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Shape dynamics and scaling laws for a body dissolving in fluid flow

Published online by Cambridge University Press:  26 January 2015

Jinzi Mac Huang ,
M. Nicholas J. Moore  and
Leif Ristroph
Jinzi Mac Huang
Affiliation:
Applied Mathematics Laboratory, Courant Institute, New York University, New York, NY 10012, USA
M. Nicholas J. Moore
Affiliation:
Applied Mathematics Laboratory, Courant Institute, New York University, New York, NY 10012, USA Department of Mathematics and Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL 32306, USA
Leif Ristroph*
Affiliation:
Applied Mathematics Laboratory, Courant Institute, New York University, New York, NY 10012, USA
*
†Email address for correspondence: [email protected]
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Abstract

While fluid flows are known to promote dissolution of materials, such processes are poorly understood due to the coupled dynamics of the flow and the receding surface. We study this moving boundary problem through experiments in which hard candy bodies dissolve in laminar high-speed water flows. We find that different initial geometries are sculpted into a similar terminal form before ultimately vanishing, suggesting convergence to a stable shape–flow state. A model linking the flow and solute concentration shows how uniform boundary-layer thickness leads to uniform dissolution, allowing us to obtain an analytical expression for the terminal geometry. Newly derived scaling laws predict that the dissolution rate increases with the square root of the flow speed and that the body volume vanishes quadratically in time, both of which are confirmed by experimental measurements.

JFM classification

Boundary Layers: Boundary Layers Geophysical and Geological Flows: Geophysical and Geological Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 765 , 25 February 2015 , R3
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Copyright
© 2015 Cambridge University Press 

