Nonlinear wavelength selection in surface faceting under electromigration

Electromigration-induced formation of percolating adsorbate islands during condensation from the gaseous phase: a computational study

We provide a computational study of a change in the morphology of a growing thin film during condensation caused by electromigration effects. It will be shown, that separated circular adsorbate islands, realized in an isotropic system, become elongated in the direction of the applied electrical field. We discuss the dependence of the critical value of the strength of the applied electrical field, responsible for the formation of percolating adsorbate islands, on main control parameters. This study provides insight into details of electromigration effects during the self-organization of adatoms into percolating adsorbate islands during condensation from the gaseous phase. We will show that the elongated morphology of adsorbate islands remains stable if the electric field is turned off.

A Note on the Solutions for a Higher-Order Convective Cahn–Hilliard-Type Equation

The higher-order convective Cahn-Hilliard equation describes the evolution of crystal surfaces faceting through surface electromigration, the growing surface faceting, and the evolution of dynamics of phase transitions in ternary oil-water-surfactant systems. In this paper, we study the H3 solutions of the Cauchy problem and prove, under different assumptions on the constants appearing in the equation and on the mean of the initial datum, that they are well-posed.

On the Well-Posedness of A High Order Convective Cahn-Hilliard Type Equations

High order convective Cahn-Hilliard type equations describe the faceting of a growing surface, or the dynamics of phase transitions in ternary oil-water-surfactant systems. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem, associated with this equation.