Partial Slip Boundary Conditions Research Articles

Gravity-driven thin film flow of a third-grade fluid on a movable inclined plane with slip boundary condition

The prime aim and essence of this study are to present a closed-form solution of the unidirectional velocity field for thin film flow generated by a third-grade liquid moving over a fixed or movable inclined plane in the presence of partial slip boundary condition. Consideration of partial slip makes this problem different from other published research works. Here lies the novelty of this study. The nondimensional, unidirectional velocity profiles rely on the material parameter of third-grade fluid, slip parameter and initial velocity of the movable plane. Study discloses that the fluid’s velocity decelerates with raising the material property of grade-3 fluid and it accelerates with the slip parameter and initial velocity of the inclined plane. The outcomes of this study are deliberated physically at length.

Leidenfrost spheres, projectiles, and model boats: Assessing the drag reduction by superhydrophobic surfaces

Superhydrophobic surfaces are expected to reduce drag on bluff bodies moving in water due to the introduction of a thin air layer around the solid and the resulting partial slip boundary condition. The use of Leidenfrost vapor layers, sustained on the surface of a heated metal body is a reliable method to estimate the maximum drag reduction possible due to such air layers. In the past such an approach was used to estimate the drag reduction on a free-falling heated sphere, in which case the form drag is the lead component of the drag force. Here, we extend this approach to evaluate the effect of the thin gas layers on the hydrodynamic drag of free-falling streamlined projectiles and towed model boats, where the form drag is minimal, and the skin friction drag is the lead component of the drag force. By comparing the drag for streamlined bodies with and without sustained air-layers, we see only incremental drag reductions, for the sub-critical Reynolds number tested herein. The same is true for towed model boats. These results hold both for superhydrophobic surface treatments and Leidenfrost vapor layers. Thus, we concluded that for the investigated range of sub-critical Reynolds numbers, the skin friction drag is less sensitive to the effect of the thin gas layers compared to the form drag. These novel findings have important implications for the practical potential of energy savings using gas layers sustained on superhydrophobic surfaces.

CHEMICALLY REACTIVE MHD FLOW THROUGH A SLENDERING STRETCHING SHEET SUBJECTED TO NON-LINEAR RADIATION FLOW OVER A LINEAR AND NON-LINEAR STRETCHING SHEET

In this analysis, the MHD flow and nth-order dispersion of chemically reactive species over a slendering stretching sheet are studied numerically. The partial slip boundary condition and non-linear form of thermal radiation are also considered in this research. To get non-linear ordinary differential equations from the system of partial differential equations governing the flow, energy, and concentration, similarity transformations are applied. Using the shooting technique and the Runge-Kutta scheme, the resultant equations are integrated numerically. The numerical results in terms of temperature, velocity, and concentration are represented graphically. Results from this research indicate that an increase in the wall thickness parameter reduces momentum and heat transfer effects when a magnetic field is present.

Oscillations of coaxial hydrophobic spherical colloidal particles in a micropolar fluid

The microstructured flow field of a micropolar model around a straight chain of multiple hydrophobic spherical particles oscillating rectilinearly along their line of centers is studied under the conditions of low Reynolds numbers. In general, the particles can exhibit variations in both radius and amplitude of oscillations, and they are allowed to be unevenly spaced. The amplitudes are required to be small in comparison with a characteristic length, which can be considered as the radius of the larger particle. The concepts of slip length and spin slip length are introduced to characterize the partial slip and spin slip boundary conditions at the hydrophobic surfaces of the colloidal particles. The differential equations that govern the system are solved through a semi-analytical approach in combination with boundary collocation techniques. The interaction effects between the particles are assessed through the in-phase and out-of-phase drag force coefficients acting on each particle for various values of geometrical and physical parameters. The numerical schemes are carried for the case of two oscillating spherical particles. The results of this investigation indicate that the drag coefficients are notably influenced by the presence of the second particle, micropolarity, frequency, and slip parameters. The current study reveals that the impact of the micropolarity parameter is not significant on the in-phase force coefficient for slippage parameter values less than one. However, it becomes significant for slippage parameter values exceeding one. Typically, when particles oscillate in opposing modes, in-phase coefficient values surpass 1, whereas they fall below 1 when oscillating in the same mode. The present study is driven by the necessity to gain a deeper comprehension of the fluid tapping mode employed in atomic force microscope devices, especially when this mode pertains to microstructures in the vicinity of a curved surface.

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°.