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.
Ladd, Anthony C., et al. "Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach." Journal of Fluid Mechanics, vol. 903, Oct. 2020. https://doi.org/10.1017/jfm.2020.609
Ladd, Anthony C., Yu, Liang, & Szymczak, Piotr (2020). Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach. Journal of Fluid Mechanics, 903. https://doi.org/10.1017/jfm.2020.609
Ladd, Anthony C., Yu, Liang, and Szymczak, Piotr, "Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach," Journal of Fluid Mechanics 903 (2020), https://doi.org/10.1017/jfm.2020.609
@article{osti_1671639,
author = {Ladd, Anthony C. and Yu, Liang and Szymczak, Piotr},
title = {Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach},
annote = {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},
url = {https://www.osti.gov/biblio/1671639},
journal = {Journal of Fluid Mechanics},
issn = {ISSN 0022-1120},
volume = {903},
place = {United States},
publisher = {Cambridge University Press},
year = {2020},
month = {10}}
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 245, Issue 1242, p. 312-329https://doi.org/10.1098/rspa.1958.0085
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 460, Issue 2045https://doi.org/10.1098/rspa.2003.1218