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

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:

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

^[1]

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

Publication Date:: 2020-11-25

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; OSTI ID: 1873372

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

Resource Type:: 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.

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                    Ladd, Anthony, Yu, Liang, & Szymczak, Piotr. Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach.  United States.  https://doi.org/10.1017/jfm.2020.609

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                    Ladd, Anthony, Yu, Liang, and Szymczak, Piotr. Wed .  
"Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach".  United States.  https://doi.org/10.1017/jfm.2020.609.  https://www.osti.gov/servlets/purl/1671641.

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@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},

  number       = ,

  volume       = 903,

  place        = {United States},

  year         = {2020},

  month        = {11}

}

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Works referenced in this record:

Reactive-infiltration instabilities in rocks. Fracture dissolution
journal, May 2012

Szymczak, Piotr; Ladd, Anthony J. C.
Journal of Fluid Mechanics, Vol. 702
DOI: 10.1017/jfm.2012.174

Average Shape of Transport-Limited Aggregates
journal, August 2005

Davidovitch, Benny; Choi, Jaehyuk; Bazant, Martin Z.
Physical Review Letters, Vol. 95, Issue 7
DOI: 10.1103/PhysRevLett.95.075504

Conformal mapping of some non-harmonic functions in transport theory
journal, May 2004

Bazant, Martin Z.
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 460, Issue 2045
DOI: 10.1098/rspa.2003.1218

The kinetics of dissolution of calcium sulphate dihydrate in water
journal, August 1976

Christoffersen, J∅rgen; Christoffersen, Margaret R.
Journal of Crystal Growth, Vol. 35, Issue 1
DOI: 10.1016/0022-0248(76)90247-5

Mineral dissolution and wormholing from a pore-scale perspective
journal, August 2017

Soulaine, Cyprien; Roman, Sophie; Kovscek, Anthony
Journal of Fluid Mechanics, Vol. 827
DOI: 10.1017/jfm.2017.499

Conformal Maps and Integrable Hierarchies
journal, October 2000

Wiegmann, P. B.; Zabrodin, A.
Communications in Mathematical Physics, Vol. 213, Issue 3
DOI: 10.1007/s002200000249

Viscous flows in two dimensions
journal, October 1986

Bensimon, David; Kadanoff, Leo P.; Liang, Shoudan
Reviews of Modern Physics, Vol. 58, Issue 4
DOI: 10.1103/RevModPhys.58.977

Modelling of multispecies reactive transport on pore-space images
journal, May 2019

Oliveira, Thomas D. S.; Blunt, Martin J.; Bijeljic, Branko
Advances in Water Resources, Vol. 127
DOI: 10.1016/j.advwatres.2019.03.012

Complex variable methods in Hele–Shaw moving boundary problems
journal, September 1992

Howison, S. D.
European Journal of Applied Mathematics, Vol. 3, Issue 3
DOI: 10.1017/S0956792500000802

A boundary-integral framework to simulate viscous erosion of a porous medium
journal, December 2018

Quaife, Bryan D.; Moore, M. Nicholas J.
Journal of Computational Physics, Vol. 375
DOI: 10.1016/j.jcp.2018.07.037

The Development of Wormholes in Laboratory‐Scale Fractures: Perspectives From Three‐Dimensional Simulations
journal, October 2018

Starchenko, Vitaliy; Ladd, Anthony J. C.
Water Resources Research, Vol. 54, Issue 10
DOI: 10.1029/2018WR022948

Multi-scale Model of Reactive Transport in Fractured Media: Diffusion Limitations on Rates
journal, March 2019

Molins, Sergi; Trebotich, David; Arora, Bhavna
Transport in Porous Media, Vol. 128, Issue 2
DOI: 10.1007/s11242-019-01266-2

Pore-scale simulation of multicomponent multiphase reactive transport with dissolution and precipitation
journal, June 2015

Chen, Li; Kang, Qinjun; Tang, Qing
International Journal of Heat and Mass Transfer, Vol. 85
DOI: 10.1016/j.ijheatmasstransfer.2015.02.035

