Slip Coefficient Research Articles

Micropolar fluid flow between a non-porous disk and a porous disk with slip: Keller-box solution

Abstract In the present analysis, a steady, laminar, incompressible and two-dimensional micropolar fluid flow between a porous disk and a nonporous disk is considered. Similarity transformations are suitably applied to reduce the complex governing equations into a set of nonlinear boundary value problems with velocity slip conditions. An efficient finite difference technique called Keller-box method is employed to obtain the numerical solutions. The aim of this investigation is to study the influence of non-zero tangential slip velocity on velocity, microrotation profiles, and shear stress for different pertinent parameters. The results are then presented in the form of tables and graphs to analyze velocity and microrotation profiles for different physical micropolar parameters, Reynolds number, and slip coefficient. The results are found to be in excellent agreement with earlier findings in the absence of slip.

Numerical simulations of a stick-slip spherical particle in Poiseuille flow

The dynamics of a stick-slip “Janus” spherical particle suspended in a Newtonian fluid flowing in a cylindrical microchannel is studied by direct numerical simulations. Partial slip is imposed on half of the particle surface, whereas the no-slip boundary condition is present on the other half. The finite element method is used to solve the balance equations under creeping flow conditions. The translational and rotational velocities of the particle are evaluated at several orientations and distances from the tube centerline. The trajectories are then reconstructed by solving the kinematic equations where the velocities are taken by interpolating the simulation data. The particle dynamics is investigated by varying the initial position and orientation, the slip parameter, and the confinement ratio. The results, presented in terms of particle trajectories and phase portraits, highlight the existence of two relevant regimes: a periodic oscillation or a migration toward the tube axis for particle positions sufficiently far from or near the centerline, respectively. The basin of attraction of the tube axis grows with particle confinement and slip coefficient although the dynamics is qualitatively unaffected.

Twice Order Slip on the Flows of Fractionalized MHD Viscoelastic Fluid

The objective of this article is to investigate the effect of twice order slip on the MHD flow of fractionalized Maxwell fluid through a permeable medium produced by oscillatory movement of an infinite bottom plate. The governing equations are developed by fractional calculus approach. The exact analytical results for velocity field and related shear stress are calculated using Laplace transforms and presented in terms of generalized M-function satisfying all imposed initial and boundary conditions. The flow results for fractionalized Maxwell, traditional Maxwell and Newtonian fluid with and without slips, in the presence and absence of magnetic and porous effects are derived as the limiting cases. The impact of fractional parameter, slip coefficients, magnetic force and porosity parameter over the velocity field and shear stress are discussed and analyzed through graphical illustrations. The outcomes demonstrate that the speed comparing to streams with slip condition is lower than that for stream with non-slip conditions, and the speed with second-slip condition is lower than that with first-order slip condition.

Electroviscous effect on electromagnetohydrodynamic flows of Maxwell fluids in parallel plate microchannels

Considering the influence of the streaming potential and electroviscous effects, the analytical solutions for electromagnetohydrodynamic (EMHD) flows in parallel plate microchannels are obtained. The electrolyte solutions in the microchannels are taken as generalized Maxwell fluids, and slip boundary conditions are adopted. To accurately analyze the EMHD flow characteristics, the variation trends of the electroviscous effects with the corresponding parameters must be understood. The results show that the electroviscous effects increase with the increase in the relaxation time De, the slip coefficient, and the wall zeta potential ψ0. However, the increase in the inverse of the electrical double-layer (EDL) thickness K, the electrical oscillating Reynolds number Re, and the ionic Peeclet number Pe can decrease the electroviscous effects. We also demonstrate that the electroviscous effect on the EMHD flows of generalized Maxwell fluids is larger than that of Newtonian fluids. This work will be useful in designing EMHD flows in parallel plate microchannels.

Structure, Thermodynamics, and Dynamics of Thin Brine Films in Oil-Brine-Rock Systems.

