Generalized hydrodynamics of a dilute suspension of finite-sized particles: Dynamic viscosity (original) (raw)
Related papers
Physical Review E, 2018
We investigate the microstructure and rheology of a hardsphere suspension in a Newtonian fluid confined in a cylindrical channel and undergoing pressure-driven flow using Monte Carlo simulations. We develop a hydrodynamic framework inspired by dynamical density functional theory approaches in which the contributions due to various flow-induced hydrodynamic interactions (HI) are included in the form of thermodynamic work done by these HI-derived forces in displacing the hardspheres. Using this framework, we can self-consistently determine the effect of the local microstructure on the average flow-field and vice versa, and co-evolve the inhomogeneous density distribution and the flattening velocity profile with increase in density of suspended particles. Specifically, we explore the effect on the local microstructure due to the inclusion of forces arising from confinement-induced inertial effects, forces due to solvent-mediated interparticle interactions and the dependence of the diffusivity on the local density. We examine the dependence of the apparent viscosity of the suspension on the volume fraction of hardspheres in the cylinder, the flow rate and the diameter of the cylinder, and investigate their effects on the local microstructure.
Influence of hydrodynamics on many-particle diffusion in 2D colloidal suspensions
The European Physical Journal E - Soft Matter, 2004
We study many-particle diffusion in 2D colloidal suspensions with full hydrodynamic interactions through a novel mesoscopic simulation technique. We focus on the behaviour of the effective scaled tracer and collective diffusion coefficients DT (ρ)/D0 and DC (ρ)/D0, where D0 is the single-particle diffusion coefficient, as a function of the density of the colloids ρ. At low Schmidt numbers Sc = O(1), we find that hydrodynamics has essentially no effect on the behaviour of DT (ρ)/D0. At larger Sc, DT (ρ)/D0 is enhanced at all densities, although the differences compared to the case without hydrodynamics are minor. The collective diffusion coefficient, on the other hand, is much more strongly coupled to hydrodynamical conservation laws and is distinctly different from the purely dissipative case.
Statistical description of the shear-induced diffusion of a suspension of non-Brownian particles
Using mesoscopic nonequilibrium thermodynamics, we calculate the entropy production of a dilute suspension of non-Brownian particles subject to an oscillatory shear flow. We find that an Onsager coupling leads to a breakdown of the fluctuation-dissipation theorem and to the shear induced diffusion effect observed in experiments. By contracting the description, we derive a Smoluchowski equation from which the scaling of the mean square displacement on the shear rate and particle diameter reported in experiments is obtained. We also perform lattice Boltzmann simulations to show the shear induced diffusion effects, and how the transition to irreversibility can be characterized through the power spectra of particle trajectories.
Deterministic and stochastic behaviour of non-Brownian spheres in sheared suspensions
Journal of Fluid Mechanics, 2002
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 velocity fluctuations and observe, with increasing φ, a transition from exponential to Gaussian distributions.
The constitutive relation of suspensions of noncolloidal particles in viscous fluids
Physics of Fluids, 2003
The motion of noncolloidal particles convected by a nonhomogeneous and nonstationary viscous fluid flow is investigated, assuming that inertial effects can be neglected. It appears that the particle volumetric flux is the sum of a convective part, V E , and a diffusive term, ϪD self "", where V E is the Eulerian mean velocity of a test particle, is the particle volume fraction, and D self is the coefficient of self-diffusion. The latter measures the local temporal growth of the mean square displacement of a tracer particle from its average position and can be written as D self (r) ϭD(r,r), where the cross-diffusion tensor D(r 1 ,r 2) is the time integral of the velocity cross-correlation function. On the other hand, the Eulerian mean velocity V E is the sum of the coarse-grained average particle velocity, V , and a drift velocity, V d (r)ϭϪ͓(ץ/ץr 2) •D T (r,r 2)͔ r 2 ϭr. This last term, which is identically zero when the suspended particles are passive tracers, indicates that the suspended particles tend to move toward regions with smaller diffusivities. This result demonstrates that the motion of each suspended particle is a random process satisfying a generalized nonlinear Langevin equation, where the fluctuating term is described through the cross diffusivity D.
Convection in colloidal suspensions with particle-concentration-dependent viscosity
The European Physical Journal E, 2010
The onset of thermal convection in a horizontal layer of a colloidal suspension is investigated in terms of a continuum model for binary-fluid mixtures where the viscosity depends on the local concentration of colloidal particles. With an increasing difference between the viscosity at the warmer and the colder boundary the threshold of convection is reduced in the range of positive values of the separation ratio ψ with the onset of stationary convection as well as in the range of negative values of ψ with an oscillatory Hopf bifurcation. Additionally the convection rolls are shifted downwards with respect to the center of the horizontal layer for stationary convection (ψ > 0) and upwards for the Hopf bifurcation (ψ < 0).
Longitudinal shear-induced diffusion of spheres in a dilute suspension
Journal of Fluid Mechanics, 1992
We present a calculation of the hydrodynamic self-diffusion coefficient of a tagged particle in a dilute mono-dispersed suspension of small neutrally buoyant spheres undergoing a steady simple shearing motion. The displacement of the tagged particle parallel to the longitudinal or streamwise direction resulting from a ' collision ' with one other particle is calculated on the assumption that inertia and Brownian motion effects are negligible. Summing over different pairs leads to a logarithmically divergent integral for the diffusivity which is rendered finite by allowing for the cutoff due to the occasional presence of another pair of particles. The longitudinal shearinduced self-diffusion coefficient is thus found to be 0.267a2y{c In c-l+ O (c) ] , where y denotes the applied shear rate, a is the radius of the spheres and c their volume concentration.
Motility-induced shear thickening in dense colloidal suspensions
arXiv (Cornell University), 2023
Phase transitions and collective dynamics of active colloidal suspensions are fascinating topics in soft matter physics, particularly for out-of-equilibrium systems, which can lead to rich rheological behaviours in the presence of steady shear flow. In this article, the role of self-propulsion in the rheological response of a dense colloidal suspension is investigated by using particle-resolved simulations. First, the interplay between activity and shear in the solid to the liquid transition of the suspension is analysed. While both self-propulsion and shear destroy order and melt the system by themselves above their critical values, self-propulsion lowers the stress barrier that needs to be overcome during the transition. Once the suspension reaches a non-equilibrium steady state the rheological response is analysed. While passive suspensions show a solid-like behaviour, turning on particle motility fluidises the system and, at low self-propulsion, the suspension behaves as a shear-thinning fluid. Increasing the self-propulsion of the colloids induces a transition from a shear-thinning to a shear-thickening behaviour, which we attribute to clustering in the suspensions induced by motility. This interesting phenomenon of motility-induced shear thickening (MIST) can be used to tailor the rheological response of colloidal suspensions.