Singularities in nonlocal interface dynamics
journal, November 1984

Shraiman, B.; Bensimon, D.
Physical Review A, Vol. 30, Issue 5
DOI: 10.1103/PhysRevA.30.2840

Upscaling pore-scale reactive transport equations using a multiscale continuum formulation: PORE-SCALE REACTIVE TRANSPORT EQUATIONS
journal, December 2007

Lichtner, P. C.; Kang, Q.
Water Resources Research, Vol. 43, Issue 12
DOI: 10.1029/2006WR005664

Investigations on the dendrite problem at zero surface tension in 2D and 3D geometries
journal, May 1994

Bedia, M. Adda; Amar, M. Ben
Nonlinearity, Vol. 7, Issue 3
DOI: 10.1088/0951-7715/7/3/004

Sculpting of an erodible body by flowing water
journal, November 2012

Ristroph, L.; Moore, M. N. J.; Childress, S.
Proceedings of the National Academy of Sciences, Vol. 109, Issue 48
DOI: 10.1073/pnas.1212286109

Steadily Translating Parabolic Dissolution Fingers
journal, January 2015

Kondratiuk, Paweł; Szymczak, Piotr
SIAM Journal on Applied Mathematics, Vol. 75, Issue 5
DOI: 10.1137/151003751

Time-dependent shapes of a dissolving mineral grain: Comparisons of simulations with microfluidic experiments
journal, May 2020

Dutka, Filip; Starchenko, Vitaliy; Osselin, Florian
Chemical Geology, Vol. 540
DOI: 10.1016/j.chemgeo.2019.119459

Two-dimensional solidification and melting in potential flows
journal, January 1999

Cummings, Linda M.; Hohlov, Yuri E.; Howison, Sam D.
Journal of Fluid Mechanics, Vol. 378
DOI: 10.1017/S0022112098003188

Pore‐scale simulation of carbonate dissolution in micro‐CT images
journal, February 2016

Pereira Nunes, J. P.; Blunt, M. J.; Bijeljic, B.
Journal of Geophysical Research: Solid Earth, Vol. 121, Issue 2
DOI: 10.1002/2015JB012117

Harmonic moment dynamics in Laplacian growth
journal, January 2010

Leshchiner, Alexander; Thrasher, Matthew; Mineev-Weinstein, Mark B.
Physical Review E, Vol. 81, Issue 1
DOI: 10.1103/PhysRevE.81.016206

Numerical modeling of pore-scale phenomena during CO2 sequestration in oceanic sediments
journal, October 2005

Kang, Qinjun; Tsimpanogiannis, Ioannis N.; Zhang, Dongxiao
Fuel Processing Technology, Vol. 86, Issue 14-15
DOI: 10.1016/j.fuproc.2005.02.001

Intrinsic Kinetics of Gypsum and Calcium Sulfate Anhydrite Dissolution: Surface Selective Studies under Hydrodynamic Control and the Effect of Additives
journal, May 2011

Mbogoro, Michael M.; Snowden, Michael E.; Edwards, Martin A.
The Journal of Physical Chemistry C, Vol. 115, Issue 20
DOI: 10.1021/jp201718b

Integrable Structure of Interface Dynamics
journal, May 2000

Mineev-Weinstein, Mark; Wiegmann, Paul B.; Zabrodin, Anton
Physical Review Letters, Vol. 84, Issue 22
DOI: 10.1103/PhysRevLett.84.5106

Scale dependence of mineral dissolution rates within single pores and fractures
journal, January 2008

Li, Li; Steefel, Carl I.; Yang, Li
Geochimica et Cosmochimica Acta, Vol. 72, Issue 2
DOI: 10.1016/j.gca.2007.10.027

Untersuchungen �ber schlichte konforme Abbildungen des Einheitskreises. I
journal, March 1923

