Molecular Dynamics Simulation of Interfacial Tension of Ultra-thin Liquid Films on a Solid Surface

The effect of wall proximity on the interfacial tension of ultra-thin liquid films of Lennard-Jones (12,6) fluid has been studied using Molecular Dynamics Simulation. The wall’s presence can potentially affect drop-wise condensation and other phase change phenomena such as boiling. Initially the LennardJones atoms are placed near a solid wall with FCC lattice structure in a doubly periodic box. Once equilibrated at a desired temperature, a thin liquid film forms on the solid wall. The surface tension of the liquid-vapor interface is computed statistically. When the film is thick ( 40 Å), surface tension at the liquidvapor interface is found to be unaffected by the presence of the solid wall and matches bulk values reported for Argon. However for thinner films ( 15 Å), surface tension of the liquid-vapor interface deviates from the macroscopic value. This has been investigated for various temperatures ranging from the triple point to the critical point. As the film thins further (1-2 molecules thickness), the liquid-vapor interface resembles a solid-vapor interface. Surface tension of this solid-vapor interface is evaluated for a solid wall modeled both by an equivalent interacted potential and discrete atoms. The two cases are found to yield different results. The Equivalent potential for the wall gives lower surface tension and liquid density near the solid wall compared to the discrete atoms case. NOMENCLATURE A Surface Area Lx Ly Lz Length of the simulation box along x y and z axes respectively R0 Lattice constant T Temperature of the system d Interfacial thickness f Force kB Boltzmann constant m Atomic mass r Separation distance between atoms rc Cutoff radius for the Lennard-Jones potential v Velocity Greek δ f Film thickness ε Lennard-Jones energy parameter εr Relative strength of the wall, εs f ε f f φ Potential function γ Surface tension ρ Density σ Lennard-Jones length parameter ψ Wall potential ∆t Time step Superscripts Non-dimensional parameters Subscripts i j Atoms index l Liquid N Normal to the interface T Tangent to the interface v Vapor 1 Copyright  2001 by ASME x Co-ordinate in the plane of interface y Co-ordinate in the plane of interface z Co-ordinate normal to interface INTRODUCTION Surface tension is an important factor in various phase change phenomenon (boiling and condensation), wetting and drying of a solid wall, and capillary effects in narrow channels. However, experimental investigation of surface tension has been limited to macroscopic study due to the difficulty of making measurements at sub-micron scale even though many processes occur at sub-micron scale, such as thin fluid film coating and micro layer dynamics underneath vapor bubble. The dynamics at these small scales need to be quantified. Surface tension can be defined thermodynamically as the isothermal work of formation of unit area of interface. However, Kirkwood and Buff [1] expressed surface tension as the integrated imbalance of normal and tangential pressures near the interface and thus enabling the evaluation of surface tension in molecular simulations. Pressure stresses are evaluated near the interface. All components of pressure tensor are the same in bulk liquid and vapor phases. However, near the interface, they differ from each other. The surface tension is computed by integrating the difference between pressure components across the interface. This method has been used extensively in the past to study the interfacial properties for Lennard-Jones fluid placed in a triply periodic box free from any external field [2; 3; 4; 10]. These studies showed that a cutoff radius of 4 5 5σ, which is significantly larger than the 2 5σ cutoff typically used, was required in addition to appropriate tail correction for the potential [6; 7] to accurately predict surface tension. However, the effect of external potential, a solid wall in our case, on surface tension has not been investigated. In this work, we study the effect of film thickness on interfacial properties. In the following sections, we derive the surface tension accounting for an externally applied potential, provide simulation details, and present and discuss results. SURFACE TENSION: WITH AN EXTERNAL FIELD Kirkwood and Buff’s expression for surface tension is γ phase2 phase1 PN z PT z dz (1) For a plane interface perpendicular to the z axis, tangential and normal pressure components are