The slip boundary condition in the dynamics of solid particles immersed in Stokesian flows

This paper reviews the classical theories of the dynamics of solid particles in a viscous flow via traditional Navier–Stokes/Stokes equations with slip or nonslip boundary conditions, and also studies a corresponding dynamical equation. The emphasis of this paper is on the explicit expressions of the slip effect at the solid-fluid boundary in the dynamics of solid particles in Stokesian fluids.     

Numerical investigation of relationship between water contact angle and drag reduction ratio of superhydrophobic surfaces

This paper proposes a novel bubble model to analyze drag reduction. The relationship between the slip length and air bubble height is discussed. The numerical relationship between the surface contact angle and slip length is obtained using the solid-liquid contact ratio in the Cassie equation. The surface drag reduction ratio increases by 40% at low velocities when the solid liquid contact ratio decreases from 90% to 10%. An experimental setup to study liquid/solid friction drag is reported. The drag reduction ratio for the superhydrophobic surface tested experimentally is 30%–35% at low velocities. These results are similar to the simulation results obtained at low velocities.     

A thin-film equation for viscoelastic liquids of Jeffreys type

We derive a novel thin-film equation for linear viscoelastic media describable by generalized Maxwell or Jeffreys models. As a first application of this equation we discuss the shape of a liquid rim near a dewetting front. Although the dynamics of the liquid is equivalent to that of a phenomenological model recently proposed by Herminghaus et al. (S. Herminghaus, R. Seemann, K. Jacobs, Phys. Rev. Lett. 89, 056101 (2002)), the liquid rim profile in our model always shows oscillatory behaviour, contrary to that obtained in the former. This difference in behaviour is attributed to a different treatment of slip in both models.     

Kapitza resistance at the liquid—solid interface

Using equilibrium and non-equilibrium molecular dynamics simulations, we determine the Kapitza resistance (or thermal contact resistance) at a model liquid-solid interface. The Kapitza resistance (or the associated Kapitza length) can reach appreciable values when the liquid does not wet the solid. The analogy with the hydrodynamic slip length is discussed.     

纳米通道内液体流动的滑移现象

采用分子动力学模拟方法研究了液态氩在铂纳米通道内的流动，通过改变流体和壁面之间的势能作用获得了流体和通道表面之间浸润性质不同时的滑移现象. 研究发现：液体分子在亲水性通道表面附近呈类固体性质，数密度和有序性较大，而在疏水性表面附近的平均数密度降低，形成一个低密度层；液体流动在固体表面的速度滑移随着液体与表面势能作用的增强而减小，当液体和表面的浸润性不同时可以发生滑移、表观无滑移和负滑移现象；液体在固体表面的表观滑移是液体在固体表面的速度滑移、粘附和流体内部滑移的综合作用的结果. 关键词： 纳米尺度流动 速度滑移 浸润性 分子动力学模拟     

Slip velocity during the flow of a liquid over a solid surface

An equation is derived for the slip velocity when a nonequilibrated drop is spreading over a solid surface. This velocity is obtained as the product of the force induced by the gradient of the chemical potential along the surface with Einstein’s expression for the mobility of the molecules. A similar approach was applied to the flow in a capillary. In that case, the surface diffusion coefficient evaluated by comparing the obtained theoretical expression with experiment is orders of magnitude larger than expected. For this reason, one concludes that the observed slip is apparent and is caused by the formation of a gap of gas separating the flowing liquid from the solid surface.     

Optical manipulation of microscale fluid flow

A novel optical method is used both to probe and to control dynamics in experiments on the spreading of microscale liquid films over solid substrates. The flow is manipulated by thermally induced surface-tension gradients that are regulated by controlling the absorption of light in the substrate. This approach permits, for the first time, the measurement of the dispersion relation for the well-known contact line instability; the measurements are compared with theoretical predictions from the slip model for spreading films. The experiments also demonstrate the use of feedback control to suppress instability. These results show that optical control can provide dynamically reconfigurable manipulations of fluid flow, thereby suggesting a general approach for constructing reprogrammable microfluidic devices.     

Simulation of single slip in FCC metals

The study of single slip was performed by imitation simulation and mathematical simulation methods. In a modified barrier model of constant linear tension, all stages of the process of nucleation and propagation of single crystallographic slip to the field of discrete dislocation obstacles have been simulated and investigated. The equation of dynamics of expansion of an isolated closed planar dislocation loop, which restricts slipping, was used to perform a comparative study of the effect of the mechanisms of resistance to dislocation motion on the characteristics of the resulting single slip. Micromechanical characteristics of each dislocation loop emitted by a dislocation source after loss of stability have been calculated. The time it takes for single slip to propagate up to the barrier configurations that restrict slipping and the total formative time of the crystallographic shear zone have been estimated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 57–68, January, 2006.     