L�wner, Karl
Mathematische Annalen, Vol. 89, Issue 1-2
DOI: 10.1007/BF01448091

Instabilities and pattern formation in crystal growth
journal, January 1980

Langer, J. S.
Reviews of Modern Physics, Vol. 52, Issue 1
DOI: 10.1103/RevModPhys.52.1

Dynamics of Conformal Maps for a Class of Non-Laplacian Growth Phenomena
journal, July 2003

Bazant, Martin Z.; Choi, Jaehyuk; Davidovitch, Benny
Physical Review Letters, Vol. 91, Issue 4
DOI: 10.1103/PhysRevLett.91.045503

Determination of mineral dissolution regimes using flow-through time-resolved analysis (FT-TRA) and numerical simulation
journal, July 2016

De Baere, Bart; Molins, Sergi; Mayer, K. Ulrich
Chemical Geology, Vol. 430
DOI: 10.1016/j.chemgeo.2016.03.014

Self-similar evolution of a body eroding in a fluid flow
journal, November 2013

Moore, Matthew N. J.; Ristroph, Leif; Childress, Stephen
Physics of Fluids, Vol. 25, Issue 11
DOI: 10.1063/1.4829644

Wormhole growth in soluble porous materials
journal, September 1990

Nilson, Robert H.; Griffiths, Stewart K.
Physical Review Letters, Vol. 65, Issue 13
DOI: 10.1103/PhysRevLett.65.1583

Three-dimensional simulations of fracture dissolution: FRACTURE DISSOLUTION IN 3-D
journal, September 2016

Starchenko, Vitaliy; Marra, Cameron J.; Ladd, Anthony J. C.
Journal of Geophysical Research: Solid Earth, Vol. 121, Issue 9
DOI: 10.1002/2016JB013321

An investigation of the effect of pore scale flow on average geochemical reaction rates using direct numerical simulation: EFFECT OF PORE SCALE FLOW ON GEOCHEMICAL REACTION RATES
journal, March 2012

Molins, Sergi; Trebotich, David; Steefel, Carl I.
Water Resources Research, Vol. 48, Issue 3
DOI: 10.1029/2011WR011404

Fingered growth in channel geometry: A Loewner-equation approach
journal, April 2008

Gubiec, T.; Szymczak, P.
Physical Review E, Vol. 77, Issue 4
DOI: 10.1103/PhysRevE.77.041602

Pore-Scale Controls on Calcite Dissolution Rates from Flow-through Laboratory and Numerical Experiments
journal, June 2014

Molins, Sergi; Trebotich, David; Yang, Li
Environmental Science & Technology, Vol. 48, Issue 13
DOI: 10.1021/es5013438

Shape dynamics and scaling laws for a body dissolving in fluid flow
journal, January 2015

Huang, Jinzi Mac; Moore, M. Nicholas J.; Ristroph, Leif
Journal of Fluid Mechanics, Vol. 765
DOI: 10.1017/jfm.2014.718

Steady advection–diffusion around finite absorbers in two-dimensional potential flows
journal, July 2005

Choi, Jaehyuk; Margetis, Dionisios; Squires, Todd M.
Journal of Fluid Mechanics, Vol. 536
DOI: 10.1017/S0022112005005008

Interfacial dynamics in transport-limited dissolution
journal, June 2006

Bazant, Martin Z.
Physical Review E, Vol. 73, Issue 6
DOI: 10.1103/PhysRevE.73.060601

Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel
journal, December 1972

Richardson, S.
Journal of Fluid Mechanics, Vol. 56, Issue 4
DOI: 10.1017/S0022112072002551

Mathematical Theory of Freezing for Flow in Porous Media
journal, November 1994

Kornev, K.; Mukhamadullina, G.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 447, Issue 1930
DOI: 10.1098/rspa.1994.0141

2D growth processes: SLE and Loewner chains
journal, October 2006

Bauer, Michel; Bernard, Denis
Physics Reports, Vol. 432, Issue 3-4
DOI: 10.1016/j.physrep.2006.06.002

