Partial Slip Boundary Conditions Research Articles

Vorticity dynamics at partial-slip boundaries

In this paper we discuss the dynamics of vorticity at partial-slip boundaries. We consider the total vector circulation, which includes both the total vorticity of the fluid and the slip velocity at the boundary (the interface vortex sheet). The generation of vector circulation is an inviscid process, which does not depend on either viscosity or the slip length at the boundary. Vector circulation is generated by the inviscid relative acceleration between the fluid and the solid, due to either tangential pressure gradients or tangential acceleration of the partial-slip wall. While the slip length does not affect the creation of vector circulation, it governs how vector circulation is distributed between the total vorticity of the fluid and the interface vortex sheet. Specifically, the partial-slip boundary condition prescribes the ratio between boundary vorticity and the strength of the interface vortex sheet, and the viscous boundary flux transfers vector circulation between the interface vortex sheet and the fluid interior to maintain this condition. The interaction between a vortex ring and a partial-slip wall is examined to highlight various aspects of this formulation. For the head-on collision, the quantity of vector circulation diffused into the fluid as secondary vorticity increases as the slip length is decreased, resulting in a stronger secondary vortex and increased rebound of the vortex ring. For the oblique interaction, the extent to which the vortex ring connects to the boundary increases as the slip length is increased.

Dual Solutions of Boundary Layer Flow and Heat Transfer in Hybrid Nanofluid over a Stretching/Shrinking Cylinder

The boundary layer flow over a stretching/shrinking cylinder in hybrid nanofluid with the effects of suction, partial slip and convective boundary condition is studied. Hybrid nanoparticles Al2O3 and TiO2 with water as based fluid are considered in the study. The partial differential equations are transformed to ordinary differential equations by employing the similarity variables. The numerical results are obtained using the bvp4c solver in MATLAB software. The influence of nanoparticles volume fraction (Al2O3-TiO2 in water-based fluid), curvature parameter, suction parameter, partial slip parameter and Biot number on the velocity profile, temperature profile, skin friction coefficient and heat transfer rate are discussed. The numerical results indicate that for shrinking surface case, the dual solutions exist for a certain range of curvature parameter and suction parameter.

Unification: Viscosity, permittivity, and hydration forces near an interface

In water-based solutions near interfaces, the hydration forces, dielectric permittivity, and viscosity depend on the short-range order in the arrangement of water molecules. The former two quantities were earlier rationalized by employing the Ginzburg–Landau expression for the solution free energy. Driven by the spirit of unification, we show that the dependence of the viscosity coefficient on the coordinate perpendicular to the interface can be rationalized in this framework as well by using in addition a linear Evans–Polanyi correlation between the activation energy determining viscosity and the solution free energy. In the conventional hydrodynamics, this effect is often formally described by introducing the partial-slip boundary conditions or a stagnant layer near interfaces. We show how the corresponding slip or stagnant-layer length can be explained and quantified.

Peristaltic mechanism in a micro wavy channel

In this article the peristaltic transport of Williamson fluid in a wavy microchannel has been discussed. Williamson fluid has number of applications in petroleum industry and power engineering. In order to determine the energy distribution, viscous dissipation is reckoned. Here we have considerd the wavelength of the wall motion much larger than the channel width to validate the theory of lubrication. For simplification of Poisson Boltzmann equation, we have applied the Debye-Hunkel linearization which is valid for small surface potential situations with zeta wall potential ≤ 25 mV. In the cases of large surface potentials, it has been found that, in comparison with the exact solution of the Poisson-Boltzmann equation, the linear solution predicts slightly lower values of the potential in the region near the wall. After a small distance from the wall, the difference between the linear solution and the exact solution diminishes. We have considered the Williamson fluid in the absence of body force. However, an external electric field has been employed. The solution of axial velocity, flow rate, pressure rise, heat transfer, mass concentration and stream functions subjected to physical partial slip boundary conditions are calculated. The effects of appropriate parameters like Debye length, Helmholtz-velocity which characterize the EDL phenomenon and external electric field are also examined. The results reveal that the peristaltic pumping varies by applying external electric field. The resulting non-linear problem has been solved analytically through the perturbation technique to analyze the distribution and change in velocity, temperature, pressure, concentration and volumetric flow rate. Results have been found through MATHEMATICA and the effects of important parameters have been discussed graphically.

