Wall slip and wall divergence are known to have large and opposing effects on the stability of flow in a two-dimensional channel. While divergence hugely destabilises, slip dramatically stabilizes the linear mode. In a non-parallel stability analysis, we study a combination of these two effects, since both will coexist in small-scale flows with wall roughness. Our main results are (i) that the stabilising effect of slip is reversed at higher angles of divergence, (ii) transient growth of disturbances is unaffected by either wall-divergence, or by slip at any divergence. Moreover, at the Reynolds numbers relevant here, transient growth is too low to be a significant player in transition to turbulence, which is more likely to be driven by linear instability.
We performed non-equilibrium Molecular Dynamics simulations of water flow in nano-channels with the aim of discriminating {\it static} from {\it dynamic} contributions of the solid surface to the slip length of the molecular flow. We show that the regularization of the slip length divergence at high shear rates, formerly attributed to the wall dynamics, is controlled instead by its static properties. Surprisingly, we find that atomic displacements at the Angstrom scale are sufficient to remove the divergence of the slip length and realize the no-slip condition. Since surface thermal fluctuatio…
We provide a comment on "Velocity slip coefficients based on the hard-sphere Boltzmann equation" by Livio Gibelli published in Phys. Fluids 24, 022001 (2012).
We discuss possible definitions for a stochastic slip velocity that describes the relative motion between large particles and a turbulent flow. This definition is necessary because the slip velocity used in the standard drag model fails when particle size falls within the inertial subrange of ambient turbulence. We propose two definitions, selected in part due to their simplicity: they do not require filtration of the fluid phase velocity field, nor do they require the construction of conditional averages on particle locations. A key benefit of this simplicity is that the stochastic slip veloc…
Superhydrophobic surfaces have been shown to produce significant drag reduction in both laminar and turbulent flows by introducing an apparent slip velocity along an air-water interface trapped within the surface roughness. In the experiments presented within this study, we demonstrate the existence of a surface tension gradient associated with the resultant Marangoni flow along an air-water interface that causes the slip velocity and slip length to be significantly reduced. In this study, the slip velocity along a millimeter-sized air-water interface was investigated experimentally. This larg…
Symmetric drainage flow of a compressible fluid from a fracture modeled as a long narrow channel is studied on the basis of linearized compressible Navier-Stokes equations with no-slip condition. The Helmholtz decomposition theorem is used to decompose the velocity field into an irrotational part and a solenoidal part. The irrotational velocity is driven by the fluid's volumetric expansion whilst the role of the solenoidal velocity is to enforce the no-slip condition for the overall velocity and it does not contribute to the mass flow rate. It is found that at large times this no-slip flow exh…
In this work we investigate the issue of non-physical slip at wall of lattice Boltzmann simulations with the bounce-back boundary scheme. By comparing the analytical solution of two lattice models with four and nine discrete velocities for the force-driven Poiseuille flow, we are able to reveal the exact mechanism causing the issue. In fact, no boundary condition is defined by the bounce-back scheme for the the discrete velocities parallel to wall. Other factors, such as initial conditions and inlet and outlet boundary conditions, can play the role and induce the non-physical slip velocity. Th…
Molecular dynamic (MD) simulation is used to study slip at the fluid-solid boundary in an unsteady flow based on the Stokes second problem. An increase in slip is observed in comparison to the steady flow for shear rates below the critical shear rate of the corresponding steady flow. This increased slip is attributed to fluid inertial forces not represented in a steady flow. An unsteady mathematical model for slip is established, which estimates the increment in slip at the boundary. The model shows that slip is also dependent on acceleration in addition to the shear rate of fluid at the wall.…
In this work, the laminar decaying inlet swirl flow in a straight micro-pipe with wall slip is solved analytically and the solution verified numerically. Based on a fully developed parabolic axial velocity profiles, the swirl velocity equation is solved by the separation of variable technique. The solution is expressed as a function of the flow Reynolds number, the axial distance within the micro-pipe from the inlet, the wall slip and the inlet swirl velocity profile. The effects of the parameters on the swirl velocity distribution and the swirl decay are analyzed along the flow. Addition of a…
A slip model for gas flows in micro/nano-channels induced by external body forces is derived based on Maxwell's collision theory between gas molecules and the wall. The model modifies the relationship between slip velocity and velocity gradient at the walls by introducing a new parameter in addition to the classic Tangential Momentum Accommodation Coefficient. Three-dimensional Molecular Dynamics simulations of helium gas flows under uniform body force field between copper flat walls with different channel height are used to validate the model and to determine this new parameter.
