The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this Letter, we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime, the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of nonlinear diffusion described by a superfast diffusion equation for saturation with distinctive mathematical character. We obtain solutions to a moving boundary problem defined by superfast diffusion equation that robustly convey a time power law of spreading as seen in our experiments.

Generation of a dynamic contact angle in the course of wetting is a fundamental phenomenon of nature. Dynamic wetting processes have a direct impact on flows at the nanoscale, and therefore, understanding them is exceptionally important to emerging technologies. Here, we reveal the microscopic mechanism of dynamic contact angle generation. It has been demonstrated using large-scale molecular dynamics simulations of bead-spring model fluids that the main cause of local contact angle variations is the distribution of microscopic force acting at the contact line region. We were able to retrieve this elusive force with high accuracy. It has been directly established that the force distribution can be solely predicted on the basis of a general friction law for liquid flow at solid surfaces by Thompson and Troian. The relationship with the friction law provides both an explanation of the phenomenon of dynamic contact angle and a methodology for future predictions. The mechanism is intrinsically microscopic, universal, and irreducible and is applicable to a wide range of problems associated with wetting phenomena.

The fluid-mechanics community is currently divided in assessing the boundaries of applicability of the macroscopic approach to fluid mechanical problems. Can the dynamics of nanodroplets be described by the same macroscopic equations as the ones used for macro-droplets? To the greatest degree, this question should be addressed to the moving contact-line problem. The problem is naturally multiscale, where even using a slip boundary condition results in spurious numerical solutions and transcendental stagnation regions in modelling in the vicinity of the contact line. In this publication, it has been demonstrated via the mutual comparison between macroscopic modelling and molecular dynamics simulations that a small, albeit natural, change in the boundary conditions is all that is necessary to completely regularize the problem and eliminate these nonphysical effects. The limits of macroscopic approach applied to the moving contact-line problem have been tested and validated from the first microscopic principles of molecular dynamic simulations.

We have established previously, that the spreading of liquids in granular porous media at low levels of saturation, typically less than 10% of the available void space, has very distinctive features in comparison to that at higher saturation levels. In particular, we showed that the spreading is controlled by a special type of diusional process, that its physics can be captured by an equation of the super-fast diusion class, and these ndings were supported by rst-of-a-kind experiments. In this paper, we take these ndings to the next level including deeper examination and exposition of the theory, an expanded set of experiments to address scaling properties, and systematic evaluations of the predictive performance against these experimental data, keeping in mind also potential practical applications.

In this paper we use molecular dynamics to answer a classical question: how does the surface tension on a liquid/gas interface appear? After defining surface tension from the first principles and performing several consistency checks, we perform a dynamic experiment with a single simple liquid nanodroplet. At time zero, we remove all molecules of the interfacial layer, creating a fresh bare interface with the bulk arrangement of molecules. After that the system evolves towards equilibrium, and the expected surface tension is re-established. We found that the system relaxation consists of three distinct stages. First, the mechanical balance is quickly re-established. During this process the notion of surface tension is meaningless. In the second stage, the surface tension equilibrates, and the density profile broadens to a value which we call "intrinsic" interfacial width. During the third stage, the density profile continues to broaden due to capillary wave excitations, which does not however affect the surface tension. We have observed this scenario for monatomic Lennard-Jones (LJ) liquid as well as for binary LJ mixtures at different temperatures, monitoring a wide range of physical observables.

