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This paper is on the motion of a neutrally buoyant but circular slip particle in a clockwise double-lid-driven square cavity. The slip flow at the particle surface is implemented by the lattice Boltzmann method with corrected slip boundary schemes. The effects of slip length (Ls), initial particle position, Reynolds number (Re), and particle size (D) are studied on the migration of the slip particle. The motion of the circular slip particle is dominated by the centrifugal and boundary-repulsion forces. The results show that the cavity center is the unique fixed point, and once the slip particle initially deviates from the cavity center, it is always stabilized at the same limit cycle. With the increase in slip length, the limit cycle of the circular slip particle is closer to the cavity boundaries, which brings a stronger centrifugal force to balance the increased boundary-confinement effect. As the slip length, Ls, exceeds 0.02D, the limit cycle forms more quickly than the circular no-slip particle. When Re increases to within 1000, the limit cycle is squashed along the leading diagonal of the cavity and pushed toward the boundaries; however, when Re increases beyond 1000, two developing secondary vortices confine the limit cycle to shrink toward the cavity center. With the increase in particle size, the enhanced boundary confinements lead to the shrinkage of the limit cycle toward the cavity center. [ABSTRACT FROM AUTHOR]

The receptivity phase located upstream from the neutral point might be significantly affected by local rarefaction effects (especially surface slip effects) in terms of the boundary-layer transition of near-space hypersonic vehicles. In this paper, the receptivity of a supersonic flat-plate boundary layer to freestream acoustic waves in no-slip and slip flows is analyzed using direct numerical simulations and linear stability theory. The Maxwell–Smoluchowski velocity-slip and temperature-jump boundary conditions are adopted at the wall to account for surface slip effects. A Mach 4.5 flow at different wall-cooling degrees is mainly analyzed, and another Mach-6 case is presented, both with freestream unit Reynolds number on the order of 1 × 10 6 /m. The main goal is to clarify the qualitative and quantitative influence of surface slip effects on the receptivity phase under different conditions. The results show that the receptivity mechanism in the slip flow is similar to that in the no-slip flow. That is, the mode S or F is excited near the leading edge due to synchronization with slow or fast acoustic waves, and the Mack second mode is excited further downstream after synchronization between modes S and F. However, the slip effects lead to distinctly quantitative differences in receptivity. The slip effects have little influence on the excitation of mode S or F near the leading edge but largely affect the evolution (intermodal exchange) of modes S and F as propagating downstream. Consequently, as for the receptivity to slow acoustic waves, the slip effects play a stabilizing role in receptivity when mode S is stable while a destabilizing role when mode S converts to the first mode in the upstream. As for receptivity to fast acoustic waves, as slip degree increases, the slip effects initially stabilize and then destabilize the receptivity, where the receptivity coefficient of the tested slip case can increase by 25% compared with the no-slip case. [ABSTRACT FROM AUTHOR]

It is widely known that a low Mach number gas flow can be approximated as incompressible at the leading order in a small Mach number expansion of the full solution. However, it has been shown recently that such an incompressible approximation becomes invalid for a semi-sealed system with no inlets and no boundary movements. Studies based on linearized compressible Navier–Stokes equations for such a system made of small capillary tubes have revealed some counter-intuitive flow characteristics such as no-slip flow with a slip-like mass flow rate. Here, we extend these works to gas drainage from a semi-sealed porous system. It is shown that gas drainage is solely driven by its volumetric expansion, and it cannot be approximated as an incompressible flow modulated by a small compressible effect. At the pore-scale, gas motion is governed by a damped rarefaction wave, and multiple scattering of the wave leads to an effective diffusion of the gas at the macroscopic scale. A large number of pore-scale simulations are performed for various pore structures, and the results are used to extract the macroscopic wave-mediated effective diffusion coefficient. Experiments are carried out to validate the wave-mediated effective diffusion model. The flow rates predicted by the effective diffusion model agree well with the experiments while results based on Darcy's law severely underestimate the flow rate. It is established that Darcy's law cannot be applied to a semi-sealed system, and no-slip flow with a slip-like flow rate is inherently embedded in the compressible Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

In this study, we investigate the laminar steady flow of a micropolar fluid along a permeable flexible surface subject to a uniform magnetic field acting normal to the surface, with wall transpiration and velocity slip at the surface. This analysis yields multiple exact solutions for the stretching/shrinking sheet, offering insights into the complex dynamics of the fluid–surface interaction. In addition, to enhance the realism of our model, we incorporate a power-law temperature distribution, providing a comprehensive understanding of the temperature profile in the context of the micropolar fluid flow. The multiplicity and existence of solutions in special cases are presented for both stretching and shrinking sheets. In particular, a unique solution is found for the stretching sheet in the cases of both suction and injection while dual solutions exist for the shrinking sheet over the range μ > μ c in suction, and no solution exist for the injection. For the skin friction, dual solutions appear in the region 0 ≤ a ≤ a c , but single solution exists for a < 0. Furthermore, dual solutions are found for the heat transfer gradient in the regions − ∞ ≤ a ≤ a c and μ c ≤ μ ≤ ∞. Moreover, this research contributes to the broader comprehension of fluid dynamics on flexible surfaces and their intricate thermal behaviors. [ABSTRACT FROM AUTHOR]