Numerical investigation of silted-up dam-break flow with different silted-up sediment heights

Abstract The silted-up sediment in the reservoir may have a significant influence on the propagation of dam-break flows. In this paper, a three-dimensional numerical simulation of the silted-up dam-break flow is carried out. In this paper, simulations of three-dimensional silted-up dam-break flow are carried out. A kind of Eulerian–Eulerian two-fluid model (TFM), coupled level set and volume of fluid (CLSVOF) methods, is presented. In order to calculate the motions of the air–water interface and the sediment simultaneously, kinetic particle theory (KPT) and computational fluid dynamics (CFD) are combined. The rheology-based constitutive equations of sediment are also considered to simulate scouring and deposition. In addition, a partial-slip boundary condition (BC) for the velocity of the sediment phase at stationary walls is implemented. The simulation results of the benchmark case demonstrate that the proposed model can effectively simulate the silted-up dam-break flow while taking into account multi-interface capturing problems. Subsequently, the simulations of the silted-up dam-break flow over dry are investigated numerically in a three-dimensional long channel. The simulated results reveal that, in the dam-break flows, the silted-up sediment height has a significant influence on wave propagation, dynamic pressure loads, sediment transport, and sediment deposition.

Viscous flow through a finite-width slit: Boundary conditions and dissipation

We study the hydrodynamic viscous electronic transport in a two-dimensional sample separated into two semi-infinite planes by a one-dimensional infinite barrier. The semi-infinite planes are electrically connected via the finite-size slit in the barrier. We calculate the current through the slit assuming finite voltage drop between the planes and neglecting disorder-induced Ohmic resistance, so dissipation and resistance are purely viscosity induced. We find that the only solution to the Stokes equation in this geometry, which yields a finite dissipation at finite resistance (and, hence, is not self-contradictory), is the one that fulfills both the no-stress and no-slip boundary conditions simultaneously. As a remarkable consequence, the obtained velocity profile satisfies the so-called partial-slip (Maxwell) boundary condition for any value of the slip length, which drops out from all final results. We also calculate the electronic temperature profile for the small and large heat conductivity and find asymmetric (with respect to the barrier) temperature patterns in the former case.

Characterization of the Aeration and Hydrodynamics in Vertical-Wheel™ Bioreactors.

In this work, the oxygen transport and hydrodynamic flow of the PBS Vertical-Wheel MINI™ 0.1 bioreactor were characterized using experimental data and computational fluid dynamics simulations. Data acquired from spectroscopy-based oxygenation measurements was compared with data obtained from 3D simulations with a rigid-lid approximation and LES-WALE turbulence modeling, using the open-source software OpenFOAM-8. The mass transfer coefficients were determined for a range of stirring speeds between 10 and 100 rpm and for working volumes between 60 and 100 mL. Additionally, boundary condition, mesh refinement, and temperature variation studies were performed. Lastly, cell size, energy dissipation rate, and shear stress fields were calculated to determine optimal hydrodynamic conditions for culture. The experimental results demonstrate that the can be predicted using , with a mean absolute error of 2.08%. Using the simulations and a correction factor of 0.473, the expression can be correlated to provide equally valid results. To directly obtain them from simulations, a partial slip boundary condition can be tuned, ensuring better near-surface velocity profiles or, alternatively, by deeply refining the mesh. Temperature variation studies support the use of this correlation for temperatures up to 37 °C by using a Schmidt exponent of 1/3. Finally, the flow was characterized as transitional with diverse mixing mechanisms that ensure homogeneity and suspension quality, and the results obtained are in agreement with previous studies that employed RANS models. Overall, this work provides new data regarding oxygen mass transfer and hydrodynamics in the Vertical-Wheel bioreactor, as well as new insights for air-water mass transfer modeling in systems with low interface deformation, and a computational model that can be used for further studies.