We investigate the propagation of a slip front in a visco-elastic body on a rigid substrate. The body is one-dimensional, and the loading stress is applied at one end. By employing a local friction law that has a quadratic form of the slip velocity and gives vanishing friction stress at vanishing velocity or above a certain velocity, we show analytically that macroscopic steady slippage and creep motion can be understood in a single framework. The critical values of the end-loading stress causing macroscopic steady slippage and the slip-front propagation velocity appear are obtained. These val…
In this work, we revisit the temporal stability of slip channel flow. Lauga & Cossu (Phys. Fluids 17, 088106 (2005)) and Min & Kim (Phys. Fluids 17, 108106 (2005)) have investigated both modal stability and non-normality of slip channel flow and concluded that the velocity slip greatly suppresses linear instability and only modestly affects the non-normality. Here we study the stability of channel flow with streamwise and spanwise slip separately as two limiting cases of anisotropic slip and explore a broader range of slip length than previous studies did. We find that, with sufficiently large…
In microfluidic applications involving high-frequency acoustic waves over a solid boundary, the Stokes boundary-layer thickness $δ$ is so small that some non-negligible slip may occur at the fluid-solid interface. This paper assesses the impact of the slip by revisiting the classical problem of steady acoustic streaming over a flat boundary with the Navier boundary condition $u|_{y=0} = L_\mathrm{s} \partial_y u|_{y=0}$, where $u$ is the velocity tangent to the boundary $y=0$, and the parameter $L_\mathrm{s}$ is the slip length. The limit outside the boundary layer provide an effective slip ve…
The lift and drag forces acting on a small, neutrally-buoyant spherical particle in a single-wall-bounded linear shear flow are examined via numerical computation. The effects of shear rate are isolated from those of slip by setting the particle velocity equal to the local fluid velocity (zero slip), and examining the resulting hydrodynamic forces as a function of separation distance. In contrast to much of the previous numerical literature, low shear Reynolds numbers are considered ($10^{-3} \lesssim Re_γ \lesssim 10^{-1}$). This shear rate range is relevant when dealing with particulate flow…
In this Letter, the 2-dimensional dense flow of polygonal particles on an incline with a flat frictional inferior boundary is analyzed by means of contact dynamics discrete element simulations, in order to develop boundary conditions for continuum models of dense granular flows. We show the evidence that the global slip phenomenon deviates significantly from simple sliding: a finite slip velocity is generally found for shear forces lower than the sliding threshold for particle-wall contacts. We determined simple scaling laws for the dependence of the slip velocity on shear rate, normal and she…
This paper has been withdrawn by the author due to the physically inconsistent assumption of constant slip velocity, instead, see a new improved model - physics/0201045.
The evolution over time of the non-linear slip behavior of a polydimethylsiloxane (PDMS) polymer melt on a weakly adsorbing surface made of short non-entangled PDMS chains densely end-grafted to the surface of a fused silica prism has been measured. The critical shear rate at which the melt enters the nonlinear slip regime has been shown to increase with time. The adsorption kinetics of the melt on the same surface has been determined independently using ellipsometry. We show that the evolution of slip can be explained by the slow adsorption of melt chains using the Brochard-de Gennes's model.
