Abstract
Energy stability theory has been formulated for two-dimensional buoyancy–thermocapillary convection in a layer with a free surface. The theory yields a critical Rayleigh number RE for which R < RE is a sufficient condition for stability of the layer. RE emerges from the variational formulation as an eigenvalue of a nonlinear system of Euler–Lagrange equations. For the case of small capillary number (large mean surface tension) explicit values are obtained for RE. The analogous linear-theory results for this case are obtained in terms of a critical Rayleigh number RL. These are compared. It is found that the existence of the deformable interface can lead to a stabilization relative to the case of a planar interface. This result is explained in physical terms. The energy theory is then generalized to include general flow problems having three-dimensional disturbances, non-Newtonian bulk fluids and general interfacial mechanics such as surface viscosity and elasticity.
Original language | English (US) |
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Pages (from-to) | 527-553 |
Number of pages | 27 |
Journal | Journal of fluid Mechanics |
Volume | 98 |
Issue number | 3 |
DOIs | |
State | Published - Jun 1980 |
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics