General Slip Boundary Condition Research Articles

Imposing slip conditions on curved boundaries for 3D incompressible flows with a very high-order accurate finite volume scheme on polygonal meshes

The conventional no-slip boundary condition does not always hold in several fluid flow applications and must be replaced with appropriate slip conditions according to the wall and fluid properties. However, not only slip boundary conditions are still a subject of discussion among fluid dynamicists, but also their numerical treatment is far from being well-developed, particularly in the context of very high-order accurate methods. The complexity of these conditions significantly increases when the boundary is not aligned with the chosen coordinate system and, even more challenging, when the fluid slips along a curved boundary. The present work proposes a simple and efficient numerical treatment of general slip boundary conditions on arbitrary curved boundaries for three-dimensional fluid flow problems governed by the incompressible Navier–Stokes equations. In that regard, two critical challenges arise: (i) achieving very high-order of convergence with arbitrary curved boundaries for the classical no-slip boundary conditions and (ii) extending the developed numerical techniques to impose general slip boundary conditions. The conventional treatment of curved boundaries relies on generating curved meshes to eliminate the geometrical mismatch between the physical and computational boundaries and achieve high-order of convergence. However, such an approach requires sophisticated meshing algorithms, cumbersome quadrature rules on curved elements, and complex non-linear transformations. In contrast, the reconstruction for off-site data (ROD) method handles arbitrary curved boundaries approximated with linear piecewise elements while employing polynomial reconstructions with specific linear constraints to fulfil the prescribed boundary conditions. For that purpose, the general slip boundary conditions are reformulated on a local orthonormal basis to allow a straightforward application of the ROD method with scalar boundary conditions. The Navier–Stokes equations are discretised with a staggered finite volume method, and the numerical fluxes are computed solely on the polygonal mesh elements. Several benchmark test cases of fluid flow problems in non-trivial three-dimensional curved domains are addressed and confirm that the proposed method effectively achieves up to the eighth-order of convergence.

OpenFOAM for Francis Turbine Transients

The flexibility and fast responsiveness of hydropower systems make them a reliable solution to overcome the intermittency of renewable energy resources and balance the electrical grid. Therefore, investigating the complex flow fields during such operation is essential to increase the reliability and lifetime of future hydropower systems. The current article concerns the utilization of OpenFOAM for the numerical study of Francis turbines during transient load change operations. The details of employed models and numerical schemes are thoroughly explained. The Laplacian smoothing algorithm is applied for the deformation of the guide vane domain. The impact of different mesh diffusivity parameters on both load rejection and acceptance operations is studied. It is shown that general slip boundary conditions cannot be used for slipping points on the guide vane upper and lower surfaces. Instead, different alternatives are introduced and compared. The developed framework is tested on a high-head Francis turbine. Different transient operations are simulated and results are compared to the experimental data. It is shown that OpenFOAM can be employed as a trustworthy CFD solver for numerical investigation of Francis turbines transient operations.

An adaptive binary friction model for multicomponent gas transport in tight porous media

A new multicomponent gas transport model called the adaptive binary friction model (ABFM) was developed. The merit of the ABFM lies in the rigorous treatment of viscous slip and diffusion slip. The ABFM uses the general slip boundary condition to characterize viscous slip and thus is applicable in multiple flow regimes. The ABFM uses the Kramers and Kistemaker model to describe diffusion slip and thus satisfies Graham's law in a natural way. The ABFM also eliminates the restrictive assumptions made in previous models, such as uniform flow. Published experimental data on multicomponent gas transport were used to test the ABFM. The agreement of the ABFM results with the experimental data is good. Moreover, the ABFM can predict the transport of different gas mixtures under various conditions based on the determined pore structure parameters. Considering its versatility, the ABFM is anticipated to be useful in heterogeneous catalysis, membrane transport, etc.

Diffusioosmotic micropolar liquid flows in parallel plate microchannels subject to boundary slip

Analytical solutions to the microrotation, linear velocity, and volume flow rate are developed for electrokinetic diffusioosmotic flows of micropolar liquids in slit microchannel geometries subject to general slip boundary conditions. The macroscopic viscosity coefficients relevant to the micropolar fluid flow investigated herein are expressed as functions of the solid volume fraction to consistently reflect and better model the particle suspension microstructure of the micropolar liquid. Results obtained from systematic parametric analysis reveal that as compared to the Newtonian solutions, the forward or reversed diffusioosmotic micropolar velocity distributions as well as volume flow rates can be increased or decreased as the solid volume fraction is increased depending on the values of the microrotation boundary condition parameter and the boundary slip length. A crossover point can be defined to identify the value of the microrotation boundary condition parameter at which the flow rate magnitudes shift or change from a decreasing to an increasing dependence, or vice versa, on the increasing solid volume fraction. The value of this crossover point is increased with the introduction of finite slip lengths to the wall boundaries. Parametric regimes on the zeta potential versus diffusivity difference parameter map available for the volume flow rates to be directed towards upstream (downstream) are increased (decreased) by increasing either the solid volume fraction or the slip length, with the dependences on the solid volume fraction being diminished by introducing finite slip lengths or reducing the microrotation boundary condition parameter to zero.

