The long-time self-diffusivity in concentrated colloidal dispersions

The long-time self-diffusivity in concentrated colloidal dispersions is determined from a consideration of the temporal decay of density fluctuations. For hydrodynamically interacting Brownian particles the long-time self-diffusivity, D^s_∞, is shown to be expressible as the product of the hydrodynamically determined short-time self-diffusivity, D^s_0(φ), and a contribution that depends on the distortion of the equilibrium structure caused by a diffusing particle. An argument is advanced to show that as maximum packing is approached the long-time self-diffusivity scales as D^s_∞(φ)~ D^s_0(φ)/g(2;φ), where g(2;φ) is the value of the equilibrium radial-distribution function at contact and φ is the volume fraction of interest. This result predicts that the longtime self-diffusivity vanishes quadratically at random close packing, φ_m ≈ 0.63, i.e. D^s_∞D_0(1-φ/φ_m)^2 as φ → φ_m, where D_0 = kT/6πηα is the diffusivity of a single isolated particle of radius α in a fluid of viscosity η. This scaling occurs because Ds_0(φ) vanishes linearly at random close packing and the radial-distribution function at contact diverges as (1 -φ/φ_m)^(−1). A model is developed to determine the structural deformation for the entire range of volume fractions, and for hard spheres the longtime self-diffusivity can be represented by: D^s_∞(φ) = D^s_∞(φ)/[1 + 2φg(2;φ)]. This formula is in good agreement with experiment. For particles that interact through hard-spherelike repulsive interparticle forces characterized by a length b(> α), the same formula applies with the short-time self-diffusivity still determined by hydrodynamic interactions at the true or ‘hydrodynamic’ volume fraction φ, but the structural deformation and equilibrium radial-distribution function are now determined by the ‘thermodynamic’ volume fraction φ_b based on the length b. When b » α, the long-time self-diffusivity vanishes linearly at random close packing based on the ‘thermodynamic’ volume fraction φ_(bm). This change in behaviour occurs because the true or ‘hydrodynamic’ volume fraction is so low that the short-time self-diffusivity is given by its infinite-dilution value D_0. It is also shown that the temporal transition from short- to long-time diffusive behaviour is inversely proportional to the dynamic viscosity and is a universal function for all volume fractions when time is nondimensionalized by α^2/D^s_∞(φ)

Entropy-driven enhanced self-diffusion in confined reentrant supernematics

We present a molecular dynamics study of reentrant nematic phases using the Gay-Berne-Kihara model of a liquid crystal in nanoconfinement. At densities above those characteristic of smectic A phases, reentrant nematic phases form that are characterized by a large value of the nematic order parameter $S\simeq1$. Along the nematic director these "supernematic" phases exhibit a remarkably high self-diffusivity which exceeds that for ordinary, lower-density nematic phases by an order of magnitude. Enhancement of self-diffusivity is attributed to a decrease of rotational configurational entropy in confinement. Recent developments in the pulsed field gradient NMR technique are shown to provide favorable conditions for an experimental confirmation of our simulations.Comment: 10 pages, 5 figure

Swapping trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres

Binary encounters between spherical particles in shear flow are studied for a system bounded by a single planar wall or two parallel planar walls under creeping flow conditions. We show that wall proximity gives rise to a new class of binary trajectories resulting in cross-streamline migration of the particles. The spheres on these new trajectories do not pass each other (as they would in free space) but instead they swap their cross-streamline positions. To determine the significance of the wall-induced particle migration, we have evaluated the hydrodynamic self-diffusion coefficient associated with a sequence of uncorrelated particle displacements due to binary particle encounters. The results of our calculations quantitatively agree with the experimental value obtained by \cite{Zarraga-Leighton:2002} for the self-diffusivity in a dilute suspension of spheres undergoing shear flow in a Couette device. We thus show that the wall-induced cross-streamline particle migration is the source of the anomalously large self-diffusivity revealed by their experiments.Comment: submited to JF

Cofinement, entropy, and single-particle dynamics of equilibrium hard-sphere mixtures

We use discontinuous molecular dynamics and grand-canonical transition-matrix Monte Carlo simulations to explore how confinement between parallel hard walls modifies the relationships between packing fraction, self-diffusivity, partial molar excess entropy, and total excess entropy for binary hard-sphere mixtures. To accomplish this, we introduce an efficient algorithm to calculate partial molar excess entropies from the transition-matrix Monte Carlo simulation data. We find that the species-dependent self-diffusivities of confined fluids are very similar to those of the bulk mixture if compared at the same, appropriately defined, packing fraction up to intermediate values, but then deviate negatively from the bulk behavior at higher packing fractions. On the other hand, the relationships between self-diffusivity and partial molar excess entropy (or total excess entropy) observed in the bulk fluid are preserved under confinement even at relatively high packing fractions and for different mixture compositions. This suggests that the partial molar excess entropy, calculable from classical density functional theories of inhomogeneous fluids, can be used to predict some of the nontrivial dynamical behaviors of fluid mixtures in confined environments.Comment: submitted to JC

