Effective Slip Boundary Condition Research Articles

Pore-Scale Study of Gas Natural Convection in Confined Porous Media Based on Lattice Boltzmann Method

Abstract Gas natural convection is one common phenomenon in industrial applications, especially for the thermal management of electronic devices. In this study, a numerical model for gas natural convection in a confined porous cavity is constructed based on the lattice Boltzmann (LB) method, which predicts the density-difference-induced flow using a multiple relaxation time (MRT) collision operator. At the gas–solid interfaces, the microscale flow and heat transfer effects are formulated using an effective slip boundary condition. The established LB model is applied to investigate the Nusselt number for heated obstacles arranged in a staggered formation in the cavity. Based on the calculated data, the Nusselt number values obtained for a five-cylinder pore-scale (single pore, SP) domain are analyzed and compared to those for a 13-cylinder (multipore, MP) one. The Nusselt number shows a sharp decrease as soon as the microscale effect is considered at the obstacle walls. It was also observed that the Nusselt number for MP domain achieved lower values than that of SP one. The findings in this work can contribute to the design of thermal management device with confined porous media.

Nanoscale flow-induced nonlinear vibration of multilayer graphene based-resonators: Slip and transition flow regimes

This paper presents a nanoscale fluid-structure interaction (FSI) model for flow-induced nonlinear vibration of multilayer graphene based-resonators in the slip and transition regimes. Based on the multibeam interlayer shear model with von Kármán geometric nonlinearity and nonlocal modified couple stress theory, the size-dependent equations of motion are obtained for beam resonators laminated of NG-graphene layer and (NG−1) interlayer crosslinks. The small-scale effect on effective viscosity and slip boundary conditions of nanoscale flow is formulated by introducing the average velocity correction factor. For unbounded and bounded (by a rigid wall) nanoflows, the closed-form expressions of velocity correction factor in terms of Knudsen number, as a dimensionless discriminant parameter, are developed to correct the pressure distribution predicted by the potential theory. The present FSI model considers the size effects through the length scale parameter for microstructure local rotation, the nonlocal parameter for long-range interatomic interactions, and Knudsen number for slip condition of nanoscale flow. The Galerkin's method in conjunction with the multiple-scale perturbation technique is used to obtain closed-form solutions of frequency ratio and time-history response. The natural frequencies of cantilever multilayer graphene nanostrips are validated with the ones existing in the literature. Parametric studies are carried out to investigate the influences of small-scale, number of layers, interlayer shear modulus, and fluid characteristics on the linear and nonlinear natural frequencies. Findings show that the critical upstream speed for dynamic instability of the coupled system can change considerably by taking into account the size effects of nanoflow and nanostructures. Therefore, the classical FSI model is inadequate for analyzing nanoscale flow-induced vibration of nanoresonators. Also, it is seen that the effect of geometric nonlinearity becomes very significant for multilayer graphene beams with small interlayer shear modulus.

A comprehensive review on the flow behaviour in shale gas reservoirs: Multi‐scale, multi‐phase, and multi‐physics

AbstractAn accurate description of fluid flow is critical for the prediction of the productivity of shale gas reservoirs. In this paper, we present the current advances and a systematic summary on the fluid flow in shale gas reservoirs. First, shale pore structures, consisting of organic pores and inorganic pores ranging from nanoscale to micro‐scale, and reservoir fluids, including free gas, absorbed gas, and water, are systematically presented. Thereafter, multi‐physics flow phenomena motivated by scale effects, such as continuum flow, slip flow, transition flow, free molecular flow, and surface diffusion for gas, as well as the effective viscosity and slip boundary condition for water, are carefully summarized. Meanwhile, these flow mechanisms are discussed with molecular dynamics (MD) simulations and theoretical analysis. Subsequently, on the basis of upscaling approaches, including capillary bundle models, the lattice Boltzmann method (LBM), and pore network models (PNMs), fluid flow through heterogeneous shale matrix is reviewed and the influences of scale effects and pore structures are clarified. Additionally, shale gas well performance is discussed by combining the multiple transport mechanisms and a fracturing‐shut‐in‐flowback‐production process. Our review concluded that the fluid flow behaviour in shale gas reservoirs is a complex multi‐scale process accompanied by multi‐physical phenomena and multi‐fluid distributions. Keeping this in mind is helpful for predicting the shale gas production and recoverable gas resources. We expect this study can not only help by providing a better understanding of the fluid flow in shale reservoirs but also provide significant implications to address other multiphase flow processes.