We study hydrodynamics, heat transfer and entropy generation in pressure-driven microchannel flow of a power-law fluid. Specifically, we address the effect of asymmetry in the slip boundary condition at the channel walls. Constant, uniform but unequal heat fluxes are imposed at the walls in this thermally developed flow. The effect of asymmetric slip on the velocity profile, on the wall shear stress, on the temperature distribution, on the Bejan number profiles, and on the average entropy generation and the Nusselt number are established through the numerical evaluation of exact analytical exp…
The ability to predict and/or control wall slip is a fundamental problem in the hydrodynamics of yield stress fluids, which is poorly understood to date and has important applications in bio- and micro-fluidic systems. Systematic measurements of steady flows of a simple yield stress fluid (Carbopol Ultrez 10) in a plane acrylic micro-channel are used to establish rigorous scaling laws for the wall velocity gradient and the slip velocity. By means of epi-fluorescent microscopy combined with a custom developed Digital Particle Image Velocimetry (DPIV) technique, times series of velocity fields w…
This paper studies the nature of the effective velocity boundary conditions for liquid flow over a plane boundary on which small free-slip islands are randomly distributed. It is found that, to lowest order in the area fraction $β$ covered by free-slip regions with characteristic size $a$, a macroscopic Navier-type slip condition emerges with a slip length of the order of $aβ$. The study is motivated by recent experiments which suggest that gas nano-bubbles may form on solid walls and may be responsible for the appearance of a partial slip boundary conditions for liquid flow. The results are a…
Zhu & Granick [Phys. Rev. Lett. 87, 096105 (2001)] have recently experimentally established existence of a boundary slip in a Newtonian liquid. They reported typical values of the slip length of the order of few micro-meters. In this light, the effect of introduction of the boundary slip into the theory of propagation of elastic waves in a fluid-saturated porous medium formulated by Biot is investigated. The new model should allow to fit the experimental seismic data in circumstances when Biot's theory fails, as the introduction of phenomenological dependence of the slip velocity upon frequenc…
The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been know that discrete Boltzmann model (DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation. It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential…
The direct numerical simulation of compressible fully developed turbulent Couette flow between two parallel plates with equal temperatures moving in opposite directions with some velocity was performed. The algorithm was tested on well known numerical solution for incompressible Poiseuille channel flow and found to provide its well description. The slip effects in studied flow are found to be negligibly small at the values of accommodation coefficients for velocity and temperature of the order of unity. The considerable increase of mean temperature with decreasing the accommodation coefficient…
This research paper is intended to study the nanoparticles shapes on peristalsis of Casson fluid in a channel flow by considering Joule heating effects. The study of such flows has various relevance applications in biomedical engineering and industries. Slip conditions is maintained at the velocity, temperature and nanoparticle concentration. The problem is modeled in terms of partial differential equations with suitable slip boundary conditions and then computed by using semi analytical technique known as Homotopy Analysis Method with Mathematica software. The influences of nanoparticles shap…
In a recent paper by Lasseux, Valdés-Parada and Porter (J.~Fluid~Mech. \textbf{805} (2016) 118-146), it is found that the apparent gas permeability of the porous media is a nonlinear function of the Knudsen number. However, this result is highly questionable, because the adopted Navier-Stokes equations and the first-order velocity-slip boundary condition are first-order (in terms of the Knudsen number) approximations of the Boltzmann equation and the kinetic boundary condition for rarefied gas flows. Our numerical simulations based on the Bhatnagar-Gross-Krook kinetic equation and regularized …
In this paper, we investigate the magnetohydrodynamic viscous flow with second order slip flow model over a permeable shrinking surface. We have obtained the closed form of exact solution of Navier-Stokes equations by using similarity variable technique. The effects of slip, suction and magnetic parameter have been investigated in detail. The results show that there are two solution branches, namely lower and upper solution branch. The behavior of velocity and shear stress profiles for different values of slip, suction and magnetic parameters has been discussed through graphs.
Lattice Boltzmann Method(LBM) has achieved considerable success on simulating complex flows. However, how to impose correct boundary conditions on the fluid-solid interface with complex geometries is still an open question. Here we proposed a velocity interpolation based bounce-back scheme where the ideas of interpolated bounce-back and non-equilibrium extrapolation are combined. The proposed scheme is validated by several well-defined benchmark cases. It is shown that the proposed scheme offers a better accuracy at high Reynolds number and less dependency on solids positions which may crucial…
A numerical study of two-dimensional flow past a confined circular cylinder with slip wall is performed. A dimensionless number, Knudsen number ($Kn$) is used to describe the slip length of cylinder wall. The Reynolds number ($Re$) and Knudsen number ($Kn$) ranges considered are $Re = [1, 180]$ and $Kn = [0, \infty)$, respectively. Time-averaged flow separation angle ($\bar{θ_s}$), dimensionless recirculation length ($\bar{L_s}$) and the tangential velocity ($\bar{u_τ}$) distributed on the cylinder's wall, drag coefficient ($\bar{C_d}$) and drag reduction ($DR$) are investigated. The time-aver…
We consider pressure-driven flows of electrolyte solutions in small channels or capillaries in which tracer particles are used to probe velocity profiles. Under the assumption that the double layer is thin compared to the channel dimensions, we show that the flow-induced streaming electric field can create an apparent slip velocity for the motion of the particles, even if the flow velocity still satisfies the no-slip boundary condition. In this case, tracking of particle would lead to the wrong conclusion that the no-slip boundary condition is violated. We evaluate the apparent slip length, co…
We consider the effective hydrophobicity of a periodically grooved surface immersed in liquid, with trapped shear-free bubbles protruding between the no-slip ridges at a $π/2$ contact angle. Specifically, we carry out a singular-perturbation analysis in the limit $ε\ll1$ where the bubbles are closely spaced, finding the effective slip length (normalised by the bubble radius) for longitudinal flow along the the ridges as $π/{\sqrt{2ε}}-(12/π)\ln 2 + (13π/24)\sqrt{2ε}+ o(\sqrtε)$, the small parameter $ε$ being the planform solid fraction. The square-root divergence highlights the strong hydropho…
We investigate the linear stability of plane Poiseuille flow in 2D under slip boundary conditions. The slip s is defined by the tangential velocity at the wall in units of the maximal flow velocity. As it turns out, the critical Reynolds number depends smoothly on s but increases quite rapidly.
In the present investigation, the development of axial velocity profile, the requirement for development length ($L^*_{fd}=L/D_{h}$) and the pressure drop in the entrance region of circular and parallel plate micro-channels have been critically analysed for a large range of operating conditions ($10^{-2}\le Re\le 10^{4}$, $10^{-4}\le Kn\le 0.2$ and $0\le C_2\le 0.5$). For this purpose, the conventional Navier-Stokes equations have been numerically solved using the finite volume method on non-staggered grid, while employing the second-order velocity slip condition at the wall with $C_1=1$. The …
In a variety of applications, most notably microfluidic 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 dom…
We model a slip boundary condition at fluid-solid interface of an arbitrary geometry in smoothed particle hydrodynamics and smoothed dissipative particle dynamics simulations. Under an assumption of linear profile of the tangential velocity at quasi-steady state near the interface, an arbitrary slip length $b$ can be specified and correspondingly, an artificial velocity for every boundary particle can be calculated. Therefore, $b$ as an input parameter affects the calculation of dissipative and random forces near the interface. For $b \to 0$, the no-slip is recovered while for $b \to \infty$, …
The motion of a viscous drop is investigated when the interface is fully covered with a stagnant layer of surfactant in an arbitrary unsteady Stokes flow for the low surface Péclet number limit. The effect of the interfacial slip coefficient on the behavior of the flow field is also considered. The hydrodynamic problem is solved by the solenoidal decomposition method and the drag force is computed in terms of Faxen's laws using a perturbation ansatz in powers of the surface Péclet number. The analytical expressions for the migration velocity of the drop are also obtained in powers of the surfa…
