In this paper, the slipping friction is considered in the problem of a progressive wave of real fluids propagating over a permeable bottom.In the interface of soil and fluid, the “no-slip” condition is relaxed and a sliding friction coefficient is introduced. Thus, the slipping effect and the permeability of the bottom on the velocity near the seabed can be studied. The results indicate that th...

We use Feireisl-Lions theory to deduce the existence of weak solutions a system describing dynamics linear oscillator containing Newtonian compressible fluid. The appropriate Navier-Stokes equation is considered on domain whose movement has one degree freedom. paired with Newton law and we assume no-slip boundary condition.

We present a loosely coupled, partitioned scheme for solving fluid–structure interaction (FSI) problems with the Navier slip boundary condition. The fluid flow is modeled by Navier–Stokes equations an incompressible, viscous fluid, interacting thin elastic structure membrane or Koiter shell type equations. and are coupled via two sets of coupling conditions: dynamic condition describing balance...

We consider the Navier-Stokes equations with Navier friction boundary conditions and prove two results. First, in the case of a bounded domain we prove that weak Leray solutions converge (locally in time in dimension ≥ 3 and globally in time in dimension 2) as the viscosity goes to 0 to a strong solution of the Euler equations provided that the initial data converges in L2 to a sufficiently smo...

In this work, I present the form of the Navier-Stokes equations implied by the Helmholtz decomposition in which the relation of the irrotational and rotational velocity fields is made explicit. The idea of self-equilibration of irrotational viscous stresses is introduced. The decomposition is constructed by first selecting the irrotational flow compatible with the flow boundaries and other pres...

In this paper we use molecular dynamics (MD) simulations to study nanochannel flows at low Reynolds numbers and present some new interesting results. We investigated a simple fluid flowing through channels of different shapes at the nano level. The Weeks-Chandler-Anderson potentials with different interaction strength factors are adopted for the interaction forces between fluid -fluid and fluid...

We present a finite element (FEM) simulation method for pore geometry fluid flow. Within the pore space, we solve the single-phase Reynold’s lubrication equation—a simplified form of the incompressible Navier–Stokes equation yielding the velocity field in a two-step solution approach. (1) Laplace’s equation is solved with homogeneous boundary conditions and a right-hand source term, (2) pore pr...

Shear localization has been observed in liquid lubricants flowing at high pressure. Two kinds have been identified: for stresscontrolled plane Couette shear at high values of Nahme No., thermal runaway can result in the appearance of a band at midplane where the temperature and shear rate become localized. Alternatively, at high pressure and high shear stress, intermittent slip can be visualize...

This paper evaluates the suitability of a newly developed hybrid “Langmuir-Maxwell” and “LangmuirSmoluchowski” slip/jump boundary conditions in the Navier-Stokes-Fourier equations for nano/micro backward-facing step geometry flow which experiences separation and reattachment. Additionally, this paper investigates the effect of different parameters such as step pressure ratio, inflow temperature...

We estimate the effective Navier-slip length for flow over a spray-fabricated liquid-repellent surface which supports a composite solid-air-liquid interface or ’Cassie-Baxter’ state. The morphology of the coated substrate consists of randomly distributed corpuscular micro-structures which encapsulate a film of trapped air (or ’plastron’) upon contact with liquid. The reduction in viscous skin f...