Wall-modeling techniques are frequently applied in the extension of immersed boundary methods to large eddy simulation (LES) of turbulent flows. In this paper, a dynamic slip wall model is incorporated into an immersed boundary method named the local domain-free discretization (DFD) method for implicitly filtered LES, which is based on a Robin-type boundary condition and free of a priori specified tunable coefficients and also does not rely on any assumptions about the boundary layer. The present study provides a detailed description of the implementation of the dynamic slip model in the DFD framework, including the evaluation of the velocity components at an exterior dependent node via the Robin-type boundary condition and the dynamic procedure for calculating the slip length. The non-zero slip velocity in the normal direction is imposed in a new way to satisfy on average the non-penetration of the curved wall and maintain the global mass conservation in the implicitly filtered LES. To validate the present wall-modeling LES/DFD method, a series of turbulent channel flows at various Reynolds numbers, the flow over periodic hills, and the high-Reynolds-number flow past a National Advisory Committee for Aeronautics (NACA) 4412 airfoil at near-stall conditions are simulated, and the predicted results agree well with the referenced experimental and numerical results. [ABSTRACT FROM AUTHOR]

An immersed boundary method for the thermo–fluid–structure interaction in rarefied gas flows is presented. In this method, the slip model is incorporated with the penalty feedback immersed boundary method to address the velocity and temperature jump conditions at the fluid–structure interface in rarefied gas flows within the slip-flow regime. In addition, the compressible flows governed by the Navier–Stokes equations are solved by using a high-order finite difference method; the elastic solid is solved by using the finite element method; the fluid and solid dynamics are solved independently, and the thermo–fluid–structure interaction is achieved by using a penalty feedback method in a partitioned way. To model the local rarefaction in the supersonic flow, an artificial viscosity is proposed by introducing the local Knudsen number to diffuse the sharp transition at the shock wave front. Several validations are conducted: the Poiseuille flow in a channel, the flow around a two-dimensional airfoil, a moving square cylinder in a channel, the flow around a sphere, and a moving sphere in quiescent flow. The numerical results from the present method show very good agreements with the previous published data obtained by other methods, confirming the good ability of the proposed method in handling the thermo–fluid–structure interaction in both weakly and highly compressible rarefied gas flows. Inspired by the micro/unmanned aerial vehicles in Martian exploration, the proposed method is applied to the aerodynamics of a flapping wing in rarefied gas flows in both two-dimensional and three-dimensional spaces to demonstrate the versatility of the proposed method for modeling flows involving large deformation and fluid–structure interaction. [ABSTRACT FROM AUTHOR]

In micro- and nanoscale channels, where the characteristic scale approaches or falls below the mean free path between gas molecules, flow characteristics exhibit pronounced discontinuity. In such scenarios, continuum-based models are inadequate, and adopting kinetic models based on statistical mechanics becomes imperative for accurately describing the gas transport phenomenon. This paper presents a novel steady-state discrete Boltzmann model (DBM) that is specifically tailored for non-equilibrium flows at the micro–nanoscale. Unlike the conventional DBM, the new model focuses on the evolution equation of the non-equilibrium component of the molecular velocity distribution function in the Lagrangian coordinate system, which follows the fluid micro-element. Through numerous numerical simulations, we demonstrate the effectiveness of our model in capturing gas flow characteristics across a wide spectrum of rarefaction parameters, ranging from slip flow to free molecular flow. Utilizing this new model, we initially examine the Onsager reciprocal relationship between heat flux generated by pressure gradients and mass flux resulting from temperature gradients in micro/nanochannels. Subsequently, we calculate higher-order non-equilibrium quantities up to the 10th order and make a comparison of their characteristics. Finally, we present and discuss the features of the non-equilibrium component of the molecular velocity distribution function. [ABSTRACT FROM AUTHOR]

The linear stability of the rotating disk boundary layer with surface roughness is investigated. Surface roughness is modeled using slip boundary conditions [M. Miklavčič and C. Y. Wang, Z. Angew. Math. Phys. 55, 235–246 (2004)], which establish concentric grooves, radial grooves, and isotropic roughness. The effect on the stationary crossflow and Coriolis instabilities is analyzed by applying slip conditions to the undisturbed flow and linear disturbances. This analysis builds on the work of Cooper et al. [Phys. Fluids 27, 014107 (2015)], who modeled slip effects on the base flow but applied the no-slip condition to the linear perturbations. Neutral stability curves and critical parameter settings for linearly unstable behavior are computed for several radial and azimuthal slip length settings. The application of slip on the linear disturbances has a significant impact on the flow stability. In particular, the Coriolis instability undergoes considerable destabilization in the instance of concentric grooves (i.e., radial slip) and radial grooves with sufficiently large azimuthal slip lengths. In addition, concentric grooves destabilize the crossflow instability when the radial slip length is small. Moreover, in the instance of isotropic roughness, the stabilizing effect is markedly less than the observations of Cooper et al. [Phys. Fluids 27, 014107 (2015)]. Finally, an energy analysis is undertaken to ascertain the physical mechanisms brought about by surface roughness. [ABSTRACT FROM AUTHOR]

The non-kinetic models typically offer a more straightforward approach than the complex kinetic models for microchannel gas flow problems. However, their applicability has traditionally been limited to a certain range of rarefaction. Hence, various modifications, including the slip boundary condition, non-linear viscosity, and diffusion phenomena, have been proposed. Although less explored, the wall-to-wall collision effect is also suggested for modifying the description of rarefied flow in confined areas. This paper presents a comprehensive non-kinetic approach for rarefied gas flow between parallel plates, covering a wide range of Knudsen numbers. This work integrates existing modifications and introduces new insights, specifically how gas particles specularly reflected from the walls impact the non-linear scaling functions for modifying the viscosity and diffusivity, and how to incorporate the wall-to-wall collision effect into the slip boundary condition. The uniform and cosine-law diffuse reflection models for gas–surface interaction are also compared and discussed. The proposed model is suitable for partially specular reflected gas–surface interactions and moving wall conditions, validated against classical Poiseuille and Couette flow problems. Overall, our findings expand the applicability of the non-kinetic model and enhance its accuracy in describing gas flow in confined spaces for more general conditions. [ABSTRACT FROM AUTHOR]

The linearized Bhatnagar–Gross–Krook equation is widely used to describe low-speed rarefied gas flows and can be solved numerically using deterministic methods such as the discrete velocity method (DVM). With the help of physics-informed neural networks (PINNs), which have experienced rapid development in recent years, we develop a new surrogate model that combines the PINNs and DVM methods (PINN–DVM) to simulate rarefied gas flows. In the proposed PINN–DVM model, the linearized Bhatnagar–Gross–Krook equation is directly encoded into the residual of an artificial neural network. A new loss function for the boundary condition based on the impermeable diffusion model is proposed to accurately capture the velocity slip and temperature jump at the boundary. PINN–DVM overcomes the limitations of conventional numerical methods, such as complex mesh generation and derivative calculations. Furthermore, the proposed model is enhanced by a self-adaptive strategy based on the neural tangent kernel, which enables the loss weight for each component of the loss function to be adjusted adaptively. Four representative numerical cases of Couette flow, Fourier heat transfer flow, triangular duct flow, and cavity flow demonstrate the superiority of the proposed PINN–DVM model in solving rarefied gas flows compared with original PINNs. [ABSTRACT FROM AUTHOR]

Large, irregular stress fluctuations under a constant applied shear rate are observed during the flow of dilute worm-like micellar solutions even at low Reynolds numbers. Statistical properties of such fluctuations showing signatures of chaos and elastic turbulence have been studied extensively. Although the mechanisms like boundary slippage, dynamics of shear band interface, time-dependent secondary flows, and inertio-elastic effects are conceived as the possible factors for such striking flow properties, their contributions in different non-linear flow regimes remain poorly understood. Here, we study the Taylor–Couette flow of a well-characterized aqueous worm-like micellar system formed by 2 wt. % cetyltrimethylammonium tosylate and 100 mM sodium chloride (2 wt. % CTAT + 100 mM NaCl). For a fixed applied shear-rate just beyond the onset of shear-thinning, high-speed optical imaging in the flow-gradient plane reveals spatiotemporally varying velocity gradients in the system. In this regime, the magnitude of stress fluctuations remains insignificant. However, the fluctuation becomes substantial beyond a critical shear rate deep inside the non-linear regime of the flow curve when significant free-surface undulations, sustained stick-slip, and elastic recoil events are observed. Imaging in the flow-vorticity and the gradient-vorticity plane indicates that such dynamics are primarily driven by the elasticity-induced turbulent flows in the system. Furthermore, in this regime, we find that the characteristic persistent time of stress fluctuations matches well with the time scales of the stick-slip events, as well as the micellar breaking time, indicating a possible connection between the striking stress dynamics and the micellar kinetics. [ABSTRACT FROM AUTHOR]

