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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: ristroph@cims.nyu.edu
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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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