Numerical Study on Gas Transport in Shale Kerogen with Adsorption Effect Using LBM

Gas transport and storage mechanism in gas reservoirs with complex pore size distribution play a key role in gas production. In the nano-scale, during the process of density disturbance caused by depressurization development, notable output gas collides with the wall as they convey along the channel. The continuum assumption of fluid flow is therefore invalid, and taking the influence of particles to collide with solid walls into account is necessary. The effective viscosity and slip boundary conditions were introduced in the simulation. Meanwhile, because of the adsorption effect is one of the most important intrinsic properties of shale, the impact of surface adsorption on the solid wall by using Langmuir adsorption kinetics was also involved in our investigation. In this work, a unified LB model was developed for gas multiple transports and surface adsorption in nanopores. In the model, the double distribution function was employed for a coupled bulk flow and gas diffusion model. The model is valid within the range of the continuum regime to the transition regime and has been verified by the analytical solution and the results of some previously published works. The results show that (1) the driven force of the fluid, the combination coefficient of slippage and the Knudsen number of the flow have an impact on the adsorption rate, (2) adsorption effect only directly influence the local small region of the solid surface, and the induced concentration gradient makes the global concentration variation, (3) once acting the surface adsorption on the boundary, the flux falls more significant as Knudsen number increases.

Liquid film entrainment during dip coating on a saturated porous substrate

The present work examines the effect of substrate surface porosity on the coating thickness and meniscus profile during dip coating under saturated porous media conditions. The classical Landau-Levich formulation is modified by encoding the influence of porosity in an effective Navier slip boundary condition at the porous substrate surface. It is shown that simplified Navier slip-based model works well for creeping flow through the porous medium. The film height profile equation is derived as a function of a rescaled capillary number (Ca‾) and a substrate permeability factor, with inertial effects neglected. Numerical solutions show that the classical 2/3rd power dependence of film thickness on capillary number is recovered only at sufficiently high Ca‾ values. As Ca‾ is decreased, a marked deviation is seen. The shrinking of the entrainment meniscus and the change in meniscus curvature are analyzed in detail. The theoretical results are also validated with a suitable experimental system.

Improved asymptotic predictions for the effective slip over a corrugated topography

• Significantly improved asymptotic predictions on effective slip in comparison to literature. • Systematic study on convergence radii of asymptotic series. • Novel use of series improvement and acceleration techniques. • Novel use of spectral analysis and symbolic computation. Accurate analytical prediction of the effective slip boundary condition in shear-driven Stokes flows directed longitudinally and transversely to a one-dimensional sinusoidal no-slip topography is explored. First, the domain perturbation technique is extended through spectral analysis and symbolic computations to obtain polynomial approximations (Taylor polynomials) of arbitrary specifiable order for the effective slip length. However, when assessed for numerical accuracy against fully-resolved numerical simulations using the finite-element-method, higher order Taylor polynomials give progressively inferior predictions in comparison to lower-order ones, unless the product of amplitude and wave-number is restricted below unity. From Domb–Sykes plots, the reason for the poor accuracy of higher order Taylor polynomials is assessed to be the finite convergence radii, approximately equaling unity, of the asymptotic power series for both longitudinal and transverse flows. For either of the flows, application of Euler transformation to the expansion parameter provide polynomial-form approximations that are accurate for amplitude values exceeding the convergence radius. The slow convergence of the Euler-transformed series can be remedied through Shanks transformation, at the cost of losing the convenience of closed forms. Finally, Padé approximants are shown to provide even more accurate but still closed-form alternatives to polynomials that work accurately at amplitudes much exceeding the above-identified convergence radii.

