We consider solutions to the Navier-Stokes equations with Navier boundary conditions in a bounded domain Ω in R with a Cboundary Γ. Navier boundary conditions can be expressed in the form ω(v) = (2κ−α)v · τ and v ·n = 0 on Γ, where v is the velocity, ω(v) the vorticity, n a unit normal vector, τ a unit tangent vector, and α is in L∞(Γ). Such solutions have been considered in [2] and [3], and, i...

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 ...

Purpose – This paper aims to examine how using lattice Boltzmann method (LBM) aids the study of the isothermal-gas flow with slight rarefaction in long microtubes. Design/methodology/approach – A revised axisymmetric lattice Boltzmann model is proposed to simulate the flow in microtubes. The wall boundary condition combining the bounce-back and specular-reflection schemes is used to capture the...

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. denote by α friction coefficient and we analyze asymptotic behavior of such a as → ∞. More precisely, prove that if take each α, then there exists sequence controls converging to same Dirichlet condition. also show convergence corresponding direct adjoint states.

The response of a quartz crystal microbalance ~QCM! is considered using a wave equation for the substrate and the Navier-Stokes equations for a finite liquid layer under a slip boundary condition. It is shown that when the slip length to shear wave penetration depth is small, the first-order effect of slip is only present in the frequency response. Importantly, in this approximation the frequen...

It is experimentally known that a pressure di¤erence is developed in a gas under continuum conditions contained in a closed capillary tube, the ends of which are maintained at di¤erent temperatures. However, in contradiction with this experimentally measurable thermomolecular pressure di¤erence, the use of the methods of irreversible thermodynamics in conjunction with the Navier-Stokes equation...

The Navier-Stokes equations for the motion of compressible, viscous fluids in the half-space R+ with the no-slip boundary condition are studied. Given a constant equilibrium state (ρ̄, 0), we construct a global in time, regular weak solution, provided that the initial data ρ0,u0 are close to the equilibrium state when measured by the norm |ρ0 − ρ̄|L∞ + |u0|H1 and discontinuities of ρ0 decay near ...

An approximate expression for Henry's function, describing the electrophoretic mobility of a spherical colloidal particle in the limit of low surface potentials, is developed through a physical analogy to a colloidal particle with a linearly slipping surface (i.e. satisfies the Navier slip condition). The resulting expression reproduces Henry's function with a relative error of no more than 0.1...