The movement of the triple contact line plays a crucial role in many applications such as ink-jet printing, liquid coating and drainage (imbibition) in porous media. To design accurate computational tools for these applications, predictive models of the moving contact line are needed. However, the basic mechanisms responsible for movement of the triple contact line are not well understood but still debated. We investigate the movement of the contact line between water, vapour and a silica-like solid surface under steady conditions in low capillary number regime. We use molecular dynamics (MD) with an atomistic water model to simulate a nanoscopic drop between two moving plates. We include hydrogen bonding between the water molecules and the solid substrate, which leads to a sub-molecular slip length. We benchmark two continuum methods, the Cahn-Hilliard phase-field (PF) model and a volume-of-fluid (VOF) model, against MD results. We show that both continuum models can reproduce the statistical measures obtained from MD reasonably well, with a trade-off in accuracy. We demonstrate the importance of the phase field mobility parameter and the local slip length in accurately modelling the moving contact line.
The relaxation dynamics of thermal capillary waves for nanoscale liquid films on anisotropic-slip substrates are investigated, using both molecular dynamics (MD) simulations and a Langevin model. The anisotropy of slip on substrates is achieved using a specific lattice plane of a face-centred cubic lattice. This surface's anisotropy breaks the simple scalar proportionality between slip velocity and wall shear stress and requires the introduction of a slip-coefficient tensor. The Langevin equation can describe both the growth of capillary wave spectra and the relaxation of capillary wave correl…
The influence of wall slip on the instability of a non-wetting liquid film placed on a solid substrate is analyzed in the limit of negligible inertia. In particular, we focus on the stability properties of the film, comparing the performance of the three lubrication models available in the literature, namely the weak, intermediate and strong slip models, with the Stokes equations. Since none of the aforementioned leading-order lubrication models is shown to be able to predict the growth rate of perturbations for the whole range of slipping lengths, we develop a parabolic model able to accurate…
This work studies the breakup of finite-size liquid filaments, when also including substrate effects, using direct numerical simulations. The study focuses on the effects of three parameters: Ohnesorge number, the ratio of the viscous forces to inertial and surface tension forces, the liquid filament aspect ratio, and where there is a substrate, a measure of the fluid slip on the substrate, i.e. slip length. Through these parameters, it is determined whether a liquid filament breaks up during the evolution toward its final equilibrium state. Three scenarios are identified: a collapse into a si…
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…
Hydrodynamic slip of a liquid at a solid surface represents a fundamental phenomenon in fluid dynamics that governs liquid transport at small scales. For polymeric liquids, de Gennes predicted that the Navier boundary condition together with the theory of polymer dynamics imply extraordinarily large interfacial slip for entangled polymer melts on ideal surfaces; this Navier-de Gennes model was confirmed using dewetting experiments on ultra-smooth, low-energy substrates. Here, we use capillary leveling - surface tension driven flow of films with initially non-uniform thickness - of polymeric fi…
Slip or not slip? A methodical examination of the interface formation model using two-dimensional droplet spreading on a horizontal planar substrate as a prototype system
我们认为薄的二维液滴在平面基板上的扩散作为原型系统，以比较基于Shikhmurzaev的界面形成的接触线运动的当代模型[Int. J. Multiphas. Flow 19，589（1993）]，更常用的连续流体动力学方程与Navier滑移条件增强。考虑准静态液滴演变和使用匹配渐近的方法，我们发现，使用界面形成模型的液滴半径的演变减少到一个等效的表达式为一个滑移模型，其中规定的微观动态接触角有一个速度依赖于其静态值的修正。这一结果被发现为原始的界面形成模型配方和一个更近的版本，其中从散装到表面层的质量传递占通过边界条件。在我们采用的原型系统中，还考虑了模型的各种特征，如接触线处的压力行为和滚动运动及其相关性。
We study steady-state thin films on a chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the one-dimensional steady-state solutions that exist on such substrates into six different branches and develop asymptotic estimates for the steady-states on each branch. We show using perturbation expansions, that leading order solutions provide good predictions of the steady-state thin films on stepwise-patterned substrates. The analysis in one dimension can be extended to axisymmetric solutions. We a…
The central open question about Rayleigh--Bénard convection -- buoyancy-driven flow in a fluid layer heated from below and cooled from above -- is how vertical heat flux depends on the imposed temperature gradient in the strongly nonlinear regime where the flows are typically turbulent. The quantitative challenge is to determine how the Nusselt number $Nu$ depends on the Rayleigh number $Ra$ in the $Ra\to\infty$ limit for fluids of fixed finite Prandtl number $Pr$ in fixed spatial domains. Laboratory experiments, numerical simulations, and analysis of Rayleigh's mathematical model have yet to …
The ubiquitous wall slip behavior of viscoplastic fluids renders the analysis of their steady torsional flow data to determine their yield stress and other parameters of their shear viscosity material function challenging. Roughened surfaces to prevent wall slip can be used but such methods frequently result in the fracturing of the sample. Instead, it is shown here that the yield stress of a viscoplastic fluid can be determined from the torque versus apparent shear rate data of steady torsional flow using a single gap. The step change in the slope of the torque versus apparent shear rate data…
Despite extensive studies on either smooth granular-fluid flow or the solid-like deformation at the slow limit, the change between these two extremes remains largely unexplored. By systematically investigating the fluctuations of tightly packed grains under steady shearing, we identify a transition zone with prominent stick-slip avalanches. We establish a state diagram, and propose a new dimensionless shear rate based on the speed dependence of inter-particle friction and particle size. With fluid-immersed particles confined in a fixed volume and forced to "flow" at viscous numbers $J$ decades…
We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer and capillarity. The resulting long-wave evolution equation for the droplet thickness is treated analytically via the method of matched asymptotic expansions in the limit of slow mass transfer rates, quasi-static dynamics and vanishingly small slip lengths to deduce a lower-dimensional system of integrodifferential equations for the two moving fronts. We demonstrate that the predictions of the deduced system agree excellently with simul…
Carbonous materials, such as graphene and carbon nanotube, have attracted tremendous attention in the fields of nanofluidics due to the slip at the interface between solid and liquid. The dependence of slip length for water on the types of supporting substrates and thickness of carbonous layer, which is critical for applications such as sustainable cooling of electronic devices, remains unknown. In this paper, using colloidal probe atomic force microscope, we measured the slip length of water on graphene ls supported by hydrophilic and hydrophobic substrates, i.e., SiO2 and octadecyltrimethoxy…
We experimentally investigate the evaporation characteristics of a sessile ethanol droplet containing Al$_2$O$_3$ and Cu nanoparticles of sizes 25 nm and 75 nm on a heated substrate using shadowgraphy and infrared imaging techniques. Our results demonstrate that the droplet contact line dynamics resulting from the presence of various nanoparticles plays a dominant role in the evaporation process. This is in contrast to the widely-held assumption that the enhanced evaporation rate observed in sessile nanofluid droplets is due to the higher thermal conductivity of the added nanoparticles. We obs…
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 $b \to \infty$, …
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes along the contact line. A matched asymptotics analysis is undertaken to derive a set of evolution equations for the Fourier harmonics of nearly circular contact lines, which is applicable in the long-wave limit of the Stokes equations with slip. Numerical experiments highlight the generally excellent agreement between the long-wave model and the derived equ…
A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading
