Volume 86, Number 6, June 2009
Article Number 64002
Number of page(s) 5
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
Published online 10 July 2009
EPL, 86 (2009) 64002
DOI: 10.1209/0295-5075/86/64002

Robust fadeout profile of an evaporation stain

T. A. Witten

James Franck Institute, University of Chicago - Chicago IL 60637 USA

received 27 March 2009; accepted in final form 27 May 2009; published June 2009
published online 10 July 2009

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.

47.57.ef - Sedimentation and migration.
02.40.Xx - Singularity theory.
47.55.D- - Drops and bubbles.

© EPLA 2009