Journal of Fluid Mechanics

Rapids

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

Jinzi Mac Huanga1, M. Nicholas J. Moorea1a2 and Leif Ristropha1 c1

a1 Applied Mathematics Laboratory, Courant Institute, New York University, New York, NY 10012, USA

a2 Department of Mathematics and Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL 32306, USA

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.

(Received October 28 2014)

(Revised December 01 2014)

(Accepted December 09 2014)

(Online publication January 26 2015)

Key words

  • boundary layers;
  • geophysical and geological flows;
  • mixing and dispersion

Correspondence

c1 Email address for correspondence: ristroph@cims.nyu.edu

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