1997/12/31 by Peter Sollich · 8 citations
Chemical Engineering · Materials Science · Physics and Astronomy · #Liquid Crystal Research Advancements #Material Dynamics and Properties #Rheology and Fluid Dynamics Studies #cond-mat.mtrl-sci #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.58.738
published as Phys. Rev. E 58: 738--759,1998 · 24 pages, REVTeX, uses multicol, epsf and amssymp; 20 postscript figures (included). Minor changes to text (relation to mode coupling theory, update on recent foam simulations etc.) and figures (emphasis on low frequency regime); typos corrected and reference added. Version to appear in Physical Review E
arxiv created 1998/04/20 · openalex publication_date 1998/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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. H'ebraud, and 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^\ensuremath' and the loss modulus G^\ensuremath'' vary with frequency as \ensuremathω^x\ensuremath-1 for 1<x<2, becoming flat near the glass transition. In the glass phase, aging of the moduli is predicted. The steady shear flow curves show power-law fluid behavior for x<2, with a nonzero yield stress in the glass phase; the Cox-Merz rule does not hold in this non-Newtonian regime. Single and double step strains further probe the nonlinear behavior of the model, which is not well represented by the Bernstein-Kearseley-Zapas relation. Finally, we consider measurements of G^\ensuremath' and G^\ensuremath'' at finite strain amplitude \ensuremathγ. Near the glass transition, G^\ensuremath'' exhibits a maximum as \ensuremathγ is increased in a strain sweep. Its value can be strongly overestimated due to nonlinear effects, which can be present even when the stress response is very nearly harmonic. The largest strain \ensuremathγc at which measurements still probe the linear response is predicted to be roughly frequency independent.