Electroosmotic flow of Eyring fluid in slit microchannel with slip boundary condition

In consideration of the electroosmotic flow in a slit microchannel, the con-stitutive relationship of the Eyring fluid model is utilized. Navier＇s slip condition is used as the boundary condition. The governing equations are solved analytically, yielding the velocity distribution. The approximate expressions of the velocity distribution are also given and discussed. Furthermore, the effects of the dimensionless parameters, the electrokinetic parameter, and the slip length on the flow are studied numerically, and appropriate conclusions are drawn.

Stokes flow of micro-polar fluids by peristaltic pumping through tube with slip boundary condition

This paper studies the Stokes flow of micro-polar fluids by peristaltic pumping through the cylindrical tube under the effect of the slip boundary condition. The motion of the wall is governed by the sinusoidal wave equation. The analytical and numerical solutions for the axial velocity, the micro-polar vector, the stream function, the pressure gradient, the friction force, and the mechanical efficiency are obtained by using the lu- brication theory under the low Reynolds number and long wavelength approximations. The impacts of the emerging parameters, such as the coupling number, the micro-polar parameter, the slip parameter on pumping characteristics, the friction force, the velocity profile, the mechanical efficiency, and the trapping phenomenon are depicted graphically. The numerical results infer that large pressure is required for peristaltic pumping when the coupling number is large, while opposite behaviors are found for the micro-polar parameter and the slip parameter. The size of the trapped bolus reduces with the increase in the coupling number and the micro-polar parameter, whereas it blows up with the increase in the slip parameter.

Effect of boundary slip on electroosmotic flow in a curved rectangular microchannel

The aim of this study is to numerically investigate the impact of boundary slip on electroosmotic flow(EOF) in curved rectangular microchannels. Navier slip boundary conditions were employed at the curved microchannel walls. The electric potential distribution was governed by the Poisson–Boltzmann equation, whereas the velocity distribution was determined by the Navier–Stokes equation. The finite-difference method was employed to solve these two equations. The detailed discussion focuses on the impact of the curvature ratio, electrokinetic width, aspect ratio and slip length on the velocity. The results indicate that the present problem is strongly dependent on these parameters. The results demonstrate that by varying the dimensionless slip length from 0.001 to 0.01 while maintaining a curvature ratio of 0.5 there is a twofold increase in the maximum velocity. Moreover, this increase becomes more pronounced at higher curvature ratios. In addition, the velocity difference between the inner and outer radial regions increases with increasing slip length. Therefore, the incorporation of the slip boundary condition results in an augmented velocity and a more non-uniform velocity distribution. The findings presented here offer valuable insights into the design and optimization of EOF performance in curved hydrophobic microchannels featuring rectangular cross-sections.

An acoustic-wave theory for casing bond evaluation using viscoelastic slip boundary modeling

Slip boundary condition is commonly utilized to model elastic wave propagation through layered earth media. The same approach is used here to characterize acoustic wave propagation along a cased borehole with various cement bond conditions. By modeling the cement layer between casing and formation as a viscoelastic slip interface with complex coupling rigidity parameters, one can not only reduce the complexity in the classical elastic wave modeling of the problem, but also efficiently model various complicated wave phenomena that are difficult for the existing modeling. More specifically, the new theory can well describe the effect of the cement bond condition change and the location of the change(i.e., whether it is in the first interface between casing and cement, or the second interface between cement and formation) on the acoustic waves,demonstrating the good modeling capability and predicting power. Application of the theory to field data shows that the theory can correctly model the acoustic wave characteristics and interpret the cement bond condition, thus providing a useful fundament theory for casing bond evaluation using acoustic logging.

On the Inviscid Limit of the 3D Navier–Stokes Equations with Generalized Navier-Slip Boundary Conditions

In this paper,we investigate the vanishing viscosity limit problem for the 3-dimensional(3D)incompressible Navier-Stokes equations in a general bounded smooth domain of R^3 with the generalized Navier-slip boundary conditions u^ε·n=0,n×(ω^ε)=[Bu^ε]τon∂Ω.Some uniform estimates on rates of convergence in C([0,T],L2(Ω))and C([0,T],H^1(Ω))of the solutions to the corresponding solutions of the ideal Euler equations with the standard slip boundary condition are obtained.