Thin brine films are ubiquitous in oil-brine-rock systems such as oil reservoirs and play a crucial role in applications such as enhanced oil recovery. We report the results of molecular simulations of brine films that are confined between model oil (n-decane) and rock (neutral or negatively charged quartz slabs), with a focus on their structure, electrical double layers (EDLs), disjoining pressure, and dynamics. As brine films are squeezed to ∼0.7 nm (∼3 water molecule layers), the structures of the water-rock and water-oil interfaces change only marginally, except that the oil surface above the brine film becomes less diffuse. As the film is thinned from ∼1.0 to ∼0.7 nm, ions are enriched (depleted) near the rock (oil) surface, especially at a bath ion concentration of 0.1 M. These changes are caused primarily by the reduced dielectric screening of water and the weakened ion hydration near water-oil interfaces and, to a smaller extent, by the increased confinement. When the brine film is ∼1.0 nm thick, hydration and EDL forces contribute to the disjoining pressure between the charged rock and the oil. The EDL forces are reduced substantially as the ion concentration increases from 0.1 to 1.0 M, and the magnitude of the reduction is close to that predicted by the Poisson-Boltzmann equation. When the brine film is thinned from ∼1.0 to ∼0.7 nm, the disjoining pressure increases by ∼10 MPa, which is mostly due to an increase in the hydration forces. The first layer of water on the rock surface is nearly stagnant, even in 0.74 nm-thick brine films, whereas the viscosity of water beyond the first layer is bulk-like, and the slip coefficient of oil-water interfaces is close to that under unconfined conditions. The insights that are obtained here help lay a foundation for the rational application of technologies such as low-salinity waterflooding.

Elastic–slip interface effect on the diffraction of plane waves around a saturated lining structure in saturated soil

By combining Biot's dynamic wave theory with the elastic and slip interface theory, the scattering of plane waves around a saturated lining structure embedded in saturated soil is studied. The lining structure is assumed to be arbitrary shape. Separating variable method of Helmholtz equations leads to the semi-analytical solutions of the potentials. By using the conformal mapping method, the lining structures of arbitrary shape can be mapped to the cirque at the same centre with different radii. The elastic and slip material constants of interface are introduced to analyze the effect of interfacial properties. The dynamic stress and pore pressure are solved by applying the displacement and stress boundary conditions with interface effect. In numerical examples, the dynamic stress and pore pressure under different interface coefficients (normal and circumferential spring coefficients and slip coefficient) are analyzed. It is found that the effect of normal spring coefficient is larger than that of circumferential spring coefficients. The imperfect interface effect on the dynamic stress and pore pressure is also related with the wave frequencies.

Stability of Poiseuille flow of a Bingham fluid overlying an anisotropic and inhomogeneous porous layer

Modal and non-modal stability analyses are performed for Poiseuille flow of a Bingham fluid overlying an anisotropic and inhomogeneous porous layer saturated with the same fluid. In the case of modal analysis, the resultant Orr–Sommerfeld type eigenvalue problem is formulated and solved via the Chebyshev collocation method, using QZ decomposition. It is found that no unstable eigenvalues are present for the problem, indicating that the flow is linearly stable. Therefore, non-modal analysis is attempted in order to observe the short-time response. For non-modal analysis, the initial value problem is solved, and the response of the system to initial conditions is assessed. The aim is to evaluate the effects on the flow stability of porous layer parameters in terms of depth ratio (ratio of the fluid layer thickness $d$ to the porous layer thickness $d_{m}$), Bingham number, Darcy number and slip coefficient. The effects of anisotropy and inhomogeneity of the porous layer on flow transition are also investigated. In addition, the shapes of the optimal perturbations are constructed. The mechanism of transient growth is explored to comprehend the complex interplay of various factors that lead to intermediate amplifications. The present analysis is perhaps the first attempt at analysing flow stability of viscoplastic fluids over a porous medium, and would possibly lead to better and efficient designing of flow environments involving such flow.

Measurements and modeling of the gas flow in a microchannel: influence of aspect ratios, surface nature, and roughnesses

This article extends in various directions of our previous studies related to gas flow in long rectangular cross-section microchannels. In the present article, the mass flow rate of various gases through microchannels with different aspect ratios, and various surface coatings (Au and SiO\(_2\)) and surface roughnesses (from 0.9 to 12 nm) is measured under isothermal conditions. Previously, we developed a method to calculate the mass flow rate through rectangular microchannels that allows taking into account the real dimensions of the rectangular channel cross-section. In the present article, this method was applied to extract the velocity slip and tangential momentum accommodation coefficients in the frame of the Maxwell diffuse-specular scattering kernel. An extension of the previous approach is also proposed in the present paper. This extension allows considering the possible difference in properties (roughness or material) between the vertical and horizontal channel walls by introducing different accommodation coefficients for each wall. By applying the new method, we can extract a single accommodation coefficient for all the channel walls under the assumption of homogeneous material and roughness and two different accommodation coefficients for the horizontal and vertical walls in the case when the two walls have different properties (roughness or material).