Assimulo: A unified framework for ODE solvers
journal, October 2015

Andersson, Christian; Führer, Claus; Åkesson, Johan
Mathematics and Computers in Simulation, Vol. 116
DOI: 10.1016/j.matcom.2015.04.007

Measurement of the pure dissolution rate constant of a mineral in water
journal, December 2008

Colombani, Jean
Geochimica et Cosmochimica Acta, Vol. 72, Issue 23
DOI: 10.1016/j.gca.2008.09.007

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

Abstract

Citation Formats

Reactive-infiltration instabilities in rocks. Fracture dissolution journal, May 2012

Average Shape of Transport-Limited Aggregates journal, August 2005

Conformal mapping of some non-harmonic functions in transport theory journal, May 2004

The kinetics of dissolution of calcium sulphate dihydrate in water journal, August 1976

Mineral dissolution and wormholing from a pore-scale perspective journal, August 2017

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The Development of Wormholes in Laboratory‐Scale Fractures: Perspectives From Three‐Dimensional Simulations journal, October 2018

Multi-scale Model of Reactive Transport in Fractured Media: Diffusion Limitations on Rates journal, March 2019

Pore-scale simulation of multicomponent multiphase reactive transport with dissolution and precipitation journal, June 2015

Singularities in nonlocal interface dynamics journal, November 1984

Upscaling pore-scale reactive transport equations using a multiscale continuum formulation: PORE-SCALE REACTIVE TRANSPORT EQUATIONS journal, December 2007

Investigations on the dendrite problem at zero surface tension in 2D and 3D geometries journal, May 1994

Sculpting of an erodible body by flowing water journal, November 2012

Steadily Translating Parabolic Dissolution Fingers journal, January 2015

Time-dependent shapes of a dissolving mineral grain: Comparisons of simulations with microfluidic experiments journal, May 2020

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Harmonic moment dynamics in Laplacian growth journal, January 2010

Numerical modeling of pore-scale phenomena during CO2 sequestration in oceanic sediments journal, October 2005

Intrinsic Kinetics of Gypsum and Calcium Sulfate Anhydrite Dissolution: Surface Selective Studies under Hydrodynamic Control and the Effect of Additives journal, May 2011

Integrable Structure of Interface Dynamics journal, May 2000

Scale dependence of mineral dissolution rates within single pores and fractures journal, January 2008

Untersuchungen �ber schlichte konforme Abbildungen des Einheitskreises. I journal, March 1923

Instabilities and pattern formation in crystal growth journal, January 1980

Dynamics of Conformal Maps for a Class of Non-Laplacian Growth Phenomena journal, July 2003

Determination of mineral dissolution regimes using flow-through time-resolved analysis (FT-TRA) and numerical simulation journal, July 2016

Self-similar evolution of a body eroding in a fluid flow journal, November 2013

Wormhole growth in soluble porous materials journal, September 1990

Three-dimensional simulations of fracture dissolution: FRACTURE DISSOLUTION IN 3-D journal, September 2016

An investigation of the effect of pore scale flow on average geochemical reaction rates using direct numerical simulation: EFFECT OF PORE SCALE FLOW ON GEOCHEMICAL REACTION RATES journal, March 2012

Fingered growth in channel geometry: A Loewner-equation approach journal, April 2008

Pore-Scale Controls on Calcite Dissolution Rates from Flow-through Laboratory and Numerical Experiments journal, June 2014

Shape dynamics and scaling laws for a body dissolving in fluid flow journal, January 2015

Steady advection–diffusion around finite absorbers in two-dimensional potential flows journal, July 2005

Interfacial dynamics in transport-limited dissolution journal, June 2006

Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel journal, December 1972

Mathematical Theory of Freezing for Flow in Porous Media journal, November 1994

2D growth processes: SLE and Loewner chains journal, October 2006

Assimulo: A unified framework for ODE solvers journal, October 2015

Measurement of the pure dissolution rate constant of a mineral in water journal, December 2008

