Rheology of Soft Glassy Materials

Abstract

We attribute similarities in the rheology of many soft materials (foams, emulsions, slurries, etc.) to the shared features of structural disorder and metastability. A generic model for the mesoscopic dynamics of "soft glassy matter" is introduced, with interactions represented by a mean-field noise temperature x. We find power law fluid behavior either with (x < 1) or without (1 < x < 2) a yield stress. For 1 < x < 2, both storage and loss modulus vary with frequency as ω x−1 , becoming flat near a glass transition (x = 1). Values of x ≈ 1 may result from marginal dynamics as seen in some spin glass models.Submitted to Physical Review 83.70.Hq, 05.40+j Many soft materials, such as foams, emulsions, pastes and slurries, have intriguing rheological properties. Experimentally, there is a well-developed phenomenology for such systems: their nonlinear flow behavior is often fit to the form σ = A + Bγ n where σ is shear stress andγ strain rate. This is the Herschel-Bulkeley equation [1,2]; or (for A = 0) the "power-law fluid" [1][2][3]. For the same materials, linear or quasi-linear viscoelastic mesurements often reveal storage and loss moduli′ is usually about 0.1) with a frequency dependence that is either a weak power law (clay slurries, paints, microgels) or negligible (tomato paste, dense emulsions, dense multilayer vesicles, colloidal glasses) [4][5][6][7][8][9][10]. This behavior persists down to the lowest accessible frequencies (about 10 −3 -1 Hz depending on the system), in apparent contradiction to linear response theory [11], which requires that G ′′ (ω) should be an odd function of ω.That similar anomalous rheology should be seen in such a wide range of soft materials suggests a common cause. Indeed, the frequency dependence indicated above points strongly to the generic presence of slow "glassy" dynamics persisting to arbitrarily small frequencies. This feature is found in several other contexts [12][13][14], such as elastic manifold dynamics in random media [15,16]. The latter is suggestive of rheology: charge density waves, vortices, contact lines, etc. can "flow" in response to an imposed "stress". In this Letter we argue that glassy dynamics is a natural consequence of two properties shared by all the soft materials mentioned above: structural disorder and metastability. In such materials, thermal motion alone is not enough to achieve complete structural relaxation. The system has to cross energy barriers (for example those associated with rearrangement of droplets in an emulsion) that are very large compared to typical thermal energies. Therefore the system adopts a disordered, metastable configuration even when (as in a monodisperse emulsion or foam) the state of least free energy would be ordered [17]. While the importance of disorder has been noted before for specific systems [7,11,18-21], we feel that its unifying role in rheological modelling has not been appreciated.To test these ideas, we construct a minimal "generic model" for soft glassy matter. For simplicity, we ignore tensorial asp...

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