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Title: Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach

Abstract

Here we apply conformal mapping to find the evolving shapes of a dissolving cylinder in a potential flow. Similar equations can be used to describe melting in a flowing liquid phase. Results are compared with microfluidic experiments and numerical simulations. Shapes predicted by conformal mapping agree almost perfectly with experimental observations, after a modest (20 %) rescaling of the time. Finite-volume simulations show that the differences with experiment are connected to the underlying assumptions of the analytical model: potential flow and diffusion-limited dissolution. Approximate solutions of the equations describing the evolution of the shape of the undissolved solid can be derived from a Laurent expansion of the mapping function from the unit circle. Asymptotic expressions for the evolution of the area of the disk and the shift in its centre of mass have been derived at low and high Péclet number. Analytic approximations to the leading-order Laurent coefficients provide additional insight into the mechanisms underlying pore-scale dissolution.

Authors:
ORCiD logo [1];  [1]; ORCiD logo [1]
  1. Univ. of Florida, Gainesville, FL (United States)
Publication Date:
Research Org.:
Univ. of Florida, Gainesville, FL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division
OSTI Identifier:
1671641
Alternate Identifier(s):
OSTI ID: 1671639; OSTI ID: 1671640
Grant/Contract Number:  
SC0018676; 2012/07/E/ST3/01734
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 903; Related Information: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/dissolution-of-a-cylindrical-disk-in-heleshaw-flow-a-conformalmapping-approach/DBDD5341E2A0DA47633D8D29D4D0F35B#fndtn-supplementary-materials; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; Hele-Shaw flows; general fluid mechanics; microfluidics

Citation Formats

Ladd, Anthony, Yu, Liang, and Szymczak, Piotr. Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach. United States: N. p., 2020. Web. doi:10.1017/jfm.2020.609.
Ladd, Anthony, Yu, Liang, & Szymczak, Piotr. Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach. United States. doi:10.1017/jfm.2020.609.
Ladd, Anthony, Yu, Liang, and Szymczak, Piotr. Wed . "Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach". United States. doi:10.1017/jfm.2020.609.
@article{osti_1671641,
title = {Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach},
author = {Ladd, Anthony and Yu, Liang and Szymczak, Piotr},
abstractNote = {Here we apply conformal mapping to find the evolving shapes of a dissolving cylinder in a potential flow. Similar equations can be used to describe melting in a flowing liquid phase. Results are compared with microfluidic experiments and numerical simulations. Shapes predicted by conformal mapping agree almost perfectly with experimental observations, after a modest (20 %) rescaling of the time. Finite-volume simulations show that the differences with experiment are connected to the underlying assumptions of the analytical model: potential flow and diffusion-limited dissolution. Approximate solutions of the equations describing the evolution of the shape of the undissolved solid can be derived from a Laurent expansion of the mapping function from the unit circle. Asymptotic expressions for the evolution of the area of the disk and the shift in its centre of mass have been derived at low and high Péclet number. Analytic approximations to the leading-order Laurent coefficients provide additional insight into the mechanisms underlying pore-scale dissolution.},
doi = {10.1017/jfm.2020.609},
journal = {Journal of Fluid Mechanics},
issn = {0022-1120},
number = ,
volume = 903,
place = {United States},
year = {2020},
month = {11}
}

Journal Article:
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