We have established the surface tension relaxation time in the liquid-solid interfaces of LennardJones (LJ) liquids by means of direct measurements in molecular dynamics (MD) simulations. The main result is that the relaxation time is found to be weakly dependent on the molecular structures used in our study and lies in such a range that in slow hydrodynamic motion the interfaces are expected to be at equilibrium. The implications of our results for the modelling of dynamic wetting processes and interpretation of dynamic contact angle data are discussed.The wetting of solid materials by a liquid is at the heart of many industrial processes and natural phenomena. The main difficulty in theoretical description and modelling of wetting processes is the formulation of boundary conditions at the moving contact line [1][2][3]. For example, the standard no-slip boundary condition of classical hydrodynamics had to be relaxed to eliminate the well-known non-integrable stress singularity at the contact line [1][2][3][4][5].The principal parameter of the theoretical description is the dynamic contact angle, which is one of the boundary conditions to determine the shape of the free surface [1][2][3]. The notion of the contact angle has two meanings in macroscopic modelling. One is apparent contact angle θ a , which is observed experimentally at some distance from the contact line defined by the resolution of experimental techniques (usually about a few µm) and another one is true contact angle θ right at the contact line. When the contact line is moving, the apparent contact angle deviates from its static values and becomes a function of velocity. For example, quite often the contactangle-velocity dependence θ a (U ) observed in experiments can be accurately described bywhere a 1 , a 2 are material parameters depending on temperature and properties of the liquid-solid combination, U is the contact-line velocity and θ 0 is the static contact angle [3]. However useful relationship (1) may be, it is neither general, due to the well known effects of nonlocality [6,7], nor it can be directly used in macroscopic modelling since it is the true contact angle which enters the boundary conditions used in macroscopic analysis. While the apparent contact angle can be experimentally observed, the true contact angle can be only inferred from theoretical considerations or from microscopic modelling such as MD simulations. This is the one of the main fundamental problems of wetting hydrodynamics, and that problem, despite decades of research, is still far from a complete understanding. The main question still remains open and debates continue: how (and why) does the true dynamic contact angle change with the contact-line velocity?The simple hypothesis that θ = θ 0 has been used in the so-called hydrodynamic theories, for example [8], where the experimentally observed changes in the apparent contact angle were attributed to viscous bending of the free surface in a mesoscopic region near the contact line. Some early observations of the menis...

A number of recent experiments suggest that, at a given wetting speed, the dynamic contact angle formed by an advancing liquid-gas interface with a solid substrate depends on the flow field and geometry near the moving contact line. In the present work, this effect is investigated in the framework of an earlier developed theory that was based on the fact that dynamic wetting is, by its very name, a process of formation of a new liquid-solid interface (newly "wetted" solid surface) and hence should be considered not as a singular problem but as a particular case from a general class of flows with forming or/and disappearing interfaces. The results demonstrate that, in the flow configuration of curtain coating, where a liquid sheet ("curtain") impinges onto a moving solid substrate, the actual dynamic contact angle indeed depends not only on the wetting speed and material constants of the contacting media, as in the so-called slip models, but also on the inlet velocity of the curtain, its height, and the angle between the falling curtain and the solid surface. In other words, for the same wetting speed the dynamic contact angle can be varied by manipulating the flow field and geometry near the moving contact line. The obtained results have important experimental implications: given that the dynamic contact angle is determined by the values of the surface tensions at the contact line and hence depends on the distributions of the surface parameters along the interfaces, which can be influenced by the flow field, one can use the overall flow conditions and the contact angle as a macroscopic multiparametric signal-response pair that probes the dynamics of the liquid-solid interface. This approach would allow one to investigate experimentally such properties of the interface as, for example, its equation of state and the rheological properties involved in the interface's response to an external torque, and would help to measure its parameters, such as the coefficient of sliding friction, the surface-tension relaxation time, and so on.

Abstract.We have established previously, in a lead-in study, that the spreading of liquids in particulate porous media at low saturation levels, characteristically less than 10% of the void space, has very distinctive features in comparison to that at higher saturation levels. In particular, we have found that the dispersion process can be accurately described by a special class of partial differential equations, the super-fast nonlinear diffusion equation. The results of mathematical modelling have demonstrated very good agreement with experimental observations. However, any enhancement of the accuracy and predictive power of the model, keeping in mind practical applications, requires the knowledge of the effective surface permeability of the constituent particles, which defines the global, macroscopic permeability of the particulate media. In the paper, we demonstrate how this quantity can be determined through the solution of the LaplaceBeltrami Dirichlet problem, we study this using the well-developed surface finite-element method.