We investigate the mixing of constituent components transported through a narrow fluidic cylindrical channel in a swirling flow environment. We solve for the flow field analytically using the separation of variables method under the framework of fully developed axial velocity and no-slip condition at fluid–solid interface and validate the same with numerical solution. The swirl velocity profile, which is a function of Reynolds number (Re), exhibits exponential decay along the length of the fluidic channel. We numerically solve the species transport equation for the Peclet number in the range of 102 to 104 coupled with the swirl velocity obtained for 0.1 ≤ R e ≤ 100 , by using our in-house developed code essentially for the concentration distribution in the field. As seen, an increase in the Reynolds number results in complete rotation of fluids in the pathway, which, in turn, forms an engulfment flow (onset of chaotic convection) and enhances the underlying mixing efficiency substantially. The results show that inlet swirl promotes advection dominated mixing, while the dominance of advection increases substantially for the higher Reynolds number. We show that adding a small magnitude of swirl velocity at the inlet significantly reduces the channel length required for complete mixing even after the swirl velocity has decayed completely. [ABSTRACT FROM AUTHOR]

All previous studies on the aerodynamics of bristled wings in miniature insects are based on continuum flows. However, the diameter of the bristle is very small, and the diameter-based Knudsen number (Kn) is approximately between 0.03 and 0.11, indicating that the flow around the bristle is in the slip-flow regime and rarefaction effect will be present. To investigate how the rarefaction will affect the aerodynamic force and flow field of the bristled wing, we calculated and analyzed the flow around a model bristled wing under two conditions: the continuum flow and the slip flow. The following is shown. Within the range of Kn considered in this study (0.01 ≤ Kn ≤ 0.1), the rarefaction has a very small effect on the aerodynamic force of the bristled wing: it decreases the aerodynamic force by less than 0.5% compared with that of the continuum flow. However, the rarefaction has a significant effect on the contributions of the viscous tangential and normal stress terms to the aerodynamic force: in the continuum flow, the force contribution of the viscous tangential stress is 50.7% and that of the viscous normal stress is zero, whereas in the slip flow, e.g., at Kn = 0.08, the contribution of the viscous tangential stress is only 37.7% and that of the viscous normal stress is 12.9% instead of zero; this is because the rarefaction-induced slip velocity in the slip flow changes the normal derivative of the velocity on the bristle surface compared with that of the continuum flow. Since the rarefaction has only a slight effect on the aerodynamic force, the results on the aerodynamic force of the bristled wing obtained based on continuum flows in previous studies are very good approximations to the correct results. [ABSTRACT FROM AUTHOR]

The investigation focuses on the effects of wall velocity slip on the solution of a viscous, laminar, incompressible channel flow subjected to small-scaled contraction and expansion of the weakly permeable walls. The study of such flow systems is often contextual for fluid transport in biological organisms. In the considered flow configuration, the vertically moving porous walls enable the fluid to enter or exit with a constant rate. The tangential slip velocity of the flow at the porous walls is modeled with the Navier slip boundary condition. The flow dynamics inside the channel is governed by the full Navier–Stokes equations. The Lie symmetry analysis and the invariant method are adopted to reduce the number of independent variables in the system of governing equations. Consequently, a single fourth-order ordinary differential equation is obtained, which is solved analytically by the double perturbation method and the variation of iteration method. The solutions are compared for different arrangements. Furthermore, the approximated analytical solutions are likened to the numerical solutions obtained from a fourth-order Runge–Kutta solver embedding the Shooting method to check the accuracy. It is observed that the boundary layers are formed, and the flow rapidly turns near the walls, when suction and wall contraction coexist. Alternatively, if injection and wall expansion are paired, the flow adjacent to the walls is delayed. The existence of wall velocity slip advances the near-wall velocity and cuts down the speed of centerline velocity. It results in a change in the volumetric flow rate and shear rate. The overall pressure is also varied by higher wall velocity slip. The results are explored for different values of the permeation Reynold number and the dimensionless wall dilation rate to capture all possible impacts of the flow parameters. The current analysis rectifies the existing errors in the work of Boutros et al. ["Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability,"Appl. Math. Model. 31(6), 1092–1108 (2007)] with the no-slip boundary condition and discusses the overall influences of slip boundary condition on the Lie symmetry solution of the flow system. [ABSTRACT FROM AUTHOR]

