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

Abstract

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 $\varphi$. 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 $\varphi$, 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 ${\varphi }^2$ as $\varphi \to 0$. In contrast, when the range of the non-hydrodynamic interaction is increased, we observe a crossover in the dependence of $D$ on $\varphi$, from ${\varphi }^2$ to $\varphi$ as $\varphi \to 0$.

Submitted to J. Fluid Mech

Cited by in corpus (17)

• Local determination of the constitutive law of a dense suspension of non-colloidal particles through MRI
• Mechanism of margination in confined flows of blood and other multicomponent suspensions
• Shear stresses of colloidal dispersions at the glass transition in equilibrium and in flow
• Swapping trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres
• Segregation by membrane rigidity in flowing binary suspensions of elastic capsules
• Directional locking in deterministic lateral displacement microfluidic separation systems
• Trajectory and distribution of suspended non-Brownian particles moving past a fixed spherical or cylindrical obstacle
• Particle migration of suspensions in a pressure-driven flow over and through a porous structure
• Fluctuations and diffusion in sheared athermal suspensions of deformable particles
• Anomalous distribution functions in sheared suspensions
• The transition to irreversibility in sheared suspensions: An analysis based on a mesoscopic entropy production
• Rheology of periodically sheared suspensions undergoing reversible-irreversible transition
• Suspension flow: do particles act as mixers?
• Nonmonotonic diffusion in sheared active suspensions of squirmers
• Hydrodynamic irreversibility of non-Brownian suspensions in highly confined duct flow
• Geometrically-protected reversibility in hydrodynamic Loschmidt-echo experiments
• Dynamics and clustering of sedimenting disc lattices