing theories aim to describe fluidic thermophoresis, the movement of particles along a temperature gradient. While thermodynamic approaches rely on local equilibrium, hydrodynamic descriptions assume a quasi-slip-flow boundary condition at the particle's surface. Evidence for slip flow is presented for the case of thermal gradients exceeding (aS_(T)(-1) with particle radius a and Sore...

A boundary condition-enforced immersed boundary-lattice Boltzmann method (IB-LBM) for the simulation of particulate flows is presented in this paper. In general, the immersed boundary method (IBM) utilizes a discrete set of force density to represent the effect of boundary. In the conventional IB-LBM, such force density is pre-determined, which cannot guarantee exact satisfaction of non-slip bo...