To guarantee the transporting efficiency of microdevices associated with fluid transportation, mixing, or separation and to promote the heat transfer performance of heat exchangers in microelectronics, the hydrodynamic behaviors at the unsteady state as well as the thermal characteristics at the steady state in a pressure-driven electrokinetic slip flow through a microannulus are studied. To present a more reliable prediction, the slip phenomenon at walls is incorporated. The Cauchy momentum equation applicable to all time scales is analytically solved by the integral transform method; thereby, the physical picture of how the flow is initiated and accelerated to the steady state is provided. The energy equation and entropy generation for the steady flow are numerically solved. Consequently, the temperature profile, heat transfer rate, and entropy generation rate are computed at different electrokinetic widths, slip lengths, Joule heating parameters, and Brinkman numbers; thereby, the coupling effect of the slip hydrodynamics, annular geometry, viscous dissipation, and Joule heating on thermal behaviors is explored. The unsteady flow takes a longer time to achieve the steady state for a smaller radius ratio. The slip length not only accelerates the flow but also alters the velocity and temperature profiles. Compared to the outer one, the inner slip length plays a more significant role on the entropy generation rate. The relevant discussion can serve as a theoretical guide for the operation and thermal management of flow actuation systems related to annular geometries. [ABSTRACT FROM AUTHOR]

We study the low Reynolds number hydrodynamics of a slip-stick sphere suspended in an arbitrary ambient Stokes flow, whose surface is partitioned into two regions with different slip lengths. The fore-aft symmetry of the sphere breaks due to the varied slip length over the surface, which causes translational and rotational motion of the slip-stick sphere. An analytical solution is developed using the double curl method to evaluate Faxén's formulae for the hydrodynamic drag and torque exerted on the slip-stick sphere for the sub-cases, namely, (a) cap/strip model and (b) patch model. Subsequently, we compute the flow field, velocity, and rotation rate, which strongly depend on the slip lengths and configuration of the patch. As a specific example, we consider the slip-stick sphere immersed in a Poiseuille flow. For the cap/strip model, we find an optimal configuration for which the velocity of the slip-stick sphere is maximum compared to the slip-stick sphere with uniform slip. We also find configurations for which the velocity is independent of the slip lengths. Subsequently, in the patch model, we obtain the optimal azimuthal angles for the maximum rotation rate of the slip-stick sphere. We observe near-field deviations in streamlines due to the heterogeneous nature of the surface of the slip-stick sphere. These findings help design efficient artificial passive swimmers with prescribed slip lengths. [ABSTRACT FROM AUTHOR]

Constitutive models for the dynamics of polymer solutions traditionally rely on closure relations for the extra stress or related microstructural variables (e.g., conformation tensor) linking them to flow history. In this work, we study the eigendynamics of the conformation tensor within the GENERIC framework in mesoscopic computer simulations of polymer solutions to separate the effects of nonaffine motion from other sources of non-Newtonian behavior. We observe that nonaffine motion or slip increases with both the polymer concentration and the polymer chain length. Our analysis allows to uniquely calibrate a mixed derivative of the Gordon–Schowalter type in macroscopic models based on a micro-macromapping of the dynamics of the polymeric system. The presented approach paves the way for better polymer constitutive modeling in multiscale simulations of polymer solutions, where different sources of non-Newtonian behavior are modelled independently. [ABSTRACT FROM AUTHOR]

Fluid-ion transport through a nanochannel is studied to understand the role and impact of different physical phenomena and medium properties on the flow. Mathematically, the system is described through coupled fourth order Poisson–Nernst–Planck–Bikerman and Navier–Stokes equations. The fourth order-Poisson–Nernst–Planck–Bikerman model accounts for ionic and nonionic interactions between particles, the effect of finite size of the particles, polarization of the medium, solvation of the ions, etc. Navier–Stokes equations are modified accordingly to include both electroviscous and viscoelectric effects and the velocity slip. The governing equations are discretized using the lattice Boltzmann method. The mathematical model is validated by comparing the analytical and experimental ion activity while the numerical model is validated by comparing the analytical and numerical velocity profiles for electro-osmotic flow through a microchannel. For a pressure driven flow, the electroviscous and viscoelectric effects decrease the fluid velocity while the velocity slip enhances it. The acidity of the medium also influences the fluid velocity by altering the ζ potential and ion concentration. The finite size of the particle limits the concentration of ionic species, thus, reducing electroviscous effects. As the external concentration decreases, the impact of finite size of particles also reduces. The inhomogeneous diffusion coefficient also influences electroviscous effects as it changes the concentration distribution. The variation in external pressure does not influence the impact of steric and viscoelectric effects significantly. The maximum impact is observed for ΔP = 0 (electro-osmotic flow). [ABSTRACT FROM AUTHOR]

