Robust fadeout profile of an evaporation stain

Abstract

We propose an explanation for the commonly-seen fading in the density of a stain remaining after a droplet has dried on a surface. The density decreases as a power $p$ of the distance from the edge. For thin, dilute drops of general shape this power is determined by a flow stagnation point in the distant interior of the drop. The power $p$ depends on the local evaporation rate J(0) at the stagnation point and the liquid depth $h(0)$ there: $p=1-2(h(0)/\bar{h})(\bar{J}/J(0))$, where $\bar{h}$ and $\bar{J}$ are averages over the drop surface.

5 pages at journal density 3 figures. v2 has Numerous wording and figure clarifications. Accepted in Europhysics Letters http://www.iop.org/EJ/journal/-page=forthart/0295-5075/1

References in corpus (3)

• Evaporative Deposition Patterns Revisited: Spatial Dimensions of the Deposit
• The Geometry of Soft Materials: A Primer
• Minimal Surfaces, Screw Dislocations and Twist Grain Boundaries

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• The model of drying sessile drop of colloidal solution
• The nascent coffee ring with arbitrary droplet contact set: an asymptotic analysis
• Evaporation of non-circular droplets