Navier Slip Boundary Research Articles

Note on evolutionary free piston problem for Stokes equations with slip boundary conditions

In this paper we study a free boundary fluid-rigid body interaction problem, the free piston problem.We consider an evolutionary incompressible viscous fluid flow through a junction of two pipes. Insidethe 'vertical' pipe there is a heavy piston which can freely slide along the pipe. On the lateralboundary of the 'vertical' pipe we prescribe Navier's slip boundary conditions. We prove the existence ofa local in time weak solution. Furthermore, we show that the obtained solution is a strong solution.

Fluid flow and heat transfer of carbon nanotubes along a flat plate with Navier slip boundary

Homogeneous flow model is used to study the flow and heat transfer of carbon nanotubes (CNTs) along a flat plate subjected to Navier slip and uniform heat flux boundary conditions. This is the first paper on the flow and heat transfer of CNTs along a flat plate. Two types of CNTs, namely, single- and multi-wall CNTs are used with water, kerosene or engine oil as base fluids. The empirical correlations are used for the thermophysical properties of CNTs in terms of the solid volume fraction of CNTs. For the effective thermal conductivity of CNTs, Xue (Phys B Condens Matter 368:302–307, 2005) model has been used and the results are compared with the existing theoretical models. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using suitable similarity transformations. These equations are solved numerically using a very efficient finite difference method with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are investigated and presented in graphical and tabular forms. The numerical results of skin friction and Nusselt numbers are compared with the available data for special cases and are found in good agreement.

Existence of Global Weak Solutions to Implicitly Constituted Kinetic Models of Incompressible Homogeneous Dilute Polymers

We show the existence of global weak solutions to a general class of kinetic models of homogeneous incompressible dilute polymers. The main new feature of the model is the presence of a general implicit constitutive equation relating the viscous part of the Cauchy stress and the symmetric part of the velocity gradient. We consider implicit relations that generate maximal monotone (possibly multivalued) graphs, and the corresponding rate of dissipation is characterized by the sum of a Young function and its conjugate depending on and , respectively. Such a framework is very general and includes, among others, classical power-law fluids, stress power-law fluids, fluids with activation criteria of Bingham or Herschel–Bulkley type, and shear-rate dependent fluids with discontinuous viscosities as special cases. The appearance of and in all the assumptions characterizing the implicit relationship is fully symmetric. The elastic properties of the flow, characterizing the response of polymer macromolecules in the viscous solvent, are modeled by the elastic part of the Cauchy stress tensor, whose divergence appears on the right-hand side of the momentum equation, and which is defined by the Kramers expression involving the probability density function, associated with the random motion of the polymer molecules in the solvent. The probability density function satisfies a Fokker–Planck equation, which is nonlinearly coupled to the momentum equation. We establish long-time and large-data existence of weak solutions to such a system, completed by an initial condition and either a no-slip or Navier's slip boundary condition, by using properties of maximal monotone operators and Lipschitz approximations of Sobolev-space-valued Bochner functions via a weak compactness arguments based on the Div-Curl Lemma and Chacon's Biting Lemma. A key ingredient in the proof is the strong compactness in L 1 of the sequence of Galerkin approximations to the probability density function and of the associated sequence of approximations to the elastic part of the Cauchy stress tensor.

Combined effects of EDL and boundary slip on mean flow and its stability in microchannels

The effects of an electrical double layer (EDL), boundary slip and their combined effects on the microchannel flow stability are investigated. Instead of applying the traditional streaming electrical current balance (ECB) mode, a newly introduced electrical current density balance (ECDB) mode is used to compute the conduction current when the effects of EDL is considered. The modified N-S equations and Poisson–Boltzmann equation together with the ECDB mode and Navier slip boundary are the theoretical basis for the present approach. The stability analysis considering the modifications of EDL and boundary slip is built up by the small perturbation method. It is found that the effect of EDL results in inflexions on the mean velocity profile near walls and destabilizes the stability of flow. On the contrary, the effect of boundary slip stabilizes the stability of flow. The effectiveness of boundary slip on the mean velocity and flow stability is influenced strongly by the effect of EDL. The effect of boundary slip can be disappeared when the Zeta potential is large enough.

SLIP BOUNDARY CONDITION FOR VISCOUS FLOW OVER SOLID SURFACES

A slip boundary condition is derived for the flow of a viscous fluid over a solid surface, using the theory of thermal activation process. The slip velocity is proportional to the hyperbolic sine of the shear stress on the solid surface, and the slip boundary condition reduces to Navier's slip boundary condition for the flow of Newtonian fluids under small shear stresses. There exists a critical shear stress determining the onset of the slip flow.

Navier's slip and incompressible limits in domains with variable bottoms

We consider unsteady flows of compressible Navier-Stokes-Fourier equations in domains with bottoms that are not flat and where the fluid fulfils Navier's slip boundary conditions. Dealing with weak solutions whose long-time and large data existence has been recently established, we investigate their behavior for vanishing Mach number (the square of this small parameter appears also in the Navier slip condition), and prove their convergence towards the weak solution of the so-called Boussinesq approximation with the no-slip boundary condition. The fact that we treat the Navier boundary condition brings several interesting features in the analysis of acoustic waves, in particular the strong convergence of the velocity field.

Analysis of lubricated planar stagnation die flow

Lubricated die flows with a low-viscosity liquid separating a viscous material from the solid walls have been proposed for extensional rheometers. Steady, two-dimensional flow through a lubricated planar stagnation die is analyzed here by Galerkin's method of weighted residuals with finite element basis functions on streamlined subdomains. For the more viscous liquid, the shear-thinning Carreau model is chosen. Alternatives for modelling the Newtonian lubricant are two-dimensional flow analysis, lubrication approximation, and Navier's slip boundary condition: all are examined. An approximate analytical solution suggested by the computations is also presented. Portraits are shown of lubricant layer thickness and pressure velocity, deformation rate, γ, and vorticity, ω, fields. From the last two, Giesekus's local flow classification, Φ =(γ − ω)(γ + ω), is evaluated. Both the approximate solution and the theoretical calculations are compared to available experimental data. The approximate analytical solution leads to a new relation between the extensional viscosity and the pressure profile in the die. Pure planar extension throughout the die is prevented by the interaction of the die shape with the normal viscous stresses at the free interface. The sign change of the normal viscous stresses as the flow switches from a diverging to a converging channel is the key feature. However, two regions of the flow are nearly extensional and can be analyzed with the analytic approximation. Implications for extensional rheometry and design of lubricated flows are discussed.