Microchannels are important components of microelectromechanical systems (MEMSs) that encounter rarefaction effects due to their small-scale characteristics. The influence of rarefaction effects on the flow stability of microchannels should be investigated to improve MEMS performance. Based on kinetic theory, a linear stability analysis approach for low-speed rarefied flows was developed by using the Bhatnagar–Gross–Krook (BGK) model of the Boltzmann equation with an external force term. This approach was applied to study the linear temporal stability of microchannel flows. A slip flow model was introduced for comparison. The corresponding eigenvalue problem was solved with a Chebyshev collocation method. This novel approach yielded a critical Reynolds number of 5778. Analysis of the validity and accuracy of the slip flow model shows that although this model cannot capture the Knudsen layer structure, this approach effectively improves the prediction accuracy of the growth rate of the least stable mode. However, the prediction accuracy gradually decreases with increasing Knudsen number. Compared with the stability results obtained from the BGK equation, the Navier–Stokes equations-based stability analysis method always underestimates the disturbance growth rate, regardless of whether a slip flow model is used. The stability analysis results show that rarefaction effects stabilize the flow. The degree of rarefaction does not affect the trends of growth rate and phase velocity with wavenumber, nor does it affect the shape of the velocity eigenfunctions. For a rarefied case, increasing the Mach number has a destabilizing effect on low-speed microchannel flows. [ABSTRACT FROM AUTHOR]

In hydrophobic surfaces, pressure-driven flows induce electrokinetic flow retardation, where the slip length decreases due to the surface charge. In the current work, we investigate the thermal transport and fluid flow behavior of a pressure-driven flow of shear-thinning fluid with an electroviscous effect, accounting for the influence of surface charge on the slip. The electrical potential field induced in the electrical double layer (EDL), velocity, streaming potential, and temperature is obtained after solving the Poisson–Boltzmann equation, mass, momentum, and energy conservation equations without invoking the Debye–Hückel linearization. Results are presented for a broad range of dimensionless parameters, such as surface charge-independent slip length, Debye–Hückel parameter, zeta potential, heat flux, and flow consistency index (n). The flow velocity decreases after considering the effect of surface charge on slip, and such decrement is more for lower value of n, higher magnitude of zeta potential, and thicker EDL. Moreover, for lower value of n (1/3), the alteration of the Nusselt number with the surface charge is non-monotonic, whereas it increases with the surface charge magnitude for higher value of n (1/2). Further, for lower value of n, the Nusselt number enhances by the surface charge effect on the slip, whereas, for higher value of n, the trend is the opposite. Also, there is a strong interplay of the rheology of the fluid and EDL thickness in dictating the variation of the Nusselt number. [ABSTRACT FROM AUTHOR]

For flow around an isolated object, the points of zero vorticity/shear stress located at fluid–solid interface, i.e., the separation, reattachment points inclusive of forward and rear stagnation points are refered to as no-slip critical points. The total number, n (≥ 2) , of such points is an even number. For flow past a diamond-section object, it is shown here that a change of the value of n by 2 alters the nature of its rear stagnation point. The rear stagnation point acts as a separation point for n = 2, 6, 10, etc. and as an attachment point for n = 4, 8, 12, etc. A pair of hypothetical mean wakes is proposed and their viability discussed with reference to results available in literature. Concerning flow past two in-line diamond cylinders, the formation of an "anti-wake" at the leading edge of the downstream cylinder renders its forward stagnation point to act as a separation point, which, otherwise for an isolated object, invariably serves as an attachment point. The forebody and afterbody of a symmetric object act as independent entities in influencing the nature of no-slip stagnation points. [ABSTRACT FROM AUTHOR]

This article studies the anisotropic particle dispersion in a continuously forced, two-dimensional turbulent flow on a β-plane. The flow is immersed in a large-scale closed basin with free-slip walls. The anisotropy is analyzed in two sets of numerical experiments characterized by the magnitude of the imposed, time-dependent forcing (weak and strong). Both experiments exhibit typical features of zonostrophic turbulence: eddy motions that, on average, form alternating east–west circulation bands due to the β-effect. The dispersion anisotropy is investigated through three Lagrangian statistics calculated by zonal and meridional components: (i) relative dispersion between pairs of particles; (ii) dispersion ellipses; and (iii) finite-scale Lyapunov exponents (FSLE), also measured with particle pairs. In the experiment with weak forcing, the relative dispersion and dispersion ellipses show anisotropy with a zonal preference toward the west; however, the FSLE did not reveal significant anisotropy. In the experiment with strong forcing, the relative dispersion and dispersion ellipses show zonal anisotropy toward the west when the particles are far from the boundaries. As the particles reach the western wall and are redistributed to fill the domain, the anisotropy ceases. The FSLE show zonal anisotropy for a wide range of particle separations. The results are examined further by using no-slip boundary conditions and a rectangular domain geometry. [ABSTRACT FROM AUTHOR]

