mm/s. The equation is obtained by making a couple of simple approximations, the first is by equating the stress at the surface due to the concentration gradient of surfactant (which drives the Marangoni flow) with the viscous stresses (that oppose flow). The Marangoni stress , i.e., gradient in the surface tension due gradient in the surfactant concentration (from high in the centre of the expanding patch, to zero far from the patch). The viscous shear stress is simply the viscosity times the gradient in shear velocity , for the depth into the water of the flow due to the spreading patch. Roché and coworkers assume that the momentum (which is directed radially) diffuses down into the liquid, during spreading, and so when the patch has reached a radius , , for the kinematic viscosity, which is the diffusion constant for momentum in a fluid. Equating the two stresses where we approximated the gradient . Taking the 2/3 power of both sides gives the expression above. The Marangoni number, a dimensionless value, can be used to characterize the relative effects of surface tension and viscous forces. Tears of wine As an example, wine may exhibit a visible effect called "tears of wine". The effect is a consequence of the fact that alcohol has a lower surface tension and higher volatility than water. The water/alcohol solution rises up the surface of the glass lowering the surface energy of the glass. Alcohol evaporates from the film leaving behind liquid with a higher surface tension (more water, less alcohol). This region with a lower concentration of alcohol (greater surface tension) pulls on the surrounding fluid more strongly than the regions with a higher alcohol concentration (lower in the glass). The result is the liquid is pulled up until its own weight exceeds the force of the effect, and the liquid drips back down the vessel's walls. This can also be easily demonstrated by spreading a thin film of water on a smooth surface and then allowing a drop of alcohol to fall on the center of the film. The liquid will rush out of the region where the drop of alcohol fell. Significance to transport phenomena Under earth conditions, the effect of gravity causing natural convection in a system with a temperature gradient along a fluid/fluid interface is usually much stronger than the Marangoni effect. Many experiments (ESA MASER 1-3) have been conducted under