Growth mechanics problems require the solution of mass balance equations that include supply terms and account for mass exchanges among constituents of a mixture. Though growth may often be accompanied by a variety of concomitant phenomena that increase modeling complexity, such as solid matrix deformation, evolving traction-free configurations, cell division, and active cell contraction, it is important to distinguish these accompanying phenomena from the fundamental growth process that consists of deposition or removal of mass from the solid matrix. Therefore, the objective of this study is to present a canonical problem of growth, namely, dissolution of a rigid solid matrix in a solvent. This problem illustrates a case of negative growth (loss of mass) of the solid in a mixture framework that includes three species, a solid, a solvent, and a solute, where the solute is the product of the solid dissolution. By analyzing both volumetric and surface dissolutions, the two fundamental modes of growth are investigated within the unified framework of mixture theory.
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January 2011
Research Papers
The Role of Mass Balance Equations in Growth Mechanics Illustrated in Surface and Volume Dissolutions
Gerard A. Ateshian
Gerard A. Ateshian
Fellow ASME
Department of Mechanical Engineering, and Department of Biomedical Engineering,
e-mail: ateshian@columbia.edu
Columbia University
, 500 West 120th Street, MC4703, New York, NY 10027
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Gerard A. Ateshian
Fellow ASME
Department of Mechanical Engineering, and Department of Biomedical Engineering,
Columbia University
, 500 West 120th Street, MC4703, New York, NY 10027e-mail: ateshian@columbia.edu
J Biomech Eng. Jan 2011, 133(1): 011010 (6 pages)
Published Online: December 23, 2010
Article history
Received:
October 20, 2010
Revised:
November 16, 2010
Posted:
November 29, 2010
Published:
December 23, 2010
Online:
December 23, 2010
Citation
Ateshian, G. A. (December 23, 2010). "The Role of Mass Balance Equations in Growth Mechanics Illustrated in Surface and Volume Dissolutions." ASME. J Biomech Eng. January 2011; 133(1): 011010. https://doi.org/10.1115/1.4003133
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