Boundary Layer Flow and Heat Transfer over a Permeable Exponentially Stretching/Shrinking Sheet with Generalized Slip Velocity

In this paper, the steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is studied. The flow and heat transfer induced by stretching/shrinking sheets are important in the study of extrusion processes and is a subject of considerable interest in the contemporary literature. Appropriate similarity variables are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary (similarity) differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual (upper and lower branch) solutions are found for a certain range of the suction and stretching/shrinking parameters. Stability analysis is performed to determine which solutions are stable and physically realizable and which are not stable. The effects of suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed in detail. It is found that the introduction of the generalized slip boundary condition resulted in the reduction of the local skin friction coefficient and local Nusselt number. Finally, it is concluded from the stability analysis that the first (upper branch) solution is stable while the second (lower branch) solution is not stable.

Bugs on a Slippery Plane : Understanding the Motility of Microbial Pathogens with Mathematical Modelling.

Many pathogenic microorganisms live in close association with surfaces, typically in thin films that either arise naturally or that they themselves create. In response to this constrained environment, the cells adjust their behaviour and morphology, invoking communication channels and inducing physical phenomena that allow for rapid colonization of biomedically relevant surfaces or the promotion of virulence factors. Thus, it is very important to measure and theoretically understand the key mechanisms for the apparent advantage obtained from swimming in thin films. We discuss experimental measurements of flows around a peritrichously flagellated bacterium constrained in a thin film, derive a simplified mathematical theory and Green's functions for flows in a thin film with general slip boundary conditions, and establish connections between theoretical and experimental results. This article aims to highlight the importance of mathematics as a tool to unlock qualitative mechanisms associated with experimental observations in the medical and biological sciences.

Analytical solution to predicting gaseous mass flow rates of microchannels in a wide range of Knudsen numbers

To predict the gaseous mass flow rate of microchannels, conventional analytical solutions based on the Navier-Stokes equation or volume diffusion hydrodynamics (bivelocity hydrodynamics) associated with first-order or second-order slip boundary condition are not very successful, especially in high-Knudsen-number flow. An analytical solution which agrees with experimental data to a Knudsen number of 50 is presented in this paper. To achieve this goal, a concept of effective volume diffusion is defined. Then, with a general slip boundary condition, the gaseous mass flow rate of microchannel is derived by solving the momentum equation of this effective volume diffusion hydrodynamics. Compared with six other analytical solutions and one group of numerical solutions of the linearized Boltzmann equation, this solution is validated by three groups of experimental data. The results not only illustrate an improvement of this solution compared with other analytical solutions but also show the importance of the effective volume diffusion hydrodynamics for compressible microfluids.

Axisymmetric Stagnation-Point Flow with a General Slip Boundary Condition over a Lubricated Surface

We investigate the axisymmetric stagnation-point flow of a viscous fluid over a lubricated surface by imposing a generalized slip condition at the fluid-fluid interface. The power law non-Newtonian fluid is considered as a lubricant. The lubrication layer is thin and assumed to have a variable thickness. The transformed nonlinear ordinary differential equation governing the flow is linearized using quasilinearization. The method of superposition is adopted to convert the boundary value problem into an initial value problem and the solution is obtained numerically by using the fourth-order Runge—Kutta method. The results are discussed to see the influence of pertinent parameters. The limiting cases of Navier and no-slip boundary conditions are obtained as the special cases and found to be in excellent agreement with the existing results in the literature.

Slip at the surface of a general axi-symmetric body rotating in a viscous fluid

The rotational motion of an arbitrary axi-symmetric body in a viscous fluid is discussed using a combined analytical-numerical technique. A singularity method based on a continuous distribution of a set of Sampson spherical singularities, namely Sampsonlets, along the axis of symmetry within the body, is applied to find the general solution for the fluid velocity that satisfies the general slip boundary condition. Employing a constant and linear approximation for the density functions and applying the collocation technique to satisfy the slip boundary condition on the surface of the body, a system of linear algebraic equations is obtained to be solved numerically. The couple exerted on a prolate and oblate spheroid and on a prolate and oblate Cassini ovals is evaluated for various values of the aspect ratio a / b and for different values of the slip parameter, where a and b are the major and minor semi-axes of the particle respectively. The CPU time elapsed during numerical calculations is measured and tabulated. Numerical work shows that convergence to at least six decimal places is achieved.