Investigation into gas lubrication performance of porous gas bearing considering velocity slip boundary condition

Porous gas bearings(PGBs)have a proactive application in aerospace and turbomachinery.This study investigates the gas lubrication performance of a PGB with the condition of velocity slip boundary(VSB)owing to the high Knudsen number in the gas film.The Darcy-Forchheimer laws and modified Navier-Stokes equations were adopted to describe the gas flow in the porous layer and gas film region,respectively.An improved bearing experimental platform was established to verify the accuracy of the derived theory and the reliability of the numerical analysis.The effects of various parameters on the pressure distribution,flow cycle,load capacity,mass flow rate,and velocity profile are demonstrated and discussed.The results show that the gas can flow in both directions,from the porous layer to the gas film region,or in reverse.The load capacity of the PGB increases with an increase in speed and inlet pressure and decreases with an increase in permeability.The mass flow rate increases as the inlet pressure and permeability increase.Furthermore,the simulation results using VSB are in agreement with the experimental results,with an average error of 3.4%,which indicates that the model using VSB achieves a high accuracy.The simulation results ignoring the VSB overrate the load capacity by 16.42%and undervalue the mass flow rate by 11.29%.This study may aid in understanding the gas lubrication mechanism in PGBs and the development of novel gas lubricants.

LOCALLY STABILIZED FINITE ELEMENT METHOD FOR STOKES PROBLEM WITH NONLINEAR SLIP BOUNDARY CONDITIONS

Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.

Effects of viscous dissipation and Joule heating on the Couette and Poiseuille flows of a Jeffrey fluid with slip boundary conditions

In this article,we have presented the exact solutions of the Couette,Poiseuille and generalized Couette flows of an incompressible magnetohydrodynamic Jeffrey fluid between parallel plates through homogeneous porous medium.The effects of slip boundary conditions and heat transfer are considered.Viscous dissipation,radiation and Joule heating are also considered in the energy equation.The governing equations of the Jeffrey fluid flow are modeled in Cartesian coordinate system.Analytical solutions for the velocity and temperature the velocity and temperature profiles are studied and the results are presented through graphs.It Temperature behaves as a decreasing function due to the impact of Hartmann number,non-Newtonian parameter and slip parameter in all noted problems.

AParallel Pressure Projection Stabilized Finite Element Method for Stokes Equation with Nonlinear Slip Boundary Conditions

For the low-order finite element pair P1􀀀P1,based on full domain partition technique,a parallel pressure projection stabilized finite element algorithm for the Stokes equation with nonlinear slip boundary conditions is designed and analyzed.From the definition of the subdifferential,the variational formulation of this equation is the variational inequality problem of the second kind.Each subproblem is a global problem on the composite grid,which is easy to program and implement.The optimal error estimates of the approximate solutions are obtained by theoretical analysis since the appropriate stabilization parameter is chosen.Finally,some numerical results are given to demonstrate the hight efficiency of the parallel stabilized finite element algorithm.

Navier-Stokes equations under slip boundary conditions:Lower bounds to the minimal amplitude of possible time-discontinuities of solutions with two components in L^(∞)(L^(3))

The main purpose of this paper is to extend the result obtained by Beirao da Veiga(2000)from the whole-space case to slip boundary cases.Denote by a two components of the velocity u.To fix ideas setū=(u_(1),u_(2),0)(the half-space)orū=?_(1)ê_(1)+?_(2)ê_(2)(the general boundary case(see(7.1))).We show that there exists a constant K,which enjoys very simple and significant expressions such that if at some timeτ∈(0,T)one has lim sup_(t→^(τ)-0)‖ū(t)‖_(L^(3)(Ω))^(3)<‖ū(τ)‖_(L^(3)(Ω))^(3)+K,then u is continuous atτwith values in L^(3)(Ω).Roughly speaking,the above norm-discontinuity of merely two components of the velocity cannot occur for steps'amplitudes smaller than K.In particular,if the above condition holds at eachτ∈(0,T),the solution is smooth in(0,T)×Ω.Note that here there is no limitation on the width of the norms‖ū(t)‖_(L^(3)(Ω))^(3)·So K is independent of these quantities.Many other related results are discussed and compared among them.

