2003/01/31 by Yuri O. Popov, Thomas A. Witten
Engineering · Physics and Astronomy · #Fluid Dynamics and Heat Transfer #Fluid Dynamics and Thin Films #Nanomaterials and Printing Technologies #cond-mat.soft
paper · pdf · doi:10.1103/physreve.68.036306
published as Physical Review E, v. 68, 036306 (2003) · v1: 36 pages, 21 figures, LaTeX; submitted to Physical Review E; v2: minor additions to Abstract and Introduction
arxiv created 2003/06/06 · openalex publication_date 2003/09/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Solids dispersed in a drying drop migrate to the (pinned) contact line. This migration is caused by outward flows driven by the loss of the solvent due to evaporation and by geometrical constraint that the drop maintains an equilibrium surface shape with a fixed boundary. Here, in continuation of our earlier paper, we theoretically investigate the evaporation rate, the flow field, and the rate of growth of the deposit patterns in a drop over an angular sector on a plane substrate. Asymptotic power laws near the vertex (as distance to the vertex goes to zero) are obtained. A hydrodynamic model of fluid flow near the singularity of the vertex is developed and the velocity field is obtained. The rate of the deposit growth near the contact line is found in two time regimes. The deposited mass falls off as a weak power gamma of distance close to the vertex and as a stronger power beta of distance further from the vertex. The power gamma depends only slightly on the opening angle alpha and stays roughly between -1/3 and 0. The power beta varies from -1 to 0 as the opening angle increases from 0 degrees to 180 degrees. At a given distance from the vertex, the deposited mass grows faster and faster with time, with the greatest increase in the growth rate occurring at the early stages of the drying process.