A general formulation of compaction problems is described and the classification of these problems in accordance with boundary conditions is presented. A basically new class of compaction boundary problems in a finite region with moving inner boundaries is specified. New models of compaction describe porous media in which qualitative microstructural changes and associated sharp changes in material properties take place. At these time moments, the permeability of the medium drops to zero at minimum porosity or the skeleton loses its cohesion and breaks down. In the latter case, the porous medium is transformed into concentrated dispersive mixtures of the suspension, emulsion or sol type. Phenomena associated with jump-like changes in material properties and resembling phase transformations in homogeneous media arise at inner boundaries. Several physicochemical and mathematical aspects of these problems are discussed. Examples of analytical solutions of some problems are presented. In particular, the related wave processes are analyzed. The theory of compaction has numerous applications in geophysics and technological problems of the chemical, petrochemical, food-processing and biochemical industries. This class of compaction models is advantageous to the study of such processes. As an example, the paper presents a review of several geophysical applications including problems of mud volcanism, sedimentation and motion of partially molten mantle rocks.
compaction problems, boundary conditions, analytical solutions.
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