Rheology of confined non-Brownian suspensions

We study the rheology of confined suspensions of neutrally buoyant rigid monodisperse spheres in plane-Couette flow using Direct Numerical Simulations. We find that if the width of the channel is a (small) integer multiple of the sphere's diameter, the spheres self-organize into two-dimensional layers that slide on each other and the suspension's effective viscosity is significantly reduced. Each two-dimensional layer is found to be structurally liquid-like but their dynamics is frozen in time.Comment: Submitted to PRL. Supplemental Material added as an appendix. Includes links to youtube video

Granular Motor in the Non-Brownian Limit

In this work we experimentally study a granular rotor which is similar to the famous Smoluchowski-Feynman device and which consists of a rotor with four vanes immersed in a granular gas. Each side of the vanes can be composed of two different materials, creating a rotational asymmetry and turning the rotor into a ratchet. When the granular temperature is high, the rotor is in movement all the time, and its angular velocity distribution is well described by the Brownian Limit discussed in previous works. When the granular temperature is lowered considerably we enter the so-called Single Kick Limit, where collisions occur rarely and the unavoidable external friction causes the rotor to be at rest for most of the time. We find that the existing models are not capable of adequately describing the experimentally observed distribution in this limit. We trace back this discrepancy to the non-constancy of the deceleration due to external friction and show that incorporating this effect into the existing models leads to full agreement with our experiments. Subsequently, we extend this model to describe the angular velocity distribution of the rotor for any temperature of the gas, and obtain a very good agreement between the model and experimental data

Universality Class of the Reversible-Irreversible Transition in Sheared Suspensions

Collections of non-Brownian particles suspended in a viscous fluid and subjected to oscillatory shear at very low Reynolds number have recently been shown to exhibit a remarkable dynamical phase transition separating reversible from irreversible behaviour as the strain amplitude or volume fraction are increased. We present a simple model for this phenomenon, based on which we argue that this transition lies in the universality class of the conserved DP models or, equivalently, the Manna model. This leads to predictions for the scaling behaviour of a large number of experimental observables. Non-Brownian suspensions under oscillatory shear may thus constitute the first experimental realization of an inactive-active phase transition which is not in the universality class of conventional directed percolation.Comment: 4 pages, 2 figures, final versio

From non-Brownian Functionals to a Fractional Schr\"odinger Equation

We derive backward and forward fractional Schr\"odinger type of equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [PRL {\bf 96}, 230601 (2006)] provide the correct fractional framework for the problem at hand. In the limit of normal diffusion we recover the Feynman-Kac treatment of Brownian functionals. For applications, we calculate the distribution of occupation times in half space and show how statistics of anomalous functionals is related to weak ergodicity breaking.Comment: 5 page

Multiple transient memories in experiments on sheared non-Brownian suspensions

A system with multiple transient memories can remember a set of inputs but subsequently forgets almost all of them, even as they are continually applied. If noise is added, the system can store all memories indefinitely. The phenomenon has recently been predicted for cyclically sheared non-Brownian suspensions. Here we present experiments on such suspensions, finding behavior consistent with multiple transient memories and showing how memories can be stabilized by noise.Comment: 5 pages, 4 figure

Steady state particle distribution of a dilute sedimenting suspension

Sedimentation of a non-Brownian suspension of hard particles is studied. It is shown that in the low concentration limit a two-particle distribution function ensuring finite particle correlation length can be found and explicitly calculated. The sedimentation coefficient is computed. Results are compared with experiment.Comment: 4 pages, 2 figure

Deterministic and stochastic behaviour of non-Brownian spheres in sheared suspensions

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 $\phi$. 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 velocity fluctuations and observe, with increasing $\phi$, 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 the effects of such a non-hydrodynamic interparticle force on the scaling of the particle tracer diffusion coefficient $D$ for very dilute suspensions, and show that, when this force is very short-ranged, $D$ becomes proportional to $\phi^2$ as $\phi \to 0$. In contrast, when the range of the non-hydrodynamic interaction is increased, we observe a crossover in the dependence of $D$ on $\phi$, from $\phi^2$ to $\phi$ as $\phi \to 0$.Comment: Submitted to J. Fluid Mec

Trajectory analysis for non-Brownian inertial suspensions in simple shear flow

We analyse pair trajectories of equal-sized spherical particles in simple shear flow for small but finite Stokes numbers. The Stokes number, \mbox{\textit{St}} \,{=}\, \dot{\gamma} \tau_p, is a dimensionless measure of particle inertia; here, $\tau_p$ is the inertial relaxation time of an individual particle and $\dot{\gamma}$ is the shear rate. In the limit of weak particle inertia, a regular small-\mbox{\textit{St}} expansion of the particle velocity is used in the equations of motion to obtain trajectory equations to the desired order in \mbox{\textit{St}}. The equations for relative trajectories are then solved, to O(\mbox{\textit{St}}), in the dilute limit, including only pairwise interactions. Particle inertia is found to destroy the fore–aft symmetry of the zero-Stokes trajectories, and finite-\mbox{\textit{St}} open trajectories suffer net transverse displacements in the velocity gradient and vorticity directions. The vorticity displacement remains O(\mbox{\textit{St}}), while the scaling of the gradient displacement increases from O(\mbox{\textit{St}}) for far-field open trajectories, to O(\mbox{\textit{St}}^{{1}/{2}}) for open trajectories with O(\mbox{\textit{St}}^{{1}/{2}}) upstream gradient offsets. The gradient displacement also changes sign, being negative close to the plane of the reference sphere (the shearing plane) on account of dominant lubrication interactions, and then becoming positive at larger off-plane separations. The transverse displacements accompanying successive pair interactions lead to a diffusive behaviour for long times. The shear-induced diffusivity in the vorticity direction is O(\mbox{\textit{St}}^2\phi \dot{\gamma} a^2), while that in the gradient direction scales as O(\mbox{\textit{St}}^2 \ln \mbox{\textit{St}}\,\phi \dot{\gamma} a^2) and O(\mbox{\textit{St}}^2 \phi \ln (1/\phi) \dot{\gamma} a^2) in the limits \phi \,{\ll}\, \mbox{\textit{St}}^{{1}/{3}} and \mbox{\textit{St}}^{{1}/{3}} \,{\ll}\, \phi \,{\ll}\, 1, respectively. Further, the region of zero-Stokes closed trajectories is destroyed, and there exists a new attracting limit cycle whose location in the shearing plane is, at leading order, independent of \mbox{\textit{St}}. The extension of the present analysis to include a generic linear flow, and the implications of the finite-\mbox{\textit{St}} trajectory modifications for coagulating systems are discussed