When a colloidal dispersion droplet evaporates from a surface, particles are dragged towards the contact line to form the well-known coffee-stain ring.1 In this work, we use micro particle image velocimetry to show that the particle velocity increases dramatically in the last moments of evaporation. This “rush-hour” for particles in an evaporating colloidal solution occurs when the contact angle and the droplet height tend to zero (see Figs. 1(a)–1(f)).

The rush-hour behavior can be explained by simple mass-balance considerations.2 The volume flow towards the contact line inside the drop is driven by the evaporation from the drop surface.1 It turns out that the rate of evaporation is approximately constant over time.3 To replenish this evaporated liquid, a continuous volume flow towards the contact line is generated inside the drop. However, the drop height is decreasing during evaporation, and hence, the same amount of liquid has to be squeezed through an area which is vanishing. Indeed, this induces a diverging radial velocity toward the end of the evaporation process.

The rush-hour behavior explains the different characteristic packing of particles in the layers of the ring (see Figs. 2(b) and 2(c)) (Ref. 2): the outer one forms a crystalline array (particles at the right-hand side in Figs. 2(b) and 2(c)), while the inner one looks more like a jammed granular fluid (left-hand side in Figs. 2(b) and 2(c)). Such effect resembles the popular computer game Tetris®, where at the beginning of the game slowly falling objects are easily arranged in regular structures, while as the game evolves, the fast falling objects become jammed and disordered.

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R. D.
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Todd F.
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Sidney R.
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Thomas A.
Witten
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Capillary flow as the cause of ring stains from dried liquid drops
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A. G.
Marín
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Lohse
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Snoeijer
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Order-to-disorder transition in ring-shaped colloidal stains
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Y. O.
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Evaporative deposition patterns: Spatial dimensions of the deposit
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