Analytical Solution of Gas Flow in Rough‐Walled Microfracture at In Situ Conditions

AbstractThe development of the unconventional gas and CO2 sequestration is moving to deep formations. Because of the small flow pathways in the matrix, the Knudsen number might be high even though the gas is dense. In fact, due to the relatively high pressure at in situ conditions, gas flow in microfractures usually manifests a strong slip and nonideal gas effects. Therefore, understanding the coupling mechanism of these two on gas flow in rough‐walled microfractures is required to accurately model subsurface flow behavior. In this study, pressure‐driven gas flow in rough‐walled microfracture is analyzed in depth. Starting from the local governing equations for gas flow, a local flow model that includes gas slip and nonideal gas effects is derived by solving the Stokes equation with a first‐order slip boundary condition. Focusing at the representative elementary volume scale, the upscaled solutions to gas flow in a fracture with sinusoidal surface are derived to obtain the apparent permeability. The impact of nonideal gas effects, fracture roughness and aperture, and the tangential momentum accommodation coefficient on CH4 and CO2 flow is analyzed. The results show that fracture roughness introduces a high degree of heterogeneity in gas flow. At in situ conditions effects of gas slip, fracture roughness and tangential momentum accommodation coefficient on gas flow are reduced. The ideal gas law is capable of estimating CH4 flow to some extent. However, it fails to estimate CO2 flow in microfractures.

Investigation of slip effects on electroosmotic mixing in heterogeneous microchannels based on entropy index

In this article electrokinetic mixing through heterogeneous microchannels has been studied and the effects of slip coefficient, zeta-potential, Debye–Hückel parameter and Reynolds number on mixing efficiency have been investigated. The microchannels studied here, have non-homogenous zeta-potential distribution at the wall, while other surface properties are considered to be homogenous. In order to investigate the electro-osmotic mixing, the Navier–Stokes, Nernst–Planck, Laplace and convection–diffusion equations have been solved numerically for velocity field, ions distribution, electrical potential and concentration field, respectively. The entropy of concentration distribution has been used as a quantitative index to evaluate the mixing performance. The results show that the behavior of electro-osmotic micromixers strongly depends on the amount and distribution of wall zeta-potential and in most cases the mixing efficiency increases with reduction of slip coefficient or Debye–Hückel or Reynolds number. It is found that in presence of slip, mixing efficiency decreases at low Reynolds numbers, while increases at high Reynolds numbers. Also, the accuracy of Helmholtz–Smoluchowski approximate model is investigated and it is found that the performance of the Helmholtz–Smoluchowski model in predicting the mixing efficiencies deteriorates for high wall zeta-potential or low values of Debye–Hückel parameter.

Heat Transfer of Oil/MWCNT Nanofluid Jet Injection Inside a Rectangular Microchannel

In the current study, laminar heat transfer and direct fluid jet injection of oil/MWCNT nanofluid were numerically investigated with a finite volume method. Both slip and no-slip boundary conditions on solid walls were used. The objective of this study was to increase the cooling performance of heated walls inside a rectangular microchannel. Reynolds numbers ranged from 10 to 50; slip coefficients were 0.0, 0.04, and 0.08; and nanoparticle volume fractions were 0–4%. The results showed that using techniques for improving heat transfer, such as fluid jet injection with low temperature and adding nanoparticles to the base fluid, allowed for good results to be obtained. By increasing jet injection, areas with eliminated boundary layers along the fluid direction spread in the domain. Dispersing solid nanoparticles in the base fluid with higher volume fractions resulted in better temperature distribution and Nusselt number. By increasing the nanoparticle volume fraction, the temperature of the heated surface penetrated to the flow centerline and the fluid temperature increased. Jet injection with higher velocity, due to its higher fluid momentum, resulted in higher Nusselt number and affected lateral areas. Fluid velocity was higher in jet areas, which diminished the effect of the boundary layer.