Numerical simulation of cavitating flow around a slender body with slip boundary condition

In this paper, we perform a numerical simulation of the cavitating flow around an underwater hemispherical-head slender body running at a high speed. For the first time, the slip boundary condition is introduced into this problem, and we find that the slip boundary condition has a big influence on the cavitation in the flow-separation zone. By simulating the cavitating flow under different cavitation numbers, we demonstrate that the slip boundary condition can effectively reduce the intensity of cavitation, as represented by the length of cavitation bubbles. The present paper provides a new method for utilization of new surface materials to control the cavitation on the underwater moving objects.

Existence of weak solutions for non-stationary flows of fluids with shear thinning dependent viscosities under slip boundary conditions in half space

This paper treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by p-potential function subject to slip boundary conditions in R_+~3. Making use of the Oseentype approximation to this model and the L~∞-truncation method, one can establish the existence theorem of weak solutions for p-potential flow with p ∈(8/5, 2] provided that large initial are regular enough.

Effects of hysteresis of static contact angle (HSCA) and boundary slip on the hydrodynamics of water striders

It is known that contact lines keep relatively still on solids until static contact angles exceed an interval of hysteresis of static contact angle (HSCA), and contact angles keep changing as contact lines relatively slide on the solid. Here, the effects of HSCA and boundary slip were first distinguished on the micro-curvature force (MCF) on the seta. Hence, the total MCF is partitioned into static and dynamic MCFs correspondingly. The static MCF was found proportional to the HSCA and related with the asymmetry of the micro-meniscus near the seta. The dynamic MCF, exerting on the relatively sliding contact line, is aroused by the boundary slip. Based on the Blake-Haynes mechanism, the dynamic MCF was proved important for water walking insects with legs slower than the minimum wave speed . As insects brush the water by laterally swinging legs backwards, setae on the front side of the leg are pulled and the ones on the back side are pushed to cooperatively propel bodies forward. If they pierce the water surface by vertically swinging legs downwards, setae on the upside of the legs are pulled, and the ones on the downside are pushed to cooperatively obtain a jumping force. Based on the dependency between the slip length and shear rate, the dynamic MCF was found correlated with the leg speed U, as , where and are determined by the dimple depth. Discrete points on this curve could give fitted relations as (Suter et al., J. Exp. Biol. 200, 2523-2538, 1997). Finally, the axial torque on the inclined and partially submerged seta was found determined by the surface tension, contact angle, HSCA, seta width, and tilt angle. The torque direction coincides with the orientation of the spiral grooves of the seta, which encourages us to surmise it is a mechanical incentive for the formation of the spiral morphology of the setae of water striders.

SQUEEZE FILM FLOW WITH NONLINEAR BOUNDARY SLIP

A nonlinear boundary slip model consisting of an initial slip length and a critical shear rate was used to study the nonlinear boundary slip of squeeze fluid film confined between two approaching spheres. It is found that the initial slip length controls the slip behavior at small shear rate, but the critical shear rate controls the boundary slip at high shear rate. The boundary slip at the squeeze fluid film of spherical surfaces is a strongly nonlinear function of the radius coordinate. At the center or far from the center of the squeeze film, the slip length equals the initial slip length due to the small shear rate. However, in the high shear rate regime the slip length increases very much. The hydrodynamic force of the spherical squeeze film decreases with increasing the initial slip length and decreasing the critical shear rate. The effect of initial slip length on the hydrodynamic force seems less than that of the critical shear rate. When the critical shear rate is very small the hydrodynamic force increases very slowly with a decrease in minimum film thickness. The theoretical predictions agree well with the experiment measurements.

THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITY BOUNDARY CONDITIONS ON NON-FLAT BOUNDARIES

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.

Hypersonic Shock Wave/Boundary Layer Interactions by a Third-Order Optimized Symmetric WENO Scheme

A novel third-order optimized symmetric weighted essentially non-oscillatory(WENO-OS3)scheme is used to simulate the hypersonic shock wave/boundary layer interactions.Firstly,the scheme is presented with the achievement of low dissipation in smooth region and robust shock-capturing capabilities in discontinuities.The Maxwell slip boundary conditions are employed to consider the rarefied effect near the surface.Secondly,several validating tests are given to show the good resolution of the WENO-OS3 scheme and the feasibility of the Maxwell slip boundary conditions.Finally,hypersonic flows around the hollow cylinder truncated flare(HCTF)and the25°/55°sharp double cone are studied.Discussions are made on the characteristics of the hypersonic shock wave/boundary layer interactions with and without the consideration of the slip effect.The results indicate that the scheme has a good capability in predicting heat transfer with a high resolution for describing fluid structures.With the slip boundary conditions,the separation region at the corner is smaller and the prediction is more accurate than that with no-slip boundary conditions.