Thermo-physical properties of fluid and gases near a solar rough rotating disk

A numerical study is assumed to analyze the small-scale influence of surface roughness near the boundary layer region of a heated rotating disk. To calculate the shear thickening and thinning behavior, we evaluate the base flow profiles and also examined the surface roughness by imposing the wall partial slip boundary conditions with radial and azimuthal anisotropic and isotropic roughness. Thermo-physical properties are adopted to study the following phenomena. Moreover, the impact of thermo-physical characteristics and solar radiation near the disk are also considered. For the transformation of governing PDEs into resultant ODEs, we consider a von Kàrmàn similarity transformation and then numerical solutions are achieved via shooting method (Runge–Kutta Fehlberg and Newton Raphson). The numerical results concerned with the base flow profiles are given physically interpreted through tables and graphs. The shear thickening and shear thinning base flow profiles are shown here. Correlations in term of velocity, temperature, and concentration are plotted graphically. The comparison of literature with present work is also presented here.

Transient Hydromagnetic Stagnation-Point Flow across a Vertical Surface with Partial Slip in a Chemically Reactive Medium

A numerical study of partial slip boundary condition is investigated. The stagnation-point flow problem involving some physio-chemical parameters has been elucidated. The process involves developing a multivariate mathematical model for the flow and transforming it into a coupled univariate equation. Key parameters of interest in the study are the buoyancy force, the surface stretching, the unsteadiness, the radiation, the dissipation effects, the slip effects, the species reaction and the magnetic field parameters. It is concluded that the impact of physio-chemical factors significantly alters the kinematics of the flow in order to optimally achieve desired product characteristics.

Qualitative analysis of magnetohydrodynamics stagnation point flow with a novel numerical approach through Shifted Chebyshev collocation method

This paper investigates the third-order nonlinear boundary value problem, resulting from the exact reduction of the Navier-Stokes equation caused by the magnetohydrodynamics boundary layer flow near a stagnation point on a rough plate. The governing partial differential equations are transformed into a nonlinear ordinary differential equation and partial slip boundary conditions by an appropriate similarity transformation. In this previous work, the boundary value problem (BVP) was investigated numerically, and a lot of speculations regarding the existence and behavior of the solutions were carried out. The primary objective of this article is to verify these speculations mathematically. In this work, we have proved that there is a unique solution for all parameters values, and further, the solution has monotonic increasing first derivative. Moreover, the resulting nonlinear boundary value problem is solved by shifted Chebyshev collocation method. We compare the present numerical results with the previous results for the particular physical parameters, concluding that the results are highly accurate. The velocity profiles and streamlines are also plotted to address the significance of the parameters. Our manuscript is a judicial mix between mathematical and numerical methods.

Diffusion-limited association of nanoparticles in fluid: Beyond the no-slip boundary conditions

In the treatments of diffusion-limited association of suspended nanoparticles (NPs), their diffusion coefficients are usually considered to be constant or depend on the interparticle distance as determined by fluid dynamics with the no-slip boundary condition. In the latter case, due to the corresponding slowdown of diffusion at short distances, the association rate constant is smaller than that calculated by ignoring this slowdown and using the diffusion coefficients corresponding to single NPs. The no-slip boundary condition can, however, be violated, and now there is evidence that it may happen more often than one could expect. In such situations, the partial-slip boundary condition is more suitable. Employing the latter boundary condition, I derive herein general integral expressions for the rate constant of association of spherically shaped NPs without and with the NP-NP interaction. Simple analytical results have been obtained in various situations.

Wall modeling for large-eddy simulation on non-body-conforming Cartesian grids

In this paper a novel methodology is proposed for wall-modeled large eddy simulation (WMLES) on non-body-conforming Cartesian grids. The proposed WMLES employs a partial-slip velocity boundary condition to reduce conservation errors at the wall. In addition, since the slip velocity reduces the shear stress in the near-wall region, a modeled turbulence shear stress is introduced to maintain the shear-stress balance in the near-wall region. The proposed WMLES robustly predicts turbulence statistics in turbulent boundary layers developed on an inclined flat plate without showing log-layer mismatch.

