Rheology dynamics of aggregating colloidal suspensions

Abstract

We study a colloidal model based on population balances in the context of complex fluid rheology. Two typical particle microstructure kinetics, orthokinetic, collisions due to shear, and perikinetic, collisions due to Brownian motion, are found to appear at continuum as different flow behaviors - those having monotonic and non-monotonic flow curves, respectively. Solving the colloidal model together with the 1D Stokes equation for laminar, incompressible flow with Couette boundary conditions, allows bridging the gap between the rheological experiments and the microstructural modeling. The analysis of such a model reveals that orthokinetic particle suspensions have a uniquely defined, continuous steady state shear profile, whereas suspensions in which also perikinetic collisions are present, the steady state can be shear banded and non-unique. Thus, the shear banded configurations at a steady state are found to depend on the initial conditions and the collision kinetics of the system. At high shear rates all the studied cases show continuous shear profiles.

Dynamic hysteresis in the rheology of complex fluids

“…In the model, the structure dynamics is proportional toγ −k , a known fact in some of the first-principles collision models for colloids [9,27,28] and also experimentally observed in numerous complex fluids [29][30][31][32][33]. Since the fluid structure dynamically relaxes at a rate imposed by the current shear rate, but the waiting time t w in the experimental protocol is fixed, below a certain shear rate, the structure fails to recover the steady state.…”

“…Furthermore, since the growth (A b , A s ) and breakage (B s ) rates are not equal the relaxation rate is asymmetric around the steady state even at the same shear rate: The time scale depends on whether the φ is increasing or decreasing. With these properties, the model follows first-principles colloidal models, in which the kernels are usually asymmetric and shear dependent [9,27,28], and complies with what is found experimenally as well [29][30][31][32][33]. Finally, the Maxwell stress element in the viscoelastic model introduces another time scale through stress evolution, which can be tuned using G 0 .…”

“…Simple-yield-stress fluids, showing only weak time dependence, also exhibit intrinsic flow curves of monotonic, Herschel-Bulkley shape, as opposed to strongly time-dependent ones, where the intrinsic flow curve has a nonmonotonic shape. As a consequence, only thixotropic fluids are expected to be prone to shear bands and the associated hysteretic behavior [8,9]. In this article, we discuss materials of a simple-yield-stress type.…”

Yield stress materials in soft condensed matter

“…Finally, regarding the local behavior of the fluid during shear start-up, recent experimental and numerical studies have shed new light on the nature of the stress maximum. In Brownian colloidal systems, the stress maximum coincides with the maximum structural anisotropy (Koumakis et al, 2012a;Mohraz and Solomon, 2005) [see Fig. 13(a,b)].…”

“…In this approach the power-law scaling for the fluidization time under creep is recovered, but with a smaller exponent β 1 (Moorcroft and Fielding, 2013). Another promising approach consists of a structural model of colloidal aggregates that incorporates viscoelasticity Lehtinen et al, 2013;Mohtaschemi et al, 2014). Such a phenomenological model recovers power-law scalings but only predicts trivial exponents α = β = 1 and thus fails to capture the link between both transients and the steady-state rheology observed in microgels.…”