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Cracking Condition of Cohesionless Porous Materials in Drying Processes

The invasion of air into porous systems in drying processes is often localized in soft materials, such as colloidal suspensions and granular pastes, and it typically develops in the form of cracks before ordinary drying begins. To investigate such processes, we construct an invasion percolation model on a deformable lattice for cohesionless elastic systems, and with this model we derive the condition under which cracking occurs. A Griffith-like condition characterized by a dimensionless parameter is proposed, and its validity is checked numerically. This condition indicates that the ease with which cracking occurs increases as the particles composing the material become smaller, as the rigidity of the system increases, and as the degree of heterogeneity characterizing the drying processes decreases.