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

Ladd, Anthony; Yu, Liang; Szymczak, Piotr

doi:10.1017/jfm.2020.609

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

Journal Article · 25 November 2020 · Journal of Fluid Mechanics

DOI: https://doi.org/10.1017/jfm.2020.609 · OSTI ID:1671641

^[1]; Yu, Liang ^[1];

^[1]

Univ. of Florida, Gainesville, FL (United States)

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.

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Research Organization:: Univ. of Florida, Gainesville, FL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division

Grant/Contract Number:: SC0018676; 2012/07/E/ST3/01734

OSTI ID:: 1671641

Alternate ID(s):: OSTI ID: 1671639; OSTI ID: 1671640; OSTI ID: 1873372

Journal Information:: Journal of Fluid Mechanics, Vol. 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; ISSN 0022-1120

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

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