Understanding the Marangoni Effect

1021 WordsFeb 26, 20184 Pages
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.

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