To understand the Marangoni effect it is essential to understand Rayleigh-Bénard instability. The Rayleigh-Bénard convection instability occurs in a plane horizontal layer of fluid heated from the bottom. The fluid develops a regular pattern of convection cells known as Bénard cells. The convection patterns are the most carefully examined example of self-organizing nonlinear systems.
Gravity and hence Buoyancy, is the major driving force for the Rayleigh-Bénard-Marangoni convection instability. The initial movement is the upwelling of lesser density fluid from the heated bottom layer. This upwelling spontaneously organizes into a regular pattern of cells called Bénard cells.
The dimensionless Rayleigh number (RaL), which essentially expresses the balance between gravity and viscous forces is given by Where,
• Tu is the Temperature of the top plate
• Tb is the Temperature of the bottom plate
• L is the height of the container.
• g is the acceleration due to gravity.
• ν is the kinematic viscosity.
• α is the Thermal diffusivity
• β is the Thermal expansion coefficient
The critical Rayleigh number (RC) is the threshold over which the convection cells appear. RC ~ 1100.65 for a Marangoni set up with controlled boundary conditions.
Rayleigh-Bénard convection experiments used fluids heated from below with a confining plate on the top surface. In case of Bénard-Marangoni convection arrangement, the top surface does not have a confining plate and is free to move and deform.