Computational Models for Gel Dynamics
A gel consists of two-phases, a networked polymer and a fluid solvent. The mechanical and rheological properties of gels can change dramatically in response to temperature, stress, and chemical stimulus. Because of their adaptivity, gels are important in many biological systems, e.g. gels make up the cytoskeleton and cytoplasm of cells and the mucus in the respiratory and digestive systems, and they are involved in the formation of blood clots. The mathematical models of gels we are considering treat the network phase as a viscoelastic fluid and the solvent phase as a viscous fluid. The dynamics are governed by a coupled system of time-dependent partial differential equations which consist of transport equations for the two phases and the viscoelastic stresses, and two coupled momentum equations for the velocity fields of the two fluids. We will give an overview of these gel models and discuss our efforts in developing efficient and robust computational models for simulating them.
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