Rheological study of two-dimensional very anisometric colloidal particle suspensions: from shear-induced orientation to viscous dissipation.

In the present study, we investigate the evolution with shear of the viscosity of aqueous suspensions of size-selected natural swelling clay minerals for volume fractions extending from isotropic liquids to weak nematic gels. Such suspensions are strongly shear-thinning, a feature that is systematically observed for suspensions of nonspherical particles and that is linked to their orientational properties. We then combined our rheological measurements with small-angle X-ray scattering experiments that, after appropriate treatment, provide the orientational field of the particles. Whatever the clay nature, particle size, and volume fraction, this orientational field was shown to depend only on a nondimensional Péclet number (Pe) defined for one isolated particle as the ratio between hydrodynamic energy and Brownian thermal energy. The measured orientational fields were then directly compared to those obtained for infinitely thin disks through a numerical computation of the Fokker-Plank equation. Even in cases where multiple hydrodynamic interactions dominate, qualitative agreement between both orientational fields is observed, especially at high Péclet number. We have then used an effective approach to assess the viscosity of these suspensions through the definition of an effective volume fraction. Using such an approach, we have been able to transform the relationship between viscosity and volume fraction (ηr = f(φ)) into a relationship that links viscosity with both flow and volume fraction (ηr = f(φ, Pe)).

Universal anomalous diffusion of weakly damped particles.

We show that anomalous diffusion arises in two different models for the motion of randomly forced and weakly damped particles: one is a generalization of the Ornstein-Uhlenbeck process with a random force, which depends on position as well as time, the other is a generalization of the Chandrasekhar-Rosenbluth model of stellar dynamics, encompassing non-Coulombic potentials. We show that both models exhibit anomalous diffusion of position x and momentum p with the same exponents: (x{2})∼C{x}t{2} and (p{2})∼C{p}t{2/5}. We are able to determine the prefactors C{x}, C{p} analytically.

Multiple regimes of diffusion.

We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviors, depending upon the limiting cases which are considered, some of which have been discussed in earlier work. Here, we explore the full space of dimensionless parameters and present an "asymptotic phase diagram" which delineates the limiting regimes.