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The dynamics of macroscopically homogeneous sheared suspensions of neutrally buoyant, non-Brownian spheres is investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics. We show that the complex dynamics of sheared suspensions can be characterized as a chaotic motion in phase space and determine the dependence of the largest Lyapunov exponent on the volume fraction ϕ. We also offer evidence that the chaotic motion is responsible for the loss of memory in the evolution of the system and demonstrate this loss of correlation in phase space. The loss of memory at the microscopic level of individual particles is also shown in terms of the autocorrelation functions for the two transverse velocity components. Moreover, a negative correlation in the transverse particle velocities is seen to exist at the lower concentrations, an effect which we explain on the basis of the dynamics of two isolated spheres undergoing simple shear. In addition, we calculate the probability distribution function of the transverse velocity fluctuations and observe, with increasing ϕ, a transition from exponential to Gaussian distributions.The simulations include a non-hydrodynamic repulsive interaction between the spheres which qualitatively models the effects of surface roughness and other irreversible effects, such as residual Brownian displacements, that become particularly important whenever pairs of spheres are nearly touching. We investigate, for very dilute suspensions, the effects of such a non-hydrodynamic interparticle force on the scaling of the particle tracer diffusion coefficients Dy and Dz, respectively, along and normal to the plane of shear, and show that, when this force is very short-ranged, both are proportional to ϕ2 as ϕ → 0. In contrast, when the range of the non-hydrodynamic interaction is increased, we observe a crossover in the dependence of Dy on ϕ, from ϕ2 to ϕ as ϕ → 0. We also estimate that a similar crossover exists for Dz but at a value of ϕ one order of magnitude lower than that which we were able to reach in our simulations.

The velocity fluctuations present in macroscopically homogeneous suspensions of neutrally buoyant, non-Brownian spheres undergoing simple shear flow, and their dependence on the microstructure developed by the suspensions, are investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics simulations. We show that, in the dilute limit, the standard deviation of the velocity fluctuations (the so-called suspension temperature) is proportional to the volume fraction, in both the transverse and the flow directions, and that a theoretical prediction, which considers only for the hydrodynamic interactions between isolated pairs of spheres, is in good agreement with the numerical results at low concentrations. Furthermore, we show that the whole velocity autocorrelation function can be predicted, in the dilute limit, based purely in two-particle encounters. We also simulate the velocity fluctuations that would result from a random hard-sphere distribution of spheres in simple shear flow, and thereby investigate the effects of the microstructure on the velocity fluctuations. Analogous results are discussed for the fluctuations in the angular velocity of the suspended spheres. In addition, we present the probability density functions for all the linear and angular velocity compo- The simulations include a non-hydrodynamic repulsive force between the spheres which, although extremely short ranged, leads to the development of fore-aft asymmetric distributions for large enough volume fractions, if the range of that force is kept unchanged.On the other hand, we show that, although the pair distribution function recovers its fore-aft symmetry in dilute suspensions, it remains anisotropic and that this anisotropy can be accurately described by assuming the complete absence of any permanent doublets of spheres.We also present a simple correction to the analysis of laser-Doppler velocimetry measurements, that only takes into account the mean angular rotation of the spheres in the vorticity direction, and which substantially improves the interpretation of these measurements at low volume fractions.

We report observations of a new electric field-and shear-induced many-body phenomenon in the behavior of suspensions. Its origin is dielectrophoresis accompanied by the field-induced phase separation. As a result, a suspension undergoes a field-driven phase separation leading to the formation of a distinct boundary between regions enriched with and depleted of particles. The theoretical predictions are consistent with experimental data even though the model contains no fitting parameters. It is demonstrated that the field-induced dielectrophoresis accompanied by the phase separation provides a new method for concentrating particles in focused regions and for separating biological and non-biological materials, a critical step in the development of miniaturizing biological assays.

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