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Ring formation on an inclined surface

Published online by Cambridge University Press:  25 June 2015

Xiyu Du  and
R. D. Deegan
Xiyu Du
Affiliation:
Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA
R. D. Deegan*
Affiliation:
Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA
*
†Email address for correspondence: [email protected]
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Abstract

A drop dried on a solid surface will typically leave a narrow band of solute deposited along the contact line. Here we examine variations of this deposit due to the inclination of the substrate using numerical simulations of a two-dimensional drop, equivalent to a strip-like drop. An asymptotic analysis of the contact line region predicts that the upslope deposit will grow faster at early times, but the growth of this deposit ends sooner because the upper contact line depins first. From our simulations we find that the deposit can be larger at either the upper or lower contact line depending on the initial drop volume and substrate inclination. For larger drops and steeper inclinations, the early lead in deposited mass at the upper contact line is wiped out by the earlier depinning of the upper contact line and subsequent continued growth at the lower contact line. Conversely, for smaller drops and shallower inclinations, the early lead of the upper contact line is insurmountable despite its earlier termination in growth. Our results show that it is difficult to reconstruct a posteriori the inclination of the substrate based solely on the shape of the deposit.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 775 , 25 July 2015 , R3
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Copyright
© 2015 Cambridge University Press 

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