Combined Kelvin–Helmholtz and Marangoni instability and its role in formation of nanostructures under electron-beam irradiation

Abstract

This paper examines the development of nanostructural layers in silumin alloyed in electrical explosion of yttrium and processed with low-energy high-current electron beams. The study has established the electron-beam processing results in columnar structures (200 nm to 1 µm) with silicon and yttrium atoms at their boundaries. A mechanism responsible for the formation of these structures is associated with a combination of Marangoni and Kelvin–Helmholtz instabilities caused by a temperature gradient and a transverse velocity of the melt. The reported research investigates a flow of a viscous double-layered incompressible heat-conducting fluid. A first stable layer is silumin, and the other one (yttrium) moves at a velocity parallel to a base plane. Navier–Stokes and heat conductivity equations, as well as boundary conditions are given for each layer. A solution to equations has been found using the method of finite elements. The results of the study indicate the ever increasing disturbance of the interface irrespectively to a velocity. Disturbances of the interface are shown to turn into “drops” penetrating as deep as 20–60 µm at a transverse velocity of 0 m/s in a time frame from 80 to 150 µs. It is much deeper than a penetration depth of yttrium due to the diffusion mechanism. An increase of a velocity up to 4 m/s transforms a melt flow. A transformation of disturbances into drops is recorded at t>800 µs, so a stabilizing effect of Kelvin–Helmholtz instability is highlighted.