Fluid Dynamics

, Volume 47, Issue 1, pp 1–9 | Cite as

Mathematical modeling of transport-growth processes in multiphase biological continua

  • N. N. Kizilova
  • S. A. Logvenkov
  • A. A. Stein


The model of a growing medium consisting of two phases, liquid and solid, is developed. Growth is treated as a combination of the irreversible deformation of the solid phase and its mass increment due to mass exchange with the liquid phase. The inelastic strain rate of the solid phase depends on the stresses in it, which are determined by the forces both external with respect to the medium and exerted by the liquid phase. In the liquid phase the pressure develops due to the presence of a chemical component whose displacement is hampered by its interaction with the solid phase. The approach developed makes it possible to waive many problems discussed in the theory of growing continua. Possible generalizations are considered.


multiphase continua biological growth deformation theory mass transfer osmosis mathematical models 


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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • N. N. Kizilova
    • 1
    • 2
  • S. A. Logvenkov
    • 1
    • 2
  • A. A. Stein
    • 1
    • 2
  1. 1.Institute of MechanicsMoscow State UniversityMoscowRussia
  2. 2.State University — Higher School of EconomicsKharkiv National UniversityKharkivUkraine

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