Power Law Gels at Finite Strains

Trevor S. K. Ng, Gareth H. McKinley

Many complex fluids exhibit power-law responses in their relaxation modulus; examples include foods, soft solids, fractal gels and other polydisperse systems. In the present study we investigate the rheological characteristics of such materials beyond the linear regime using a gluten-water gel as a prototypical system. The material functions of gluten dough under finite strains can be described by combining the linear viscoelastic response of a critical gel (Chambon and Winter 1987) with a Lodge rubber-like network to develop a frame invariant constitutive equation (Winter and Mours 1997). This generalized gel equation is a simple but accurate description of the material functions in the linear regime and also at large strains, using only two parameters. We compare the model predictions with experimental measurements in transient shear and elongational flows of gluten gels over a wide range of deformation rates. An essential feature of both the experimental data and the generalized gel model is a strain/rate separability in the system response. Further modifications to the generalized gel equation can be made by incorporating a damping function to include non-linear strain softening effects seen in more complex gels such as wheat flour doughs. From the rheological data, we find compelling evidence that indicates gluten to be a polymeric network consisting of flexible or semi-flexible chains between junction points and has a typical mesh size of approximately 20 nm.