Normal impact of a liquid drop on a dry surface: model for spreading and receding
- 8 June 2002
- journal article
- research article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 458 (2022), 1411-1430
- https://doi.org/10.1098/rspa.2001.0923
Abstract
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.Keywords
This publication has 22 references indexed in Scilit:
- Newtonian drop impact with a solid surfaceAIChE Journal, 1995
- IMPACT OF DROPS ON SOLID-SURFACES - SELF-SIMILAR CAPILLARY WAVES, AND SPLASHING AS A NEW-TYPE OF KINEMATIC DISCONTINUITYJournal of Fluid Mechanics, 1995
- On the collision of a droplet with a solid surfaceProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1991
- The deformation of a liquid drop moving normal to a plane wallJournal of Fluid Mechanics, 1990
- On the ability of drops or bubbles to stick to non-horizontal surfaces of solidsJournal of Fluid Mechanics, 1983
- The spreading of a drop by capillary actionJournal of Fluid Mechanics, 1982
- An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surfaceProceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 1981
- Splashing of water drops on solid and wetted surfaces: hydrodynamics and charge separationPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1971
- The dynamics of thin sheets of fluid II. Waves on fluid sheetsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1959
- XXVIII. On the forms assumed by drops of liquids falling vertically on a horizontal plateProceedings of the Royal Society of London, 1877