Boundary slip phenomena in multicomponent gas mixtures

The slip phenomena in multicomponent gas mixtures are studied. The moment equations, derived from the linearized Boltzmann equation by using the 13-moment approximation of the Grad’s method, are used to obtain the full (containing the contribution from the Knudsen layer) and asymptotic (valid far from the plane physical boundary of the domain) expressions for the nonequilibrium macroscopic parameters of the mixture species. The latter relations are employed to deduce the expressions for the mixture slip velocity and the viscous, thermal, and diffusion slip coefficients by using the modified Maxwell method and the diffuse-specular model of molecule scattering on the wall. The derived relations for the slip coefficients are given in the convenient form expressed in terms of basic transport coefficients, such as partial viscosity and thermal conductivity coefficients, diffusion and thermal diffusion coefficients, and coefficients of molecule momentum accommodation at the wall. The expressions found are used to calculate the slip coefficients for binary (He-Ar) and ternary (He-Ar-Xe) gas mixtures. The numerical results are in good agreement with the data calculated by using other methods.

Magneto-Hydrodynamic Flow of a Viscous Fluid in a Channel with a Porous Bounding Wall of Different Permeabilities

In this paper, the effects of permeability parameter on the magneto-hydrodynamic laminar flow of a viscous incompressible fluid in a channel with a porous bounding wall have been investigated. A transverse magnetic field has been applied in the channel flow of viscous fluid and the stream function is used to reduce the governing partial differential equations into non-linear ordinary differential equation which is solved by applying Perturbation method. Numerical simulation is used to analyze the problem and the graphs have been plotted using MATLAB. It has been observed that an increase of magnetic parameter increases the velocity of the viscous fluid while the velocity decreases with the increase of permeability parameter. The flow of viscous fluid has also been investigated with the variation of Reynolds number and the slip coefficient.

Creation of electric vehicle ABS operation algorithm with possibility of hybrid braking based on slip-slope approach at wheels slip determining

This paper represents an Anti-lock Braking System (ABS) operation algorithm implementing hybrid braking; the paper considers braking with a high deceleration of an electric passenger vehicle during the rectilinear driving on the roads with different friction coefficients; a short analysis of the approaches used for evaluation of the target vehicle wheels slip is also performed. The main ABS task consists in maintenance of the target wheel slip coefficient based on the tyre-road friction coefficient. The tyre-road friction coefficient φx is determined using the algorithm proposed in the papers by Semmler. The algorithm is about finding the curve peak φx−S using the least square method. Based on the calculated target slip coefficient, the braking torque at the electric motor shaft operating in the regeneration mode is determined. The electric motor ensures relatively low braking torque at the vehicle wheels preventing the tyres from a significant slip. Reaching the target slip coefficient is ensured by means of friction brake mechanisms. Virtual tests showed that the values of the wheel slip coefficient are close to the required ones. Thus, this system makes it possible to implement hybrid braking with two sources creating the brake torque.

Calculating the Motion of a Viscous Fluid that Partially Fills a Cylindrical Cavity

The plane-parallel steady motion of a viscous incompressible fluid that partially fills a cylindrical rotating cavity is under consideration. The region occupied by the fluid is simply connected, with two points of a sliding three-phase contact, and the contact angles at which the fluid approaches the walls are specified at these points. The free boundary of the fluid is curvilinear. There is a slip condition at the interface between the fluid and solid wall, which corresponds to proportionality of tangential stresses of a velocity difference of the solid and fluid particles. The flow region is conformally mapped onto a rectangle. The vortex and current function with a given slip coefficient and different rotation velocities of the cylinder are calculated.

Magnetohydrodynamic flow and heat transfer impact on ZnO-SAE50 nanolubricant flow over an inclined rotating disk

The present article has been fine-tuned with the investigation of mixed convection Darcy-Forchheimer flow of ZnO-SAE50 oil nanolubricant over an inclined rotating disk under the influence of uniform applied magnetic field applied to various industries. The current study has been enriched with additional consideration of slip flow, thermal radiation, viscous dissipation, Joulian dissipation and internal heating. In view of augmentation of thermal conductivity of nanolubricant, a new micro-nano-convection model namely Patel model has been invoked. The specialty of this model involves the effects of specific surface area and nano-convection due to Brownian motion of nanoparticles, kinetic theory based micro-convection, liquid layering and particle concentration. Suitably transformed governing equations have been solved numerically by using Runge-Kutta-Fehlberg scheme. An analysis of the present study has shown that applied magnetic field, porosity of the medium, velocity slip and inertia coefficient account for the slowing down of radial as well as tangential flow of ZnO-SAE50 oil nanolubricant, thereby leading to an improvement in velocity and thermal boundary layers.