Stochastic roughness is widespread feature of natural surfaces and is an inherent by-product of most fabrication techniques. In view of rapid development of microfluidics, the important question is how this inevitable evil affects the low-Reynolds flows which are common for micro-devices. Moreover, one could potentially turn the flaw into a virtue and control the flow properties by means of specially "tuned" random roughness. In this paper we investigate theoretically the statistics of fluctuations in fluid velocity produced by the waviness irregularities at the surface of a no-slip wall. Part…
The process of breaking of inviscid incompressible flows along a rigid body with slipping boundary conditions is studied. Such slipping flows are compressible, which is the main reason for the formation of a singularity for the gradient of the velocity component parallel to rigid border. Slipping flows are studied analytically in the framework of two- and three-dimensional inviscid Prandtl equations. Criteria for a gradient catastrophe are found in both cases. For 2D Prandtl equations breaking takes place both for the parallel velocity along the boundary and for the vorticity gradient. For thr…
We propose a novel strategy for designing chaotic micromixers using curved channels confined between two flat planes. The location of the separatrix between the Dean vortices, induced by centrifugal force, is dependent on the location of the maxima of axial velocity. An asymmetry in the axial velocity profile can change the location of the separatrix. This is achieved physically by introducing slip alternatingly at the top and bottom walls. This leads to streamline crossing and Lagrangian chaos. An approximate analytical solution of the velocity field is obtained using perturbation theory. Thi…
The shear rate dependence of the slip length in thin polymer films confined between atomically flat surfaces is investigated by molecular dynamics simulations. The polymer melt is described by the bead-spring model of linear flexible chains. We found that at low shear rates the velocity profiles acquire a pronounced curvature near the wall and the absolute value of the negative slip length is approximately equal to thickness of the viscous interfacial layer. At higher shear rates, the velocity profiles become linear and the slip length increases rapidly as a function of shear rate. The gradual…
Glacier ice flow is shaped and defined by several properties, including the bedrock elevation profile and the basal slip distribution. The effect of these two basal properties can present in similar ways in the surface. For bedrock recovery this makes distinguishing between them an interesting and complex problem. The results of this paper show that in some synthetic test cases it is indeed possible to distinguish and recover both bedrock elevation and basal slip given free surface elevation and free surface velocity. The unidirectional shallow ice approximation is used to compute steady state…
A experimental study of low Reynolds numbers unsteady pipe flows of a yield stress shear thinning fluid (Carbopol- 980) is presented. The investigation of the solid-fluid transition in a rheometric flow in the presence and in the ab- sence of the wall slip reveals a coupling between the irreversible deformation states and the wall slip phenomenon. Particularly, the presence of wall slip nearly suppresses the scaling of the deformation power deficit associated to the rheological hysteresis with the rate at which the material is forced. The irreversible solid-fluid transition and the wall slip b…
A deterministic theory describing the melting of an ultrathin lubricant film between two atomically smooth solid surfaces has been developed. The lubricant state is described by introducing a parameter of excess volume that arises owing to the solid structure chaotization at its melting. The thermodynamic and shear kinds of melting are described consistently. The dependences of the stationary friction force on the lubricant temperature and the shear velocity of rubbing surfaces that move with respect to each other with a constant velocity have been analyzed. In the framework of a simple tribol…
Substantial experimental, theoretical, as well as numerical effort has been invested to understand the effect of boundary slippage in microfluidic devices. However, even though such devices are becoming increasingly important in scientific, medical, and industrial applications, a satisfactory understanding of the phenomenon is still lacking. This is due to the extremely precise experiments needed to study the problem and the large number of tunable parameters in such systems. In this paper we apply a recently introduced algorithm to implement hydrophobic fluid-wall interactions in the lattice …
