A finite element stability analysis for the Marangoni problem in a rectangular container with rigid sidewalls

Abstract

Abstract A two-dimensional rectangular box is partially filled with a fluid containing a solute which evaporates at the upper surface. The system is considered under zero-gravity. For sufficiently large Marangoni number the quiesent state becomes unstable due to surface tension effects. By aid of a Galerkin method using splines the eigenvalues and eigenvectors of the linearized system are determined. Each eigenvalue corresponds to a critical Marangoni number for a certain mode (eigenvector). The eigenvalues have been investigated as functions of the aspect ratio of the box. Two different symmetries are possible for the modes and it is shown that only eigenvalues pertaining to modes of different symmetry can coincide.