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

Published online by Cambridge University Press:  06 October 2020

Anthony J. C. Ladd Open the ORCID record for Anthony J. C. Ladd [Opens in a new window] ,
Liang Yu  and
Piotr Szymczak Open the ORCID record for Piotr Szymczak [Opens in a new window]
Anthony J. C. Ladd*
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL32611-6005, USA
Liang Yu
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL32611-6005, USA
Piotr Szymczak
Affiliation:
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093Warsaw, Poland
*
†Email address for correspondence: tladd@che.ufl.edu
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Abstract

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.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Mathematical Foundations: General fluid mechanics Micro-/Nano-fluid dynamics: Microfluidics

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A46
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© The Author(s), 2020. Published by Cambridge University Press

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References

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