The Marangoni effect (also called the Gibbs–Marangoni effect) is the mass transfer along an interface between two phases due to a gradient of the surface tension. In the case of temperature dependence, this phenomenon may be called thermo-capillary convection (or Bénard–Marangoni convection). History This phenomenon was first identified in the so-called "tears of wine" by physicist James Thomson (Lord Kelvin's brother) in 1855. The general effect is named after Italian physicist Carlo Marangoni, who studied it for his doctoral dissertation at the University of Pavia and published his results in 1865. A complete theoretical treatment of the subject was given by J. Willard Gibbs in his work On the Equilibrium of Heterogeneous Substances (1875-8). Mechanism Since a liquid with a high surface tension pulls more strongly on the surrounding liquid than one with a low surface tension, the presence of a gradient in surface tension will naturally cause the liquid to flow away from regions of low surface tension. The surface tension gradient can be caused by concentration gradient or by a temperature gradient (surface tension is a function of temperature). In simple cases, the speed of the flow , where is the difference in surface tension and is the viscosity of the liquid. Water has a surface tension of around 0.07 N/m, and a viscosity of approximately 10−3 Pa s, at room temperature. So even variations of a few percent in the surface tension of water can generate Marangoni flows of almost 1 m/s. Thus Marangoni flows are common and easily observed. For the case of a small drop of surfactant dropped onto the surface of water, Roché and coworkers performed quantitative experiments and developed a simple model that was in approximate agreement with the experiments. This described the expansion in the radius of a patch of the surface covered in surfactant, due to an outward Marangoni flow at a speed . They found that speed of expansion of the surfactant-covered patch of the water surface occurred at speed of approximately for the surface tension of water, , the (lower) surface tension of the surfactant-covered water surface, the viscosity of water, and the mass density of water. For N/m, i.e., of order tens of per cent reduction in surface tension of water, and as for water N m−6s3, we obtain the second equality above. This gives speeds that decrease as surfactant-covered region grows, but are of order cms/s to