Theory of Deformation and Flow in Gels

The Tanaka-Fillmore theory (Tanaka et al. 1973 Tanaka and Fillmore 1979) is a purely mechanical theory based on the theory of elasticity (Lifshitz et al. 1986). The gel network is described by a displacement vector field uir). This field describes how every point in a certain state is shifted compared to the equilibrium reference state. A point that is at r in the reference state is shifted to r (r) = r -F u r) in the deformed state. In the reference state, u(r) is zero for all r. Expansion and contraction of the network corresponds to solvent flowing into or out of the gel. 

---