Dynamic structure factor study of diffusion in strongly sheared suspensions

Diffusion of neutrally buoyant spherical particles in concentrated monodisperse suspensions under simple shear flow is investigated. We consider the case of non-Brownian particles in Stokes flow, which corresponds to the limits of infinite Péclet number and zero Reynolds number. Using an approach based upon ideas of dynamic light scattering we compute self- and gradient diffusion coefficients in the principal directions normal to the flow numerically from Accelerated Stokesian Dynamics simulations for large systems (up to 2000 particles). For the self-diffusivity, the present approach produces results identical to those reported earlier, obtained by probing the particles' mean-square displacements (Sierou & Brady, J. Fluid Mech. vol. 506, 2004 p. 285). For the gradient diffusivity, the computed coefficients are in good agreement with the available experimental results. The similarity between diffusion mechanisms in equilibrium suspensions of Brownian particles and in non-equilibrium non-colloidal sheared suspensions suggests an approximate model for the gradient diffusivity: {\textsfbi D}^\triangledown\,{\approx}\,{\textsfbi D}^s/S^{eq}(0), where {\textsfbi D}^s is the shear-induced self-diffusivity and $S^{eq}(0)$ is the static structure factor corresponding to the hard-sphere suspension at thermodynamic equilibrium

Impact of surface roughness on diffusion of confined fluids

Using event-driven molecular dynamics simulations, we quantify how the self diffusivity of confined hard-sphere fluids depends on the nature of the confining boundaries. We explore systems with featureless confining boundaries that treat particle-boundary collisions in different ways and also various types of physically (i.e., geometrically) rough boundaries. We show that, for moderately dense fluids, the ratio of the self diffusivity of a rough wall system to that of an appropriate smooth-wall reference system is a linear function of the reciprocal wall separation, with the slope depending on the nature of the roughness. We also discuss some simple practical ways to use this information to predict confined hard-sphere fluid behavior in different rough-wall systems

Self-diffusion in sheared suspensions

Self-diffusion in a suspension of spherical particles in steady linear shear flow is investigated by following the time evolution of the correlation of number density fluctuations. Expressions are presented for the evaluation of the self-diffusivity in a suspension which is either raacroscopically quiescent or in linear flow at arbitrary Peclet number Pe = ẏa^2/2D, where ẏ is the shear rate, a is the particle radius, and D = k_BT/6πηa is the diffusion coefficient of an isolated particle. Here, k_B is Boltzmann's constant, T is the absolute temperature, and η is the viscosity of the suspending fluid. The short-time self-diffusion tensor is given by k_BT times the microstructural average of the hydrodynamic mobility of a particle, and depends on the volume fraction ø = 4/3πa^3n and Pe only when hydrodynamic interactions are considered. As a tagged particle moves through the suspension, it perturbs the average microstructure, and the long-time self-diffusion tensor, D_∞^s, is given by the sum of D_0^s and the correlation of the flux of a tagged particle with this perturbation. In a flowing suspension both D_0^s and D_∞^s are anisotropic, in general, with the anisotropy of D_0^s due solely to that of the steady microstructure. The influence of flow upon D_∞^s is more involved, having three parts: the first is due to the non-equilibrium microstructure, the second is due to the perturbation to the microstructure caused by the motion of a tagged particle, and the third is by providing a mechanism for diffusion that is absent in a quiescent suspension through correlation of hydrodynamic velocity fluctuations. The self-diffusivity in a simply sheared suspension of identical hard spheres is determined to O(φPe^(3/2)) for Pe « 1 and ø « 1, both with and without hydro-dynamic interactions between the particles. The leading dependence upon flow of D_0^s is 0.22DøPeÊ, where Ê is the rate-of-strain tensor made dimensionless with ẏ. Regardless of whether or not the particles interact hydrodynamically, flow influences D_∞^s at O(øPe) and O(øPe^(3/2)). In the absence of hydrodynamics, the leading correction is proportional to øPeDÊ. The correction of O(øPe^(3/2)), which results from a singular advection-diffusion problem, is proportional, in the absence of hydrodynamic interactions, to øPe^(3/2)DI; when hydrodynamics are included, the correction is given by two terms, one proportional to Ê, and the second a non-isotropic tensor. At high ø a scaling theory based on the approach of Brady (1994) is used to approximate D_∞^s. For weak flows the long-time self-diffusivity factors into the product of the long-time self-diffusivity in the absence of flow and a non-dimensional function of Pe = ẏa^2/2D^s_0(φ)$. At small Pe the dependence on Pe is the same as at low ø