Reactive-infiltration instabilities in rocks. Fracture dissolution
journal, May 2012

Average Shape of Transport-Limited Aggregates
journal, August 2005

Conformal mapping of some non-harmonic functions in transport theory
journal, May 2004

The kinetics of dissolution of calcium sulphate dihydrate in water
journal, August 1976

Mineral dissolution and wormholing from a pore-scale perspective
journal, August 2017

Conformal Maps and Integrable Hierarchies
journal, October 2000

Viscous flows in two dimensions
journal, October 1986

Modelling of multispecies reactive transport on pore-space images
journal, May 2019

Complex variable methods in Hele–Shaw moving boundary problems
journal, September 1992

A boundary-integral framework to simulate viscous erosion of a porous medium
journal, December 2018

The Development of Wormholes in Laboratory‐Scale Fractures: Perspectives From Three‐Dimensional Simulations
journal, October 2018

Multi-scale Model of Reactive Transport in Fractured Media: Diffusion Limitations on Rates
journal, March 2019

Pore-scale simulation of multicomponent multiphase reactive transport with dissolution and precipitation
journal, June 2015

Singularities in nonlocal interface dynamics
journal, November 1984

Upscaling pore-scale reactive transport equations using a multiscale continuum formulation: PORE-SCALE REACTIVE TRANSPORT EQUATIONS
journal, December 2007

Investigations on the dendrite problem at zero surface tension in 2D and 3D geometries
journal, May 1994

Sculpting of an erodible body by flowing water
journal, November 2012

Steadily Translating Parabolic Dissolution Fingers
journal, January 2015

Time-dependent shapes of a dissolving mineral grain: Comparisons of simulations with microfluidic experiments
journal, May 2020

Two-dimensional solidification and melting in potential flows
journal, January 1999

Pore‐scale simulation of carbonate dissolution in micro‐CT images
journal, February 2016

Harmonic moment dynamics in Laplacian growth
journal, January 2010

Numerical modeling of pore-scale phenomena during CO2 sequestration in oceanic sediments
journal, October 2005

Intrinsic Kinetics of Gypsum and Calcium Sulfate Anhydrite Dissolution: Surface Selective Studies under Hydrodynamic Control and the Effect of Additives
journal, May 2011

Integrable Structure of Interface Dynamics
journal, May 2000

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journal, January 2008

Untersuchungen �ber schlichte konforme Abbildungen des Einheitskreises. I
journal, March 1923

Instabilities and pattern formation in crystal growth
journal, January 1980

Dynamics of Conformal Maps for a Class of Non-Laplacian Growth Phenomena
journal, July 2003

Determination of mineral dissolution regimes using flow-through time-resolved analysis (FT-TRA) and numerical simulation
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Self-similar evolution of a body eroding in a fluid flow
journal, November 2013

Wormhole growth in soluble porous materials
journal, September 1990

Three-dimensional simulations of fracture dissolution: FRACTURE DISSOLUTION IN 3-D
journal, September 2016

An investigation of the effect of pore scale flow on average geochemical reaction rates using direct numerical simulation: EFFECT OF PORE SCALE FLOW ON GEOCHEMICAL REACTION RATES
journal, March 2012

Fingered growth in channel geometry: A Loewner-equation approach
journal, April 2008

Pore-Scale Controls on Calcite Dissolution Rates from Flow-through Laboratory and Numerical Experiments
journal, June 2014

Shape dynamics and scaling laws for a body dissolving in fluid flow
journal, January 2015

Steady advection–diffusion around finite absorbers in two-dimensional potential flows
journal, July 2005

Interfacial dynamics in transport-limited dissolution
journal, June 2006

Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel
journal, December 1972

Mathematical Theory of Freezing for Flow in Porous Media
journal, November 1994

2D growth processes: SLE and Loewner chains
journal, October 2006

Assimulo: A unified framework for ODE solvers
journal, October 2015

Measurement of the pure dissolution rate constant of a mineral in water
journal, December 2008