A lubricant boundary condition for a biological body lined by a thin heterogeneous biofilm

We study the asymptotic behavior of an incompressible viscous fluid flow in a biological body lined by a thin biological film with a cellular microstructure, varying thickness, and a heterogeneous viscosity regulated by a time random process. Letting the thickness of the film tend to zero, we derive an effective biological slip boundary condition on the boundary of the body. This law relates the tangential fluxes to the tangential velocities via a proportional coefficient corresponding to the energy of some local problem. This law describes the ability of the biological film to function as a lubricant reducing friction at the wall of the body. The tangential velocities are functions of the random trajectories of a finely concentrated biological particle.

Viscous interfacial layer formation causes electroosmotic mobility reversal in monovalent electrolytes.

We study the ion density, shear viscosity and electroosmotic mobility of an aqueous monovalent electrolyte at a charged solid surface using molecular dynamics simulations. Upon increasing the surface charge density, ions are displaced first from the diffuse layer to the outer Helmholtz layer, increasing its viscosity, and subsequently to the hydrodynamically stagnant inner Helmholtz layer. The ion redistribution causes both charge inversion and reversal of the electroosmotic mobility. Because of the surface-charge dependent interfacial hydrodynamic properties, however, the charge density of mobility reversal differs from the charge density of charge inversion, depending on the salt concentration and the chemical details of the ions and the surface. Mobility reversal cannot be described by an effective slip boundary condition alone - the spatial dependence of the viscosity is essential.

Numerical modeling of Stokes flows over a superhydrophobic surface containing gas bubbles

This paper continues the numerical modeling of Stokes flows near cavities of a superhydrophobic surface, occupied by gas bubbles, based on the Boundary Element Method (BEM). The aim of the present study is to estimate the friction reduction (pressure drop) in a microchannel with a bottom superhydrophobic surface, the texture of which is formed by a periodic system of striped rectangular microcavities containing compressible gas bubbles. The model proposed takes into account the streamwise variation of the bubble shift into the cavities, caused by the longitudinal pressure gradient in the channel flow. The solution for the macroscopic (averaged) flow in the microchannel, constructed using an effective slip boundary condition on the superhydrophobic bottom wall, is matched with the solution of the Stokes problem at the microscale of a single cavity containing a gas bubble. The 2D Stokes problems of fluid flow over single cavities containing curved phase interfaces with the condition of zero shear stress are reduced to the boundary integral equations which are solved using the BEM method.

Polymer Flow Through Porous Media: Numerical Prediction of the Contribution of Slip to the Apparent Viscosity

The flow of polymer solutions in porous media is often described using Darcy’s law with an apparent viscosity capturing the observed thinning or thickening effects. While the macroscale form is well accepted, the fundamentals of the pore-scale mechanisms, their link with the apparent viscosity, and their relative influence are still a matter of debate. Besides the complex effects associated with the rheology of the bulk fluid, the flow is also deeply influenced by the mechanisms occurring close to the solid/liquid interface, where polymer molecules can arrange and interact in a complex manner. In this paper, we focus on a repulsive mechanism, where polymer molecules are pushed away from the interface, yielding a so-called depletion layer in the vicinity of the wall. This depletion layer acts as a lubricating film that may be represented by an effective slip boundary condition. Here, our goal is to provide a simple mean to evaluate the contribution of this slip effect to the apparent viscosity. To do so, we solve the pore-scale flow numerically in idealized porous media with a slip length evaluated analytically in a tube. Besides its simplicity, the advantage of our approach is also that it captures relatively well the apparent viscosity obtained from core-flood experiments, using only a limited number of inputs. Therefore, it may be useful in many applications to rapidly estimate the influence of the depletion layer effect over the macroscale flow and its relative contribution compared to other phenomena, such as non-Newtonian effects.

