Thermocapillary instabilities in a horizontal liquid layer under partial basal slip

Kowal, K. N. , Davis, S. H. and Voorhees, P. W. (2018) Thermocapillary instabilities in a horizontal liquid layer under partial basal slip. Journal of Fluid Mechanics, 855, pp. 839-859. (doi: 10.1017/jfm.2018.684)

Abstract

We investigate the onset of three-dimensional hydrothermal waves in a low-capillarynumber liquid layer of arbitrary depth, bounded by a free liquid–gas interface from above and a partial slip, rigid surface from below. A selection of two- and threedimensional hydrothermal waves, longitudinal rolls and longitudinal travelling waves, form the preferred mode of instability, which depends intricately on the magnitude of the basal slip. Partial slip is destabilizing for all modes of instability. Specifically, the minimal Marangoni number required for the onset of instability follows Mm ∼ a(β−1 + b) −c for each mode, where a, b, c > 0 and β −1 is the slip parameter. In the limit of free slip, longitudinal travelling waves disappear in favour of longitudinal rolls. With increasing slip, it is common for two-dimensional hydrothermal waves to exchange stability in favour of longitudinal rolls and oblique hydrothermal waves. Two types of oblique hydrothermal waves appear under partial slip, which exchange stability with increasing slip. The oblique mode that is preferred under no slip persists and remains near longitudinal for small slip parameters.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kowal, Dr Katarzyna
• Authors: Kowal, K. N., Davis, S. H., and Voorhees, P. W.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Fluid Mechanics
• Publisher: Cambridge University Press
• ISSN: 0022-1120
• ISSN (Online): 1469-7645
• Published Online: 20 September 2018