Rheological constitutive equation for model of soft glassy materials

Details Rheological constitutive equation for model of soft glassy materials Rheological constitutive equation for model of soft glassy materials

1997-11-29

arxiv.org/abs/cond-mat/9712001v2

Phys. Rev. E 58: 738--759,1998

Physics

Condensed Matter

Soft Condensed Matter

24 pages, REVTeX, uses multicol, epsf and amssymp; 20 postscript figures (included). Minor changes to text (relation to mode c

Scientific paper

10.1103/PhysRevE.58.738

We solve exactly and describe in detail a simplified scalar model for the low frequency shear rheology of foams, emulsions, slurries, etc. [P. Sollich, F. Lequeux, P. Hebraud, M.E. Cates, Phys. Rev. Lett. 78, 2020 (1997)]. The model attributes similarities in the rheology of such ``soft glassy materials'' to the shared features of structural disorder and metastability. By focusing on the dynamics of mesoscopic elements, it retains a generic character. Interactions are represented by a mean-field noise temperature x, with a glass transition occurring at x=1 (in appropriate units). The exact solution of the model takes the form of a constitutive equation relating stress to strain history, from which all rheological properties can be derived. For the linear response, we find that both the storage modulus G' and the loss modulus G'' vary with frequency as \omega^{x-1} for 1

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