Barodiffusion in Slow Flows of a Gas Mixture

Barodiffusion in slow flows of a gas mixture is studied with an approximation using hydrodynamic equations of motion for the individual mixture components. It is shown that consideration of the viscous momentum transfer and the contribution of Knudsen layers for the mixture flowing in a channel has a considerable effect on the value of the barodiffusion factor. The relations are obtained for the mean diffusion fluxes of components and for the total flux of the mixture in a circular cylindrical capillary; these relations are valid for moderately small Knudsen numbers used for calculation of the diffusion baroeffect and separation effect when the gas mixture flows in a set of capillaries connecting two volumes. The modification of the relations for the barodiffusion factor (and for the diffusion slip coefficient cross-linked with it) allows interpreting the sign alteration of these effects observed experimentally for some gas mixtures at intermediate Knudsen numbers.

Direct Simulation of Moderately Rarefied Gas Flows within Core Samples

This paper is devoted to the numerical simulation of isothermal moderately rarefied gas flows in three-dimensional spaces with a complex voxel geometry corresponding to the pore space of core (rock) samples. Classical Maxwell slip boundary conditions are used to take into account the slippage effect on the solid boundaries. The simulation results for several core samples under different averaged pressures are presented. The qualitatively correct dependence of the Klinkenberg slippage coefficient on the absolute intrinsic permeability is obtained.

Investigation of Nanofluid Heat Transfer in a Microchannel Under Magnetic Field Via Lattice Boltzmann Method: Effects of Surface Hydrophobicity, Viscous Dissipation, and Joule Heating

In this paper, effect of Joule heating (JH), viscous dissipations (VD), and super hydrophobic surfaces on heat transfer of water–Al2O3 and water–CuO nanofluids in a microchannel has been investigated using lattice Boltzmann method (LBM). The microchannel is under a uniform and transverse magnetic field. The lower wall of the microchannel is insulated and a uniform heat flux has been applied to the upper wall. Results are generated at constant Reynolds number of 150, volume fraction of 2%, and a diameter of 25 nm with variable Hartmann numbers ranging from 0 to 20 and nondimensional slip coefficients from 0 to 0.05. The results of the developed code are in good agreement with other analytical, numerical, and experimental reports. Moreover, the results show that in such case, ignoring the JH and VD leads to a significant error in the prediction of Nusselt number up to 62% and 56%, respectively, for water–Al2O3 and water–CuO nanofluids. It has also been shown that using a super hydrophobic surface with a slip coefficient of 0.05 leads to a significant reduction in VD; however, it increases the effect of JH. On the other hand, it is found that, despite JH and viscous dissipation effects, using super hydrophobic surfaces (up to a slip coefficient of 0.05) leads to an increase in Nusselt number and decrease in shear stress for all the studied Hartmann numbers. Finally, it has been concluded that super hydrophobic surfaces can be used as a passive tool to enhance the heat transfer rate and simultaneously decrease the pumping power demand.

Flow Characteristics Considering the Temperature Viscosity of Oils in the Gap based on Micro Geometric Roughness Fractal Surface

Due to the limitation of manufacturing conditions in China, the valve core will always exhibit random, disordered and multi-scale micro geometric characteristics in recent years. Based on the fractal features of the micro-scale surfaces of the cores and the chambers of a multi-way valve, this research establishes3-danisotropic models for the surface shapes of the valve cores and chambers using the Weierstrass-Mandelbrot (W-M) function. Then, the boundary conditions of the Navier slip model and computational fluid dynamics (CFD) are used to analyse the flow characteristics of the hydraulic oil in the gap and the wall slip. The research results demonstrate that the surface roughness of the solid walls exerts a significant influence on the flow characteristics of the hydraulic oil as it flows in the gaps: the greater the surface roughness, the higher the probability of occurrence of slip between the surfaces of the solid walls. With varying surface roughness of the solid walls, the greater the slip coefficient b is, the larger the slip velocity on the walls, and the greater the flow velocity of the hydraulic oil in the whole gap; meanwhile, this phenomenon occurs when the temperature difference between the upper and lower walls increases as well, and the flow velocity of the hydraulic oil increases significantly.