How Marangoni stress affects falling films

LiDong Huang, Principal Engineer, Experimental Research
 

Anyone who drinks wine may notice that droplets (or tears) of wine form on the inside wall of a wine glass. But what causes this phenomenon? The short answer: it is all about Marangoni stress and evaporation, both of which are linked to falling film evaporation.

Carlo G. M. Marangoni, a high school physics teacher, was the first to give a rigorous explanation of the “tears of wine” phenomenon. He formulated a theory for flows driven by surface tension gradients due to variations in composition or temperature. Wine is mostly a mixture of alcohol and water, with alcohol being the more volatile component and having a lower surface tension than water. Where the surface of the wine meets the side wall of a glass, capillary action makes the wine climb up the wall. More alcohol evaporates at the wall than in the center of the glass, resulting in a higher concentration of water with a higher surface tension. The surface tension gradient, a Marangoni stress, pulls more wine up the wall, and droplets that form fall back down by gravity. This is what we call the Marangoni effect.

In addition to a change in concentration, temperature also causes a change in the surface tension. Most fluids demonstrate a normal thermocapillary, in which surface tension decreases as temperature increases. However, some systems (e.g., liquid crystals) display the opposite behavior, known as anomalous thermocapillary [1]

Both surface tension and the surface tension gradient play an important role in falling liquid film heat transfer. Liquid film falling down a vertical plate or tube typically has a wavy nature, as illustrated in Figure 1. Higher surface tension results in a more stable liquid film with less turbulence. However, the surface tension gradient may stabilize or break down the liquid film.

Falling liquid film with wavy surface inside a tube
(photograph taken from a transparent tube setup at HTRI's Research and Technology Center)

As illustrated in Figure 2, temperature at the liquid-gas interface is higher at wave troughs, because the interface is closer to the hot wall and lower at the wave crest. For a normal thermocapillary fluid, the interface temperature gradient creates a Marangoni stress that moves liquid from the trough to the crest, resulting in the film becoming thinner at the trough until no liquid exists at that spot, leading to film breakdown with dry patches.

Illustration of Marangoni stress on a wavy liquid film

For evaporation of a mixture, changes of both concentration and temperature impact surface tension variation. If the surface tension of the more volatile component in the mixture is lower than that of the less volatile component (which is true for most hydrocarbon mixtures), evaporation may cause an increase in surface tension even with an increase in temperature. In such a case, the Marangoni stress may work in the opposite direction and stabilize the liquid film. For a mixture of ethylene glycol and water, water with its higher surface tension evaporates first, resulting in an even lower surface tension at the wave trough and a higher potential for film breakdown.

It is interesting how our daily experiences are often linked with process heat transfer technology. A simple glass of wine can help us understand the mechanisms of falling film evaporation.

Reference

1. S. Kalliadasis, C. Ruyer-Quil, B. Scheid, and M. G. Velarde, Falling Liquid Films, Springer, New York (2012).