The Role of the Double-Layer Potential in Regularised Stokeslet Models of Self-Propulsion

The method of regularised stokeslets is widely used to model microscale biological propulsion. The method is usually implemented with only the single-layer potential, the double-layer potential being neglected, despite this formulation often not being justified a priori due to nonrigid surface deformation. We describe a meshless approach enabling the inclusion of the double layer which is applied to several Stokes flow problems in which neglect of the double layer is not strictly valid: the drag on a spherical droplet with partial-slip boundary condition, swimming velocity and rate of working of a force-free spherical squirmer, and trajectory, swimmer-generated flow and rate of working of undulatory swimmers of varying slenderness. The resistance problem is solved accurately with modest discretisation on a notebook computer with the inclusion of the double layer ranging from no-slip to free-slip limits; the neglect of the double-layer potential results in up to 24% error, confirming the importance of the double layer in applications such as nanofluidics, in which partial slip may occur. The squirming swimmer problem is also solved for both velocity and rate of working to within a small percent error when the double-layer potential is included, but the error in the rate of working is above 250% when the double layer is neglected. The undulating swimmer problem by contrast produces a very similar value of the velocity and rate of working for both slender and nonslender swimmers, whether or not the double layer is included, which may be due to the deformation’s ‘locally rigid body’ nature, providing empirical evidence that its neglect may be reasonable in many problems of interest. The inclusion of the double layer enables us to confirm robustly that slenderness provides major advantages in efficient motility despite minimal qualitative changes to the flow field and force distribution.

Diffusion of Lipid Nanovesicles Bound to a Lipid Membrane Is Associated with the Partial-Slip Boundary Condition.

During diffusion of nanoparticles bound to a cellular membrane by ligand–receptor pairs, the distance to the laterally mobile interface is sufficiently short for their motion to depend not only on the membrane-mediated diffusivity of the tethers but also in a not yet fully understood manner on nanoparticle size and interfacial hydrodynamics. By quantifying diffusivity, velocity, and size of individual membrane-bound liposomes subjected to a hydrodynamic shear flow, we have successfully separated the diffusivity contributions from particle size and number of tethers. The obtained diffusion-size relations for synthetic and extracellular lipid vesicles are not well-described by the conventional no-slip boundary condition, suggesting partial slip as well as a significant diffusivity dependence on the distance to the lipid bilayer. These insights, extending the understanding of diffusion of biological nanoparticles at lipid bilayers, are of relevance for processes such as cellular uptake of viruses and lipid nanoparticles or labeling of cell-membrane-residing molecules.

Thermal Radiation in Nanofluid Penetrable Flow Bounded with Partial Slip Condition

Thermal radiation enhances heat transfer, and it is used widely in manufacturing and materials processing applications. Thus, steady two-dimensional boundary layer flow over an exponentially porous shrinking sheet of nanofluids was considered in the influence of thermal radiation related to partial slip boundary conditions and suction. This paper aims to study the nanofluid penetrable flow over an exponentially shrinking sheet with thermal radiation and partial slip. The effects of silver (Ag) nanoparticles with two different types of base fluids named water and kerosene oil are investigated in this study. First, the governing equations and boundary conditions are transformed to a non-linear ordinary differential equation and then solved using bvp4c solver. Using Matlab software, it is found that the dual solution exists in some values from the suction parameter. Furthermore, we identified both nanoparticle volume fraction and suction parameter increase, leading to the rise in velocity profile. Moreover, the suction parameter increases both skin friction coefficient and Nusselt number increase.

Chiral propulsion: The method of effective boundary conditions

We propose to apply an “effective boundary condition” method to the problem of chiral propulsion. For the case of a rotating helix moving through a fluid at a low Reynolds number, the method amounts to replacing the original helix (in the limit of small pitch) by a cylinder, but with a special kind of partial slip boundary conditions replacing the non-slip boundary conditions on the original helix. These boundary conditions are constructed to reproduce far-field velocities of the original problem and are defined by a few parameters (slipping lengths) that can be extracted from a problem in planar rather than cylindrical geometry. We derive the chiral propulsion coefficients for spirals, helicoids, helically modulated cylinders and some of their generalizations using the introduced method. In the case of spirals, we compare our results with the ones derived by Lighthill and find a very good agreement. The proposed method is general and can be applied to any helical shape in the limit of a small pitch. We have established that for a broad class of helical surfaces the dependence of the chiral propulsion on the helical angle θ is universal, χ∼ cos θ sin 2θ with the maximal propulsion achieved at the universal angle θm=tan−1(1/2)≈35.26°.