Molecular kinetic theory of boundary slip on textured surfaces by molecular dynamics simulations

A theoretical model extended from the Frenkel-Eyring molecular kinetic theory (MKT) was applied to describe the boundary slip on textured surfaces. The concept of the equivalent depth of potential well was adopted to characterize the solid-liquid interactions on the textured surfaces. The slip behaviors on both chemically and topographically textured surfaces were investigated using molecular dynamics (MD) simulations. The extended MKT slip model is validated by our MD simulations under various situations, by constructing different complex surfaces and varying the surface wettability as well as the shear stress exerted on the liquid. This slip model can provide more comprehensive understanding of the liquid flow on atomic scale by considering the influence of the solid-liquid interactions and the applied shear stress on the nano-flow. Moreover, the slip velocity shear-rate dependence can be predicted using this slip model, since the nonlinear increase of the slip velocity under high shear stress can be approximated by a hyperbolic sine function.     

LAMB WAVE MODES IN A TWO-LAYERED SOLID MEDIUM WITH A WEAK INTERFACE

Using the "spring" model for a weak interface between two solids, we derive the charac-teristic equation for the Lamb waves in a two-layered solid composite and make numerical computations for dispersion curves in an aluminum/copper structure with a rigid or slip interface. The influence of the shear stiffness of the interface on the low order Lamb wave modes is considered.     

非对称纳米通道内流体流动与传热的分子动力学

采用分子动力学方法研究了流体在非对称浸润性粗糙纳米通道内的流动与传热过程,分析了两侧壁面浸润性不对称对流体速度滑移和温度阶跃的影响,以及非对称浸润性组合对流体内部热量传递的影响.研究结果表明,纳米通道主流区域的流体速度在外力作用下呈抛物线分布,但是纳米通道上下壁面浸润性不对称导致速度分布不呈中心对称,同时通道壁面的纳米结构也会限制流体的流动.流体在流动过程中产生黏性耗散,使流体温度升高.增强冷壁面的疏水性对近热壁面区域的流体速度几乎没有影响,滑移速度和滑移长度基本不变,始终为锁定边界,但是会导致近冷壁面区域的流体速度逐渐增大,对应的滑移速度和滑移长度随之增大.此时,近冷壁面区域的流体温度逐渐超过近热壁面区域的流体温度,流体出现反转温度分布,流体内部热流逆向传递.随着两侧壁面浸润性不对称程度增加,流体反转温度分布更加明显.     

Slippage and nanorheology of thin liquid polymer films

Thin liquid films on surfaces are part of our everyday life; they serve, e.g.,?as coatings or lubricants. The stability of a thin layer is governed by interfacial forces, described by the effective interface potential, and has been subject of many studies in recent decades. In recent years, the dynamics of thin liquid films has come into focus since results on the reduction of the glass transition temperature raised new questions on the behavior of especially polymeric liquids in confined geometries. The new focus was fired by theoretical models that proposed significant implication of the boundary condition at the solid/liquid interface on the dynamics of dewetting and the form of a liquid front. Our study reflects these recent developments and adds new experimental data to corroborate the theoretical models. To probe the solid/liquid boundary condition experimentally, different methods are possible, each bearing advantages and disadvantages, which will be discussed. Studying liquid flow on a variety of different substrates entails a view on the direct implications of the substrate. The experimental focus of this study is the variation of the polymer chain length; the results demonstrate that inter-chain entanglements and in particular their density close to the interface, originating from non-bulk conformations, govern the liquid slip of a polymer.     

Theoretical and numerical studies of non-equilibrium slip effects on a catalytic surface

A new concentration slip model to describe the rarefied gas effect on the species transport in microscale chemical reactors was derived from the approximate solution of the Boltzmann equation. The present model is more general and recovers the existing models in the limiting cases. The analytical results showed that the concentration slip is dominated by two different mechanisms, the reaction induced concentration slip (RIC) and the temperature slip induced concentration slip (TIC). The magnitude of RIC slip is proportional to the product of the Damköhler number and Knudsen number. The impact of the velocity, concentration and temperature slips on the coupling between the surface catalytic reactions and the homogeneous gas phase reactions was examined using the detailed chemistry of hydrogen and methane within a wide range of accommodation coefficients in a two-dimensional microscale chemical reactor. The results showed that the impact of reaction induced concentration slip (RIC) effects on catalytic reactions strongly depends on the Damköhler number, the Knudsen number and the surface accommodation coefficient. It was found that the TIC slip had a strong effect on the fuel oxidation rates and the RIC slip dramatically changed the mass fraction distributions of radicals, especially when the mass accommodation coefficients were far less than unity.     

