Phenomena

Ink Drops Spreading

Ink drops atop a layer of glycerol spread in a beautiful fan of blue and white. The ink’s motion is the result of two processes: molecular diffusion and the Marangoni effect. Molecular diffusion is the mixing that occurs due to the random background motion of molecules. Since glycerol is a very viscous liquid, the ink is quite slow to spread in this manner.

The second factor, the Marangoni effect, is driven by differences in surface tension. The ink and glycerol have different surface tensions, and the exact values depend on concentration. Notice how the ink drops spread fastest from areas where the ink is densely concentrated. This tells us that the ink’s surface tension is lower than the glycerol’s. As a result, the glycerol’s higher surface tension tends to pull ink toward it. As the ink spreads and its concentration decreases relative to the glycerol, the ink-glycerol mixture’s surface tension increases. Since the difference between the surface tension of the mixture and the pure glycerol is not as large, the Marangoni force is reduced and the spreading slows. (Image credit: C. Kalelkar, source)

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