Eur. Phys. J. E (2009) 29: 205-218
https://doi.org/10.1140/epje/i2009-10469-7

Regular Article

A study of the evaporative deposition process: Pipes and truncated transport dynamics

James Franck Institute and Department of Physics, The University of Chicago, 929 E. 57th Street, 60637, Chicago, Illinois, USA

^* e-mail: rui.zheng@ubs.com

Received: 5 October 2008
Revised: 29 March 2009
Accepted: 5 May 2009
Published online: 21 June 2009

Abstract

We consider contact line deposition of an evaporating thin drop. Following Dupont’s proposal (unpublished), we focus on transport dynamics truncated by a maximal concentration as the single deposition mechanism. The truncated transport process, formalized as the “pipe model”, admits a characteristic shock front that has a robust functional form and depends only on local hydrodynamic properties. By applying the pipe model, we solve the density profile in different asymptotic regimes. In particular, we find that near the contact line the density profile follows a scaling law that is proportional to the square root of the concentration ratio defined as the initial solute volume concentration divided by the maximal concentration. The maximal deposit density occurs at about 2/3 of the total drying time for uniform evaporation and 1/2 for diffusion-controlled evaporation. Away from the contact line, areal density decays exponentially with the radial distance to the power of -3 for the uniform evaporation and -7 for the diffusion-controlled evaporation.