In the present work experimental, numerical, and theoretical investigations of a normal drop impact onto a liquid film of finite thickness are presented. The dynamics of drop impact on liquid surfaces, the shape of the cavity, the formation and propagation of a capillary wave in the crater, and the residual film thickness on the rigid wall are determined and analyzed. The shape of the crater within the film and the uprising liquid sheet formed upon the impact are observed using a high-speed video system. The effects of various influencing parameters such as drop impact velocity, liquid film thickness and physical properties of the liquids, including viscosity and surface tension, on the time evolution of the crater formation are investigated. Complementary to experiments the direct numerical simulations of the phenomena are performed using an advanced free-surface capturing model based on a two-fluid formulation of the classical volume-of-fluid (VOF) model in the framework of the finite volume numerical method. In this model an additional convective term is introduced into the transport equation for phase fraction, contributing decisively to a sharper interface resolution. Furthermore, an analytical model for the penetration depth of the crater is developed accounting for the liquid inertia, viscosity, gravity, and surface tension. The model agrees well with the experiments at the early times of penetration far from the wall if the impact velocity is high. Finally, a scaling analysis of the residual film thickness on the wall is conducted demonstrating a good agreement with the numerical predictions.

This paper presents results of an experimental investigation of a single drop impact onto a dry, partially wettable substrate and its numerical simulation. Particularly, the drop spreading diameter and the dynamic contact angle are measured at different time instants after impact. Two surfaces, wax (low wettability) and glass (high wettability), are used to study the effect of surface wettability (static contact angle) on the impact dynamics. It is shown that existing empirical models for the dynamic contact angle (e.g., Hoffman–Voinov–Tanner law) do not predict well the change of the dynamic contact angle, especially at high capillary numbers. In addition to the experimental investigations, the drop impact was studied numerically, focusing primarily on the contact angle treatment. The singularity in the neighborhood of the moving contact line is removed from the computational domain and replaced by a local force with some dependence on the instantaneous advancing/receding contact-line velocity. The predicted time dependence of the drop spreading diameter and of the dynamic contact angle agrees well with the experimental data for both the advancing and receding phases of the impact process.

This study is devoted to a theoretical description of an unsteady laminar viscous flow in a spreading film of a Newtonian fluid. Such flow is generated by normal drop impact onto a dry substrate with high Weber and Reynolds numbers. An analytical self-similar solution for the viscous flow in the spreading drop is obtained which satisfies the full Navier–Stokes equations. The characteristic thickness of a boundary layer developed near the wall uniformly increases as a square root of time. An expression for the thickness of the boundary layer is used for the estimation of the residual film thickness formed by normal drop impact and the maximum spreading diameter. The theoretical predictions agree well with the existing experimental data. A possible explanation of the mechanism of formation of an uprising liquid sheet leading to splash is also proposed.

While there has been some significant progress in the study of piezoelectric behaviour of composite materials, the success has been primarily confined to the linear range. The linear behaviour of such a system involves issues of homogenization and many well–developed methods in the uncoupled fields can be readily extended to the coupled field. Nonlinear properties of piezoelectric materials (such as ferroelectricity) involve not only issues of homogenization but, equally importantly, the irreversible thermodynamics and physics of domain switch. This paper seeks to integrate the aspects of thermodynamics, physics and mechanics (homogenization) involved to develop a nonlinear theory for the coupled electromechanical properties of ferroelectrics. The theory starts out with the formulation of Gibbs free energy of the system at its generic state and, by considering the thermodynamic driving force and resistance force during domain switching, a kinetic equation is established to determine the volume concentration of the new domain at a given applied stress and/or electrical field. The overall strain and the overall polarization of the system are then determined. The developed theory is a coupled theory with an evolving microstructure, and is applied to calculate the nonlinear stress–strain relation and depolarization of a poled lead zirconate titanate (PZT) under a compressive stress. The calculated results display the essential features of ferroelectric behaviour, and are found to be in good quantitative accord with experimental data.