A Poroviscoelasto-plastic Model to Predict Creeping and Delayed Sedimentation in Colloidal Gels Under Gravity

Colloidal gels, used in food, cosmetics, and medicines, often change under gravity. They may undergo "creeping sedimentation," where they slowly compress while keeping their structure, or "delayed sedimentation," where they stay stable before collapsing suddenly. Current models, like the poroelastic model, explain creeping sedimentation but cannot fully describe delayed sedimentation, leaving some gel-product stability unpredictable. To bridge this gap, we propose a poroviscoelasto-plastic model that combines three elements: viscous (to slow deformation), elastic (to handle strain from compression), and plastic (to account for permanent deformation during collapse). A structural parameter λ ranging from 1 (gel intact) to 0 ( gel collapsed), is introduced to link microscopic changes in the gel to the yield stress and elastic modulus. When yield stress exceeds gravitational stress, the gel experiences elastic strain without collapsing, described by the poroviscoelastic part of the model. If yield stress drops below gravitational stress, the gel collapses, leading to plastic strain, described by the poroviscoplastic part. Our findings underscore the importance of linking microscopic changes in the gel to its macroscopic behavior, providing a clearer understanding of when a gel shifts from slow deformation to rapid collapse.