We present a theory for the chemically-induced volume transitions of hydrogels. Consistent with experimental observations, we account for a sharp interface separating swelled and collapsed phases of the underlying polymer network. The polymer chains are treated as a solute with an associated diffusion potential and their concentration is assumed to be discontinuous across the interface. In addition to the standard bulk and interfacial equations imposing force balance and solute balance, the theory involves an ancillary interfacial equation imposing configurational force balance. Motivated by experimental observations, we specialize the theory to the situation where the time scale associated with the interface motion is slow compared to those associated with diffusion in the bulk phases. We present a hybrid eXtended-Finite-Element/Level-Set Method (XFE/LSM) for obtaining approximate solutions to the equations arising under this specialization. As an application, we consider the swelling of a spherical specimen whose boundary is traction-free and is in contact with a reservoir of uniform chemical potential. Our numerical results exhibit good qualitative comparison with experimental observations and predict characteristic swelling times that are proportional to the square of the specimen radius. Our results also suggest several possible synthetic pathways that might be pursued as a means to engineer hydrogels with optimal response times.
Publisher
Department of Theoretical and Applied Mechanics (UIUC)
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