Modeling flow in porous media with rough surfaces: Effective slip boundary conditions and application to structured packings

Understanding and modeling flows in columns equipped with structured packings is crucial to enhance the efficiency of many processes in chemical engineering. As in most porous media, an important factor that affects the flow is the presence of rough surfaces, whether this roughness has been engineered as a texture on the corrugated sheets or is the result of hydrodynamic instabilities at the interface between a gas and a liquid phase. Here, we develop a homogenized model for flows in generic porous media with rough surfaces. First, we derive a tensorial form of an effective slip boundary condition that replaces the no-slip condition on the complex rough structure and captures surface anisotropy. Second, a Darcy-Forchheimer model is obtained using the volume averaging method to homogenize the pore-scale equations with the effective slip condition. The advantage of decomposing the upscaling in these two steps is that the effective parameters at the Darcy-scale can be calculated in a representative volume with smooth boundaries, therefore considerably simplifying mesh construction and computations. The approach is then applied to a variety of geometries, including structured packings, and compared with direct numerical solutions of the flow to evaluate its accuracy over a wide range of Reynolds number. We find that the roughness can significantly impact the flow and that this impact is accurately captured by the effective boundary condition for moderate Reynolds numbers. We further discuss the dependance of the permeability and generalized Forchheimer terms upon the Reynolds number and propose a classification into distinct regimes.

Effective slip boundary conditions for sinusoidally corrugated surfaces

Molecular dynamics simulations are used to investigate fluid structure near walls with different types of roughness. Slip depends on both large-scale changes in slope and atomic-scale corrugations that are modulated by local curvature.

Effect of Surfactant on Retention Behaviors of Polystyrene Latex Particles in Sedimentation Field-Flow Fractionation: Effective Boundary Slip Model Approach

A retention theory in sedimentation field-flow fractionation (SdFFF) was developed by exploiting the effective slip boundary condition (BC) that allows a finite velocity for particles to have at the wall, thereby alleviating the limitations set by the no-slip BC constraint bound to the standard retention theory (SRT). This led to an expression for the retention ratio R as R = (R(o) + v*(b))/(R(o) + v*(b)), where R(o) is the sterically corrected SRT retention ratio and v*(b) is the reduced boundary velocity. Then, v*(b) was modeled as v*(b) = v*(b,o)/[1 + (7K*S(o))(1/2)], where S(o) is the surfactant (FL-70) concentration and K* is the distribution coefficient associated with the langmuirian isotherm of the apparent effective mass against S(o). We applied this to study the surfactant effect on the retention behaviors of polystyrene (PS) latex beads of 170-500 nm in diameter. As a result, an empirical relation was found to hold between v*(b,o) and d(o) (estimated from R(o) at S(o) = 0) as v*(b,o) - v*(o,o)[1 - (d(c)/d(o))], where v*(o,o) is the asymptotic value of v*(b,o) in the vanishing d(c)/d(o) limit and d(c) is the cutoff value at which v*(b,o) would vanish. According to the present approach, the no-slip BC (v*(b,o) = 0) was predicted to recover when d(o) ∼ d(c), and the boundary slip effect could be significant for S(o) ≤ 0.05%, particularly for large latex beads.

Effective slip boundary conditions for arbitrary one-dimensional surfaces

AbstractIn many applications it is advantageous to construct effective slip boundary conditions, which could fully characterize flow over patterned surfaces. Here we focus on laminar shear flows over smooth anisotropic surfaces with arbitrary scalar slip $b(y)$, varying in only one direction. We derive general expressions for eigenvalues of the effective slip-length tensor, and show that the transverse component is equal to half of the longitudinal one, with a two times larger local slip, $2b(y)$. A remarkable corollary of this relation is that the flow along any direction of the one-dimensional surface can be easily determined, once the longitudinal component of the effective slip tensor is found from the known spatially non-uniform scalar slip.