Numerical study of homogeneous–heterogeneous reactions on stagnation point flow of ferrofluid with non-linear slip condition

This study deals with the stagnation point flow of ferrofluid over a flat plate with non-linear slip boundary condition in the presence of homogeneous-heterogeneous reactions.Three kinds of ferroparticles,namely,magnetite(Fe_3O_4),cobalt ferrite(CoFe_2O_4) and manganese zinc ferrite(Mn-ZnFe_2O_4) are taken into account with water and kerosene as conventional base fluids.The developed model of homogeneous-heterogeneous reactions in boundary layer flow with equal and unequal diffusivities for reactant and autocatalysis is considered.The governing partial differential equations are converted into system of non-linear ordinary differential equations by mean of similarity transformations.These ordinary differential equations are integrated numerically using shooting method.The effects of pertinent parameters on velocity and concentration profiles are presented graphically and discussed.We found that in the presence of Fe_3O_4-kerosene and CoFe_2O_4-kerosene,velocity profiles increase for large values of α and β whereas there is a decrement in concentration profiles with increasing values of if and K_s.Furthermore,the comparison between non-magnetic(A1_2O_3) and magnetic Fe_3O_4 nanoparticles is given in tabular form.

Near continuum boundary layer flows at a flat plate

The problem of boundary layer flows at a flat plate surface with velocity-slip and temperature-jump boundary conditions is analyzed. With the velocity slip conditions, there are multiple physical factors lumped together, and the boundary layer solutions significantly change their behaviors. The self-similarity in the solutions degenerates, however, the problem is still an ordinary differential equation which can be solved. Shooting methods are applied to solve the flowfield. The results include velocity and temperature for both the surface and flowfield. Unlike the traditional Blasius fiat plate boundary layer solutions which are self-similar through all the plate boundary layer, the new solutions indicate that the front tip is actually a singularity point, especially at locations within one mean flee path from the leading edge.

Unsteady Mixed Convection Slip Flow around a Stretching Sheet in Porous Medium

The heat and mass transfer of unsteady MHD two-dimensional mixed convection boundary layer flow over an exponentially porous stretching sheet is presented in this paper. Multiple slip conditions, radiation, suction or blowing, heat generation or absorption along with magnetism and porous medium are incorporated. We reduce the leading equations which are partial differential equations into a family of ordinary differential equations that are non-linear using a set of similarity transformations. The resulting equations with coupled boundary conditions are solved numerically with the aid of bvp4c solver with MATLAB package. The impacts of several non-dimensional governing parameters on the flow fields such as velocity, temperature and concentration profiles along with friction coefficient, temperature gradient and concentration gradient are portrayed graphically and discussed in detail. The result indicates that the magnetic parameter decreases the skin friction coefficient. Thermal boundary layer thickness reduces with increasing radiation parameters and enhances with increasing Prandtl number. It is also observed that the thermal slip parameter depreciates the heat transfer rate and the mass slip parameter diminishes the mass transfer rate. A comparison has been made between the current results and the numerical results of previous studies and observed a very close good agreement.

Grain-scale Stress and GND Density Distributions around Slip Traces and Phase Boundaries in a Titanium Alloy

For TA15 titanium alloy, slip is the dominant plastic deformation mechanism because of relatively high Al content. In order to reveal the grain-scale stress field and geometrically necessary dislocation（GND） density distribution around the slip traces and phase boundaries where the slip lines are blocked due to Burgers orientation relationship（OR） missing. We experimentally investigated tensile deformation on TA15 titanium alloy up to 2.0% strain at room temperature. The slip traces were observed and identified using high resolution scanning electron microscopy（SEM） and electron backscatter diffraction（EBSD） measurements. The grain-scale stress fields around the slip traces and phase boundaries were calculated by the cross-correlationbased method. Based on strain gradient theories, the density of GND was calculated and analyzed. The results indicate that the grain-scale stress is significantly concentrated at phase/grain boundaries and slip traces. Although there is an obvious GND accumulation in the vicinity of phase and subgrain boundaries, no GND density accumulation appears near the slip traces.