Relaxation of Surface Tension in the Liquid–Solid Interfaces of Lennard-Jones Liquids

Abstract

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...

Dynamic Contact Angle at the Nanoscale: A Unified View

“…One can also rule out contributions from non-equilibrium surface tensions, in particular considering very short relaxation times of the surface phase. 29 At the same time, the MKT hypothesis about concentrated force of microscopic origin acting on the contact line is fully consistent with our results. 7,15,[19][20][21] Comparison with the MKT.…”

“…The velocity dependence of the out-off-balance force demonstrates the standard trend routinely observed in experiments on dynamic contact angle -monotonic increase with velocity increases. 12,15,17 Given that surface tension relaxation time in simple interfaces of our LJ liquids is practically zero, 29 all surface tensions of the liquid are expected to be at equilibrium values. This implies that the out-of-balance surface tension force F can only be balanced by a friction force from the substrate.…”

Pinning of the Contact Line during Evaporation on Heterogeneous Surfaces: Slowdown or Temporary Immobilization? Insights from a Nanoscale Study

“…49 In our simulations, the contact line velocity outside the jump phase is on the order of 1 nm/ns, i.e., 1 m/s. The fact that the contact angle under both equilibrium and nonequilibrium conditions can be predicted by the LCB equation again supports the idea of the local nature of interaction that drives the droplet's shape.…”

Influence of Contact-Line Curvature on the Evaporation of Nanodroplets from Solid Substrates

“…We used the droplet geometry at various stages during the evaporation to probe the dependence of its contact angle on its radius. Although Young's equation describes the shape of a droplet at equilibrium, it was recently shown that the solidliquid interface rapidly relaxes such that the interfacial tension should take its equilibrium value when the contact line moves during evaporation [25]. We assume that the droplet shape remains in quasiequilibrium as evaporation proceeds.…”