Effective slip boundary conditions for arbitrary periodic surfaces: the surface mobility tensor

In a variety of applications, most notably microfluidics design, slip-based boundary conditions have been sought to characterize fluid flow over patterned surfaces. We focus on laminar shear flows over surfaces with periodic height fluctuations and/or fluctuating Navier scalar slip properties. We derive a general formula for the ‘effective slip’, which describes equivalent fluid motion at the mean surface as depicted by the linear velocity profile that arises far from it. We show that the slip and the applied stress are related linearly through a tensorial mobility matrix, and the method of domain perturbation is then used to derive an approximate formula for the mobility law directly in terms of surface properties. The specific accuracy of the approximation is detailed, and the mobility relation is then utilized to address several questions, such as the determination of optimal surface shapes and the effect of random surface fluctuations on fluid slip.

Thin-Film Fluid Flows over Microdecorated Surfaces: Observation of Polygonal Hydraulic Jumps

Liquid films flowing over rough substrates are influenced by asperities whose sizes are comparable to the film thickness. We investigate flows driven by jet impact on a regular array of micron-size posts. We show that the topography modifies the size and the shape of the observed hydraulic jumps: in addition to circular jumps, we obtain a variety of stable polygonal shapes. We rationalize our results by considering a leakage flow through the texture and the free-surface flow above it, coupled by an effective slip boundary condition accounting for the symmetry of the texture. This model is in good agreement with our experiments and allows us to account for the interplay between flow properties and roughness parameters, which has applicability in many other thin-film configurations.

Stability analysis of thin film flow along a heated porous wall

The time evolution of a thin liquid film flowing down a heated solid porous substrate is investigated. Using the Navier–Stokes and Darcy–Brinkman equations in the film and the porous layer, respectively, the problem is reduced to the study of the evolution equation for the free surface of the liquid film derived through a long-wave approximation. A linear stability analysis of the base flow is performed and the critical Reynolds and Marangoni numbers are obtained. A nonlinear analysis using continuation techniques shows that the base flow yields to stationary surface structures ranging from surface waves to large amplitude structures resembling sliding drops or ridges. It is also shown under what conditions the porous layer can be replaced by an effective slip boundary condition at the liquid-solid interface. Then, the corresponding slip length is calculated from the porous layer characteristics (thickness, porosity, and Darcy number).

Effective slip boundary conditions for flows over nanoscale chemical heterogeneities

We study slip boundary conditions for simple fluids at surfaces with nanoscale chemical heterogeneities. Using a perturbative approach, we examine the flow of a Newtonian fluid far from a surface described by a heterogeneous Navier slip boundary condition. In the far field, we obtain expressions for an effective slip boundary condition in certain limiting cases. These expressions are compared to numerical solutions which show they work well when applied in the appropriate limits. The implications for experimental measurements and for the design of surfaces that exhibit large slip lengths are discussed.

Molecular dynamics study of slip at the interface between immiscible polymers.

Nonequilibrium molecular dynamics simulations were used to study the structural properties and viscous response of interfaces in binary blends of symmetric polymers. The polymers were made immiscible by increasing the repulsion between unlike species. As the repulsion increased, the interface narrowed, and the fraction of chain ends in the interfacial region increased. The viscosity in the interfacial region eta(I) was lower than the bulk viscosity, leading to an effective slip boundary condition at the interface. As the degree of immiscibility increased, the interfacial viscosity decreased, and the slip length increased. When the radius of gyration of the chains was much larger than the interfacial width, eta(I) was independent of chain length. As predicted by de Gennes and co-workers, eta(I) corresponds to the bulk viscosity of chains whose radius of gyration is proportional to the width of the interfacial region.

Slip over rough and coated surfaces

We study the effect of surface roughness and coatings on fluid flow over a solid surface. In the limit of small-amplitude roughness and thin lubricating films we are able to derive asymptotically an effective slip boundary condition to replace the no-slip condition over the surface. When the film is absent, the result is a Navier slip condition in which the slip coefficient equals the average amplitude of the roughness. When a layer of a second fluid covers the surface and acts as a lubricating film, the slip coefficient contains a term which is proportional to the viscosity ratio of the two fluids and which depends on the dynamic interaction between the film and the fluid. Limiting cases are identified in which the film dynamics can be decoupled from the outer flow.