MATHEMATICAL MODELING OF THE RHEOLOGY
OF SWELLING SYSTEMS

N. B. Pleshchinskii, M. G. Khramchenkov,
and É. M. Khramchenkov

UDC 552.52,624.131.54

Consideration is given to a mathematical model of the rheology of 
swelling systems, the basis for which is provided by generalization 
of the filtration-consolidation theory to the case where the mass 
of the solid phase of a porous skeleton changes due to the flow of 
a fluid during the swelling and shrinkage processes under the action 
of osmotic pressure. The problem on swelling and shrinkage of a clay 
layer has been formulated and solved. The features of the model, which 
are important for explanation of certain characteristic features of 
the processes in swelling systems, have been investigated based on 
an analysis of the solution. It has been shown that the solutions 
obtained are in good agreement with experimental results.

Kazan' State University, 17, Universitetskaya Str., Kazan', 
420008, Russia; email: Maxim.Khramchenkov@ksu.ru. Translated from 
Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 6, pp. 93-99, November-December, 
2005. Original article submitted March 19, 2004.