Robust fadeout profile of an evaporation stain

T. A. Witten

doi:10.1209/0295-5075/86/64002

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arXiv · 0903.4919

Robust fadeout profile of an evaporation stain

T. A. Witten

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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.

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T. A. Witten. 2009-03-27. Robust fadeout profile of an evaporation stain. https://doi.org/10.1209/0295-5075/86/64002

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