Long-time and large-data existence of weak solutions for initial- boundary-value problems concerning three-dimensional flows \emph{incompressible} fluids is nowadays available not only Navier--Stokes but also various fluid models where the relation between Cauchy stress tensor symmetric part velocity gradient \emph{nonlinear}. The majority such studies however concerns a dependence \emph{explic...

Rarefied Couette flow between concentric rotating cylinders is investigated using Maxwell’s slip-velocity boundary treatment. The study provides an independent reassessment of the velocity inversion process and demonstrates that the occurrence of an inverted velocity profile depends solely on the accommodation coefficient of the stationary outer cylinder. From the analysis, criteria are derived...

Bio-inspired mechanics of locomotion generally consist of the interaction of flexible structures with the surrounding fluid to generate propulsive forces. In this work, we extend, for the first time, the viscous vortex particle method (VVPM) to continuously deforming two-dimensional bodies. The VVPM is a high-fidelity Navier–Stokes computational method that captures the fluid motion through evo...

We analyze the influence of choice of boundary condition (no-slip and Navier’s slip boundary conditions) on linear stability of Hagen–Poiseuille flow. Several heuristic arguments based on detailed analysis of spectrum of the Stokes operator are given, and it is concluded that Navier’s slip boundary condition should have a destabilizing effect on the flow. Finally the linear stability problem is...

In immiscible two-phase flows, the contact line denotes the intersection of the fluid– fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a non-integrable singularity. The rec...

This paper is devoted to the construction of analytic solution of stick-slip waves crossing the interface between an elastic half-space and a rigid one under unilateral contact and Coulomb friction. The method of solution is based on the analytic continuation method of Radok's complex potentials within the framework of steady elastodynamical problems. The governing equations combined with the b...

Molecular dynamics (MD) and continuum simulations are carried out to investigate the influence of shear rate and surface roughness on slip flow of a Newtonian fluid. For weak wall-fluid interaction energy, the nonlinear shear-rate dependence of the intrinsic slip length in the flow over an atomically flat surface is computed by MD simulations. We describe laminar flow away from a curved boundar...

In this study, an analysis has been performed to study the problem of fully developed flow of a fourth grade nonNewtonian fluid between two stationary parallel plates in the presence of an externally applied uniform vertical magnetic field. Slip conditions is taken into account at the wall of the channel. Employing the similarity variables, the governing partial differential equations including...

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...

In this paper, we study the flow of two immiscible fluids namely, couple stress fluid and Jeffrey in a porous channel. Instead classical no-slip conditions on boundaries, used slip boundary conditions, which are more realistic meaningful. addition, inclined magnetic field effects flow. The flowing adjacent to each other region I II, respectively, horizontal nondimensionalized governing equation...