Numerical investigation of flow around a structure using Navier-slip boundary conditions

PurposeComplicated motion of vortex is frequently observed in the wake of islands. These kinds of swirling fluid cause the trap of sediments or pollutants, subsequently inducing the dead zone, odor or poor water quality. Therefore, the understanding of flow past a circular cylinder is significant in predicting water quality and positioning the immersed structures. This study aims to investigate the flow properties around a structure using Navier-slip boundary conditions.Design/methodology/approachBoundary conditions are a major factor affecting the flow pattern because the magnitude of flow detachment on a surface can redistribute the tangential stress on the wall. Therefore, the authors performed an analysis of laminar flow passing through a circular structure to investigate the effect of boundary conditions on the flow pattern.FindingsThe authors examined the relationship between the partial-slip boundary conditions and the flow behavior at low Reynolds number past a circular cylinder considering velocity and vorticity distributions behind the cylinder, lift coefficient and Strouhal number. The amplitude of lift coefficient by the partial slip condition had relatively small value compared with that of no-slip condition, as the wall shear stress acting on the cylinder became smaller by the velocity along the cylinder surface. The frequency of the asymmetrical vortex formation with partial slip velocity was increased compared with no-slip case due to the intrinsic inertial effect of Navier-slip condition.Originality/valueThe ability to engineer slip could have dramatic influences on flow, as the viscous dominated motion can lead to large pressure drops and large axial dispersion. By the slip length control, no-slip, partial-slip and free-slip boundary conditions are tunable, and the velocity distributions at the wall, vortex formation and wake pattern including the amplitude of lift coefficient and frequency were significantly affected by slip length parameter.

General expression of aerodynamic force under different boundary conditions (slip, partial slip, no-slip)

Integral expression is derived for aerodynamic forces in unsteady separated flows of an incompressible Newtonian fluid via the characteristics of the flow on the body surface including the vortex flux generated by it. The expression obtained is valid for unsteady and steady flows under the no-slip or the partial slip boundary conditions in a viscous fluid as well as for complete slip in the case of an ideal fluid including the flows with tangential discontinuity of the velocity field. Unlike the number of existing formulas, the expression does not contain the volume integrals and is applicable for the case of multiple bodies. The expression greatly simplifies a calculation of the hydrodynamic force when using vortex meshless methods. The formula obtained satisfies the fundamental law of hydrodynamic momentum conservation. It is derived mathematically rigorously without any assumptions.

Analytical model for drag reduction on liquid-infused structured non-wetting surfaces.

Liquid-infused structured non-wetting surfaces provide alternating no-slip and partial slip boundary conditions to the fluid flow, resulting in reduced friction at the interface. In this paper, an analytical model is developed for the evaluation of effective slip and, in turn, friction factor and drag reduction on liquid-infused structured non-wetting surfaces. By considering the entire range of anisotropy and heterogeneity of the surface structures as well as the full range of partial slip offered by the infusion liquid, the present model eliminates empirical fitting or correlations that are inherent in previous studies. Based on the effective slip length, drag reduction and skin friction coefficient values for Newtonian flow between two infinite parallel plates and flow in round tubes are presented. Extension of Moody charts for non-wetting surfaces and design maps of surface meso/micro/nano texturing for achieving desired drag reduction are presented for a broad range of engineering applications. The article further presents independent validation of the model across experimental and computational data from the literature and brings together several previous studies in a unified manner.

Unsteady MHD mixed convective Casson fluid flow over a flat surface in the presence of slip

In this paper, we address a two-dimensional unsteady MHD mixed convective boundary layer flow past a flat surface of an electrically conducting Casson fluids taking radiative heat transfer. The partial slip boundary condition is imposed in the presence of suction/blowing. By adopting the continuous group of symmetry transformations, the symmetries and scaling laws are determined for the governing nonlinear partial differential equations along with boundary conditions. Finally, the set of coupled self-similar nonlinear ODEs is obtained. These equations are solved numerically for finding similar velocity and temperature for different parameter values. The effects of physical parameters on velocity and temperature are determined. The main findings are that the velocity profiles grow concavely and after reaching a critical point, the profiles overshoot by decreasing the velocity. This is due to the change of stress behavior which is an intrinsic property of the Casson fluid model. The imposition of partial slip condition on the flat surface leads to enhancement of the velocity overshoot.