Effect of viscoelastic relaxation on moisture transport in foods. Part I: Solution of general transport equation

Pawan P. Singh, Dirk E. Maier, John H. Cushman, Kamyar Haghighi, Carlos Corvalan

Research output: Contribution to journalArticlepeer-review


Within the framework of continuum mechanics, Singh et al. [1] developed an integro-differential equation, which applies to both Darcian (Fickian) and non-Darcian (non-Fickian) modes of fluid transport in swelling biological systems. A dimensionless form of the equation was obtained and transformed from moving Eulerian to the stationary Lagrangian coordinates. Here a solution scheme for the transport equation is developed to predict moisture transport and viscoelastic stresses in spheroidal biopolymeric materials. The equation was solved numerically and results used for predicting drying and sorption curves, moisture profiles, and viscoelastic stresses in soybeans. The Lagrangian solution was obtained by assembling together several schemes: the finite element method was used to discretize the equation in space; non-linearity was addressed using the Newton-Raphson method; the Volterra term was handled via a time integration scheme of Patlashenko et al. [2] and the Galerkin rule was used to solve the time-differential term. The solution obtained in Lagrangian coordinates was transformed back to the Eulerian coordinates. In part II of this sequence we present the numerical results.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalJournal of Mathematical Biology
Issue number1
StatePublished - Jul 2004
Externally publishedYes


  • Biopolymers
  • Finite element method
  • Glass transition
  • Non-Darcian
  • Non-Fickian
  • Volterra term

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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