Work

Weierstrass’ variational theory for analysing meniscus stability in ribbon growth processes

Year: 2020

Type: article

Abstract: We use the method of free energy minimization to analyse static meniscus shapes for crystal ribbon growth systems. To account for the possibility of multivalued curves as solutions to the minimization problem, we choose a parametric representation of the meniscus geometry. Using Weierstrass’ form of the Euler–Lagrange equation we derive analytical solutions that provide explicit knowledge on the behavior of the meniscus shapes. Young’s contact angle and Gibbs pinning conditions are analysed and shown to be a consequence of the energy minimization problem with variable end-points. For a given ribbon growth configuration, we find that there can exist multiple static menisci that satisfy the boundary conditions. The stability of these solutions is analysed using second order variations and are found to exhibit saddle node bifurcations. We show that the arc length is a natural representation of a meniscus geometry and provides the complete solution space, not accessible through the classical variational formulation. We provide a range of operating conditions for hydro-statically feasible menisci and illustrate the transition from a stable to spill-over configuration using a simple proof of concept experiment.

Source: Journal of Crystal Growth

DOI: 10.1016/j.jcrysgro.2020.125945

Authors: Eyan P. Noronha, German A. Oliveros, B. Erik Ydstie

Institution: Carnegie Mellon University

Language: English

Topic: Solidification and crystal growth phenomena

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,900

Funders: National Science Foundation, Division of Chemical, Bioengineering, Environmental, and Transport Systems