Long-wave Marangoni instability with vibration

Long-wave Marangoni instability with vibration

Cascade of structures in long-wavelength Marangoni instability

The long-wavelength instability for thermocapillary-driven convection in two dimensions is studied numerically. The system under consideration consists of a horizontal periodical liquid layer bounded from below by a rigid wall and from above by a deformable free surface. The liquid is heated from the bottom wall and cooled from above. The problem can be approximated by the Stokes equation and h...

Linear and nonlinear Rayleigh–Bénard–Marangoni instability with surface deformations

Thermoconvective instabilities in a bilayer liquid–gas system with a deformed interface are investigated. In the first part of the work which is devoted to a linear approach, emphasis is put on the role of the upper gas layer on the instability phenomenon. The condition to be satisfied by the gas to remain purely conductive is established. The so-called Oberbeck–Boussinesq approximation is disc...

Long-wave Marangoni convection in a thin film heated from below.

We consider long-wave Marangoni convection in a liquid layer atop a substrate of low thermal conductivity, heated from below. We demonstrate that the critical perturbations are materialized at the wave number K ∼ √Bi, where Bi is the Biot number which characterizes the weak heat flux from the free surface. In addition to the conventional monotonic mode, a novel oscillatory mode is found. Applyi...

Instabilities and spatio-temporal chaos of long-wave hexagon patterns in rotating Marangoni convection.

We consider surface-tension driven convection in a rotating fluid layer. For nearly insulating boundary conditions we derive a long-wave equation for the convection planform. Using a Galerkin method and direct numerical simulations we study the stability of the steady hexagonal patterns with respect to general side band instabilities. In the presence of rotation, steady and oscillatory instabil...