Viscoelasticity weakens the asymmetry of laminar shedding flow behind a blunt body in a free domain. In the present study, this finding is confirmed by four unsteady viscoelastic flows with asymmetric flow configuration, i.e., flow over an inclined flat plate with various angles of incidence, flow over a rotating circular cylinder, flow over a circular cylinder with asymmetric slip boundary distribution, and flow over an inclined row of eight equally closely spaced circular cylinders (which can be considered as a single large blunt body) through direct numerical simulation combined with the Peterlin approximation of the finitely extensible nonlinear elastic model. At high Weissenberg number, an arc shape region with high elastic stress, which is similar to shock wave, forms in the frontal area of the blunt body. This region acts as a stationary shield to separate the flow into different regions. Thus, it seems that the free stream passes this shield instead of the original blunt body. As this shield has symmetric feature, the wake flow restores symmetry. [ABSTRACT FROM AUTHOR]

A linear stability investigation is undertaken on the two-dimensional flow that develops in a channel whose walls are coated with a superhydrophobic material. The surfaces are modeled as classical slip surfaces, exploiting a linear Navier slip condition imposed on the channel walls. Both symmetric and asymmetric slip walls are considered, whereby the linearized stability of the flow is determined via an Orr–Sommerfeld normal-mode approach. In both instances, the application of slip establishes a significant stabilizing effect and increases the critical Reynolds number associated with the onset of linearly unstable behavior. Indeed, for sufficiently large slip lengths, the upper and lower branches of the neutral stability curve coalesce. Consequently, the flow becomes linearly stable to all disturbances for all wavelengths and Reynolds numbers. [ABSTRACT FROM AUTHOR]

To explore the anisotropic slip on hydrophobic surfaces, a new anisotropic slip boundary condition is proposed for three-dimensional simulations of liquid microflows using the lattice Boltzmann method with adjustable streamwise/spanwise slip length. The proposed boundary condition is derived based on the moment method, which is no longer limited to the assumption of the unidirectional steady flow. Numerical tests validated the effectiveness of the proposed method. Compared with the bounce-back and specular reflection scheme, the proposed method is more accurate and stable for capturing velocity profiles. The proposed method was applied to explore the effects of anisotropic slip on three-dimensional micro-lid-driven cavity flow. The numerical simulation results showed that the anisotropic slip has a greater influence on the flow than the pure streamwise/spanwise slip, and the streamwise slip plays a more important role in influencing the flow than the spanwise slip. The findings may hold significance for efficient development of microfluidic systems and micro-devices. [ABSTRACT FROM AUTHOR]

To achieve high speed, nano-resolution, and large stroke, a resonance/non-resonance hybrid piezoelectric stick–slip actuator with a lever-type flexure hinge (LTFH-PSSA) is proposed in this work. The actuator can achieve high speed and large stroke in the resonance mode by the stick–slip working principle and achieve nano-resolution in the non-resonant mode by the direct drive working principle. The excitation electrical signals used in the two working modes are the sine waveform and half-sine waveform, respectively. Compared with the traditional sawtooth waveform, the excitation signal of the sine and half-sine waveforms have no sudden change of voltage, which are more conducive to reduce the impact and vibration of the system. Moreover, a series of static analysis and modal analysis of the stator are carried out by the finite element method. The experimental system is built to test the output characteristics of the LTFH-PSSA. In the resonance state by the stick–slip working principle, the impedance analysis and frequency characteristic test of the LTFH-PSSA are carried out, which states that the tested resonance frequency agrees well with the simulated ones. When the locking force, the voltage, and the frequency are 2 N, 100 Vp–p, and 1850 Hz, the speed of the LTFH-PSSA is up to 52.71 mm/s, and the backward motion is suppressed completely as well. In the non-resonance state, the resolution can reach 2.19 nm and 2.69 nm in the forward and backward motion, respectively. So far, the proposed actuator ranks first in speed and resolution among all reported LTFH-PSSAs. [ABSTRACT FROM AUTHOR]

The article presents the results of studying the flow of a Newtonian fluid in a narrow wedge-shaped slot with a moving wall. A solution to the problem with slip boundary conditions on the channel walls is obtained. The influence of the slip conditions on the walls on the flow parameters is shown. In diverging and converging sections of the channel, different types of flow take place. In the region of the diverging flow near the stationary wall, a reverse flow zone is formed, the width of which increases with an increase in the Knudsen number, which is due to an increase in the flow velocity on the stationary wall due to the slip condition. Calculations elucidated the effect of slippage on the variation of the hydrostatic lifting force and hydraulic resistance in the slot channel. The dependence of the relative hydrostatic lifting force on the Knudsen number and the opening angle of the channel were revealed. It has been determined that with an increase in the Knudsen number, the magnitude of the hydrostatic lifting force decreases, since in this case the influence of the flow on the wall weakens. With an increase in the opening angle of the channel, slip effect weakens. [ABSTRACT FROM AUTHOR]