STRETCHING FLOWS WITH GENERAL SLIP BOUNDARY CONDITION

General slip boundary condition is used to solve the viscous incompressible flows induced by a stretching sheet. These flow problems corresponds to the planar and axisymmetric stretching. A similarity solution is developed by shooting method using Runge–Kutta algorithm. The results are graphically displayed and discussed under the influence of slip parameter and critical shear rate. The comparison of stretching flow problem subject to Navier's boundary condition in the planar case is made with the available numerical results in the literature.

Existence of weak solutions for steady viscous fluids with general slip boundary conditions

We study the existence of weak solutions for stationary viscous fluids with general slip boundary conditions in this paper. Applying monotone operator theory, we first establish the existence result of weak solutions for an approximation problem. Then using the compactness methods and the point-wise convergence property of velocity gradients, we get the desired results.

Low Pressure Gas Percolation Characteristic in Ultra-low Permeability Porous Media

Low pressure gas percolation characteristic in ultra-low permeability porous media is investigated in this article through core flow experiments. The results show that the wall-slip layer covers more than 10% of the average porous channel radius on account of minimum pore size when the permeability is below 0.1 × 10−3μ m 2 order, and seepage behavior is contrasted to that in mid-high permeability pore media. When the gas pressure is not high enough, the flow regime turns into transitional flow instead of slip flow, and nonlinear relationship between the measured gas permeability and the reciprocal of average pressure exists. The gas measuring permeability experiment would be influenced by the non-linear relationship. If Klinkenberg-corrected method is applied to speculate the equivalent liquid permeability, the extrapolated value will become less or minus. Simultaneously, actual gas flow velocity at the outlet is beyond the calculated value with Klinkenberg formula. A new gas seepage model based on the general slip boundary condition is derived from the homogenization technique in this article. At last the flow model is examined to be suitable for representing the gas flow behavior in ultra-low permeability media and estimating the absolute permeability from single-point, steady-states measurements.

Slip velocity and velocity inversion in a cylindrical Couette flow

Velocity inversion in a nanoscale cylindrical Couette flow is investigated with the Navier-Stokes (NS) equation and molecular-dynamics (MD) simulation. With general slip boundary conditions in the NS equation, the flow can be classified into five distinct profiles. The condition of velocity inversion is explored in the whole space of four dimensionless variables of beta , slip velocity ratio u('), radius ratio a('), and angular velocity ratio omega('). MD computer simulations are performed to estimate the constitutive coefficient of the slip velocities at the walls. The flow is generated by a rotating inner wall and a stationary outer wall in conformity with the theoretical result. By varying an attraction parameter in the Lennard-Jones potential, the slip velocities can be easily controlled. The theoretical predictions are compared with the simulation results. We find that in the intermediate range of the attraction parameter the two results are quite comparable to some extent, but at both extreme values of the attraction parameter, they are quite different.

General continuum boundary conditions for miscible binary fluids from molecular dynamics simulations

Molecular dynamics simulations are used to explore the flow behavior and diffusion of miscible fluids near solid surfaces. The solid produces deviations from bulk fluid behavior that decay over a distance of the order of the fluid correlation length. Atomistic results are mapped onto two types of continuum model: Mesoscopic models that follow this decay and conventional sharp interface boundary conditions for the stress and velocity. The atomistic results, and mesoscopic models derived from them, are consistent with the conventional Marangoni stress boundary condition. However, there are deviations from the conventional Navier boundary condition that states that the slip velocity between wall and fluid is proportional to the strain rate. A general slip boundary condition is derived from the mesoscopic model that contains additional terms associated with the Marangoni stress and diffusion, and is shown to describe the atomistic simulations. The additional terms lead to strong flows when there is a concentration gradient. The potential for using this effect to make a nanomotor or pump is evaluated.

The Initial Value Problem for the Navier-Stokes Equations with General Slip Boundary Condition in Hölder Spaces

The initial-boundary value problem for the Navier-Stokes equations including the slipping on the solid boundary is considered. The unique solvability is established in Holder spaces locally in time for the three-dimensional problem and globally in time for the two-dimensional problem without so-called smallness restrictions.

The initial value problem for the non-homogeneous Navier—Stokes equations with general slip boundary condition

The initial-boundary value problem for the non-homogeneous Navier-Stokes equations including the slipping on the solid boundary is considered. The unique solvability is established locally in time for the three-dimensional problem and globally in time for the two-dimensional problem without so-called smallness restrictions.

Hydrodynamic boundary conditions and radii

A generalized hydrodynamic surface boundary condition is proposed which encompasses both kinematic and general slip boundary conditions. Use of this boundary condition in some cases results in a considerable reduction in the number of steps needed to solve a hydrodynamic problem. Epstein's expression for the friction coefficient of a rotating rough sphere is obtained using this approach. The result is applied to the experimental data of VanderHart for chloroform. This analysis gives β a = 7.3 cP and a = 1.5 Å where β is the coefficient of sliding friction and a is the hydrodynamic radius. This value of a obtained from the reorientational correlation times is consistent with the value of 1.66 Å obtained from self-diffusion data using the same β a.