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References

Bai, G. E. & Armenante, P. M. 2009 Hydrodynamic, mass transfer, and dissolution effects induced by tablet location during dissolution testing. J. Pharm. Sci. 98 (4), 1511–1531.Google Scholar
Blumberg, P. N. & Curl, R. L. 1974 Experimental and theoretical studies of dissolution roughness. J. Fluid Mech. 65 (04), 735–751.Google Scholar
Childress, S. 2009 An Introduction to Theoretical Fluid Mechanics, Courant Lecture Notes in Mathematics, vol. 19. Courant Institute of Mathematical Sciences. AMS.Google Scholar
Colombani, J. 2008 Measurement of the pure dissolution rate constant of a mineral in water. Geochim. Cosmochim. Acta 72 (23), 5634–5640.CrossRefGoogle Scholar
Daccord, G. 1987 Chemical dissolution of a porous medium by a reactive fluid. Phys. Rev. Lett. 58 (5), 479–482.Google Scholar
Daccord, G. & Lenormand, R. 1987 Fractal patterns from chemical dissolution. Nature 325 (6099), 41–43.Google Scholar
Dokoumetzidis, A. & Macheras, P. 2006 A century of dissolution research: from Noyes and Whitney to the biopharmaceutics classification system. Intl J. Pharm. 321 (1), 1–11.Google Scholar
Duda, J. L. & Vrentas, J. S. 1971 Heat or mass transfer-controlled dissolution of an isolated sphere. Intl J. Heat Mass Transfer 14 (3), 395–407.CrossRefGoogle Scholar
Feldman, S. 1959 On the instability theory of the melted surface of an ablating body when entering the atmosphere. J. Fluid Mech. 6 (01), 131–155.CrossRefGoogle Scholar
Fokas, A. S. & Ablowitz, M. J. 2003 Complex Variables: Introduction and Applications. Cambridge University Press.Google Scholar
Ford, D. C. & Williams, P. W. 2007 Karst Hydrogeology and Geomorphology. John Wiley & Sons.Google Scholar
Garner, F. H. & Grafton, R. W. 1954 Mass transfer in fluid flow from a solid sphere. Proc. R. Soc. Lond. A 224 (1156), 64–82.Google Scholar
Garner, F. H. & Hoffman, J. M. 1961 Mass transfer from single solid spheres by free convection. AIChE J. 7 (1), 148–152.Google Scholar
Garner, F. H. & Keey, R. B. 1958 Mass-transfer from single solid spheres I: transfer at low Reynolds numbers. Chem. Engng Sci. 9 (2), 119–129.Google Scholar
Garner, F. H. & Suckling, R. D. 1958 Mass transfer from a soluble solid sphere. AIChE J. 4 (1), 114–124.Google Scholar
Grijseels, H., Crommelin, D. J. A. & De Blaey, C. J. 1981 Hydrodynamic approach to dissolution rate. Pharm. Weekbl. 3 (1), 1005–1020.Google Scholar
Hanratty, T. J. 1981 Stability of surfaces that are dissolving or being formed by convective diffusion. Annu. Rev. Fluid Mech. 13 (1), 231–252.CrossRefGoogle Scholar
Hao, Y. L. & Tao, Y.-X. 2002 Heat transfer characteristics of melting ice spheres under forced and mixed convection. J. Heat Transfer 124 (5), 891–903.Google Scholar
Heitz, E. 1991 Chemo-mechanical effects of flow on corrosion. Corrosion 47 (2), 135–145.Google Scholar
Hureau, J., Brunon, E. & Legallais, P. 1996 Ideal free streamline flow over a curved obstacle. J. Comput. Appl. Maths 72 (1), 193–214.Google Scholar
Jeschke, A. A., Vosbeck, K. & Dreybrodt, W. 2001 Surface controlled dissolution rates of gypsum in aqueous solutions exhibit nonlinear dissolution kinetics. Geochim. Cosmochim. Acta 65 (1), 27–34.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.Google Scholar
Linton, M. & Sutherland, K. L. 1960 Transfer from a sphere into a fluid in laminar flow. Chem. Engng Sci. 12 (3), 214–229.Google Scholar
Mahmood, T. & Merkin, J. H. 1988 Similarity solutions in axisymmetric mixed-convection boundary-layer flow. J. Engng Maths 22 (1), 73–92.Google Scholar
Mbogoro, M. M., Snowden, M. E., Edwards, M. A., Peruffo, M. & Unwin, P. R. 2011 Intrinsic kinetics of gypsum and calcium sulfate anhydrite dissolution: surface selective studies under hydrodynamic control and the effect of additives. J. Phys. Chem. 115 (20), 10147–10154.Google Scholar
Meakin, P. & Jamtveit, B. 2010 Geological pattern formation by growth and dissolution in aqueous systems. Proc. R. Soc. Lond. A 466 (2115), 659–694.Google Scholar
Missel, P. J., Stevens, L. E. & Mauger, J. W. 2004 Reexamination of convective diffusion/drug dissolution in a laminar flow channel: accurate prediction of dissolution rate. Pharmaceut. Res. 21 (12), 2300–2306.CrossRefGoogle Scholar
Moore, M. N. J., Ristroph, L., Childress, S., Zhang, J. & Shelley, M. J. 2013 Self-similar evolution of a body eroding in a fluid flow. Phys. Fluids 25 (11), 116602.Google Scholar
Nelson, K. G. & Shah, A. C. 1975 Convective diffusion model for a transport-controlled dissolution rate process. J. Pharm. Sci. 64 (4), 610–614.CrossRefGoogle ScholarPubMed
Noyes, A. A. & Whitney, W. R. 1897 The rate of solution of solid substances in their own solutions. J. Am. Chem. Soc. 19 (12), 930–934.Google Scholar
Ristroph, L., Moore, M. N. J., Childress, S., Shelley, M. J. & Zhang, J. 2012 Sculpting of an erodible body by flowing water. Proc. Natl Acad. Sci. USA 109 (48), 19606–19609.CrossRefGoogle ScholarPubMed
Schlichting, H. & Gersten, K. 2000 Boundary-Layer Theory. Springer.Google Scholar
Sparrow, E., Eichhorn, R. & Gregg, J. 2004 Combined forced and free convection in a boundary layer flow. Phys. Fluids 2 (3), 319–328.CrossRefGoogle Scholar
Steinberger, R. L. & Treybal, R. E. 1960 Mass transfer from a solid soluble sphere to a flowing liquid stream. AIChE J. 6 (2), 227–232.Google Scholar
Vanier, C. R. & Tien, C. 1970 Free convection melting of ice spheres. AIChE J. 16 (1), 76–82.CrossRefGoogle Scholar
Verniani, F. 1961 On meteor ablation in the atmosphere. Il Nuovo Cimento 19 (3), 415–442.Google Scholar