Slip flow is a common phenomenon in micro-/nano-electromechanical systems. It is well known that the mass and heat transfers in slip flow show many unique behaviors, such as the velocity slip and temperature jump near the wall. However, the kinetic understanding of slip flow is still an open problem. This paper first clarifies that the Thermodynamic Non-Equilibrium (TNE) flows can be roughly classified into two categories: near-wall TNE flows and TNE flows away from the wall. The origins of TNE in the two cases are significantly different. For the former, the TNE mainly results from the fluid–wall interaction; for the latter, the TNE is primarily due to the considerable (local) thermodynamic relaxation time. Therefore, the kinetic modeling methods for the two kinds of TNE flows are significantly different. Based on the Discrete Boltzmann Modeling (DBM) method, the non-equilibrium characteristics of mass and heat transfers in slip flow are demonstrated and investigated. The method is solidly verified by comparing with analytic solutions and experimental data. In pressure-driven flow, the DBM results are consistent with experimental data for the Knudsen number up to 0.5. It is verified that, in the slip flow regime, the linear constitutive relations with standard viscous or heat conduction coefficients are no longer applicable near the wall. For the Knudsen layer problem, it is interesting to find that a heat flux (viscous stress) component in the velocity (temperature) Knudsen layer approximates a hyperbolic sinusoidal distribution. The findings enrich the insights into the non-equilibrium characteristics of mass and heat transfers at micro-/nano-scales. [ABSTRACT FROM AUTHOR]

This paper presents the Taylor-series expansion solution of near-wall velocity and temperature for a compressible Navier–Stokes–Fourier system with a no-slip curved boundary surface. When the shear viscosity is a single-valued function of local fluid temperature, the near-wall velocity and temperature are explicitly expressed using the surface quantities including skin friction, surface pressure, surface dilatation, surface heat flux, surface temperature, surface curvature, and their relevant derivatives at the wall. In addition, the wall-normal pressure gradient at the wall is found to be contributed by three physical mechanisms including the skin friction divergence and surface dilatation effect as well as the coupled skin friction and surface heat flux with varying shear viscosity. Furthermore, without losing generality, we derive the near-wall Taylor-series expansion solution for the Lamb vector under the assumption of constant viscosities. Different physical mechanisms that are responsible for initial formation of the Lamb vector in the viscous sublayer are elucidated. The significance of the skin friction divergence and surface dilatation to the near-wall Lamb vector is highlighted. [ABSTRACT FROM AUTHOR]

We investigate flow characteristics for an electroosmotic flow of viscoelastic fluids through a hydrophobic plane microchannel, considering the coupled effect of interfacial slip and zeta potential. We employ a simplified Phan–Thien–Tanner model to describe the constitutive behavior of the fluid. The governing equations are solved analytically to obtain electric double layer (EDL) potential distribution, flow velocity, flow rate, stresses, and viscosity. We have compared the obtained analytical flow field with the established theoretical and experimental works at the limiting cases. We demonstrate that ignoring the effect of the interfacial slip on zeta potential will lead to underprediction of the flow rate, and this underprediction is amplified with the increase in the Deborah number, decrease in the EDL thickness, and increase in the slip coefficient. Moreover, the relative flow rate augmentation by the rheological behavior strictly depends on the range of slip coefficients with the change in the EDL thickness. Accordingly, we have identified three regions of the slip coefficient. In addition, the viscosity near the wall decreases with the slip coefficient for the slip dependent zeta potential model. In contrast, the normal and shear stresses are augmented with the slip coefficient. Outcomes of the present investigation may help one to understand the enhanced flow behavior for the transport of complex fluids through a hydrophobic microchannel. [ABSTRACT FROM AUTHOR]

In this paper, a systematic study on the supersonic boundary-layer modal stability for a slightly rarefied gas is conducted by considering velocity slip and temperature jump effects in the Navier–Stokes (NS) equations. The effects of slip boundary on the first- and second-mode instability at different conditions are presented in detail. The laminar flow is obtained by solving the NS equations along with no-slip and slip boundary conditions, which shows that the slip boundary causes the boundary layer becoming thinner and the supersonic region near the wall becoming narrower. The perturbation slip boundary conditions at the wall and their influence on the stability are carefully discussed. The tangential momentum accommodation coefficient and the thermal accommodation coefficient are set equal or unequal for a broad range to study the combined or leading effects of velocity slip and temperature jump, respectively. It is found that velocity slip significantly stabilizes the second-mode disturbances while largely destabilizes the first-mode perturbations. On the contrary, the temperature jump apparently enhances the second-mode instability, while it has little influence on the first mode. When velocity slip and temperature jump are both present, the first mode is more destabilized, while a competitive effect acts on the second mode. Additional results show that the neutral stability curves for the second and third modes as well as the synchronization between fast and slow modes are delayed further downstream due to velocity slip. These findings are shown consistently regardless of the wall cooling for both supersonic and hypersonic flows. [ABSTRACT FROM AUTHOR]