Two half-space problems based on a synthetic-kernel model of the linearized Boltzmann equation

An analytical discrete-ordinates method is used to solve two basic half-space problems based on a new synthetic-kernel model of the linearized Boltzmann equation. In particular, Kramers’ problem and the half-space problem of thermal creep, both basic to the general area of rarefied-gas dynamics, are defined by model equations that are solved (essentially) analytically in terms of a modern version of the discrete-ordinates method. The developed algorithms are implemented to yield numerical results for the slip coefficients and the velocity and heat-flow profiles that compare well with solutions derived from much more computationally intensive techniques.     

Study of Friction between Liquid Crystals and Crystalline Surfaces by Molecular Dynamic Simulations

The lubrication characteristics of liquid crystal (LC) molecules sheared between two crystalline surfaces obtained from molecular dynamics (MD) simulations are reported in this article. We consider a coarse-grained rigid bead-necklace model of the LC molecules confined between two atomic surfaces subject to different shearing velocities. A systematic study shows that the slip length of LC lubrication changes significantly as a function of the LC-surface interaction energy, which can be well described though a theoretical curve. The slip length increases as shear rate increases at high LC-surface interaction energy. However, this trend can not be observed for low interaction energy. The orientation of the LC molecules near the surface is found to be guided by the atomics surfaces. The influence of temperature on the lubrication characteristics is also discussed in this article.     

A molecular dynamics study of effective parameters on nano-droplet surface tension

The main purpose of this paper is to numerically study the effect of droplet radius, temperature, and surface wettability on droplet surface tension. Moreover, the validity of Young-Laplace equation (Y-L) for nano-droplet is examined. Simulations of droplet surrounded by its vapor and droplet on solid surface are carried out and the results are compared to each other in order to comprehend the role of surface wettability on droplet surface tension. The pair potential for the liquid-liquid and liquid-solid interaction is considered using Lennard-Jones model. Different numbers of atoms and surface wettabilities are employed to generate droplet of different radiuses. In addition, contact angle of droplet on solid surface is computed. Pressure tensor and density profile is locally calculated. Furthermore, liquid pressure is evaluated far from the interface using the virial theorem and gas pressure is obtained using an equation of state. In order to calculate the surface tension, two different approaches are employed; Young-Laplace equation and direct molecular dynamics (MD) simulation. The surface tension increases with increase in droplet radius and it is seen that the surface wettability does not directly influence the surface tension.     

A mesoscopic model for (de)wetting

We present a mesoscopic model for simulating the dynamics of a non-volatile liquid on a solid substrate. The wetting properties of the solid can be tuned from complete wetting to total non-wetting. This model opens the way to study the dynamics of drops and liquid thin films at mesoscopic length scales of the order of the nanometer. As particular applications, we analyze the kinetics of spreading of a liquid drop wetting a solid substrate and the dewetting of a liquid film on a hydrophobic substrate. In all these cases, very good agreement is found between simulations and theoretical predictions.     

A dislocation model for the viscosity of water

A dislocation model for the shear viscosity of water is proposed, based upon the dislocation theory of melting and liquid state. This model, studied extensively within the last years in relation to phase transitions in two-dimensional systems, makes rigorous use of the similarity between the structure of a liquid and that of a crystalline solid. Viscous flow in water due to slip of dislocation loops is proposed as an alternative point of view to the hole theories and the cluster models of hydrogen bonded molecules. The model correctly yields the temperature dependence of the viscosity at normal pressure between melting and boiling point.     

Determination of Slip Length in Couette Flow Based on an Analytical Simulation Incorporating Surface Interaction

An analytical simulation based on a new model incorporating surface interaction is conducted to study the slip phenomenon in the Couette flow at different scales.The velocity profile is calculated by taking account of the micro-force between molecules and macro-force from the viscous shearing effect,as they contribute to the achievement of the slip length.The calculated results are compared with those obtained from the molecular dynamics simulation,showing an excellent agreement.Further,the effect of the shear rate on the slip is investigated.The results can well predict the fluid flow behaviors on a solid substrate,but has to be proved by experiment.     

Slip at high shear rates

There are contradictory published data on the behavior of fluid slip at high shear rates. Using three methodologies (molecular dynamics simulations, an analytical theory of slip, and a Navier-Stokes-based calculation) covering a range of fluids (bead-spring liquids, polymer solutions, and ideal gas flows) we show that as shear rate increases, the amount of slip, as measured by the slip length, asymptotes to a constant value. The results clarify the molecular mechanics of how slip occurs. Furthermore, they indicate that in this limit, molecular dynamics simulations must accurately account for heat transfer to the solid.