Viscosity of Colloidal Suspensions

Simple expressions are given for the Newtonian viscosity $\eta_N(\phi)$ as well as the viscoelastic behavior of the viscosity $\eta(\phi,\omega)$ of neutral monodisperse hard sphere colloidal suspensions as a function of volume fraction $\phi$ and frequency $\omega$ over the entire fluid range, i.e., for volume fractions $0 < \phi < 0.55$. These expressions are based on an approximate theory which considers the viscosity as composed as the sum of two relevant physical processes: $\eta (\phi,\omega) = \eta_{\infty}(\phi) + \eta_{cd}(\phi,\omega)$, where $\eta_{\infty}(\phi) = \eta_0 \chi(\phi)$ is the infinite frequency (or very short time) viscosity, with $\eta_0$ the solvent viscosity, $\chi(\phi)$ the equilibrium hard sphere radial distribution function at contact, and $\eta_{cd}(\phi,\omega)$ the contribution due to the diffusion of the colloidal particles out of cages formed by their neighbors, on the P\'{e}clet time scale $\tau_P$, the dominant physical process in concentrated colloidal suspensions. The Newtonian viscosity $\eta_N(\phi) = \eta(\phi,\omega = 0)$ agrees very well with the extensive experiments of Van der Werff et al and others. Also, the asymptotic behavior for large $\omega$ is of the form $\eta_{\infty}(\phi) + A(\phi)(\omega \tau_P)^{-1/2}$, in agreement with these experiments, but the theoretical coefficient $A(\phi)$ differs by a constant factor $2/\chi(\phi)$ from the exact coefficient, computed from the Green-Kubo formula for $\eta(\phi,\omega)$. This still enables us to predict for practical purposes the visco-elastic behavior of monodisperse spherical colloidal suspensions for all volume fractions by a simple time rescaling.Comment: 51 page

Sound-propagation gap in fluid mixtures

We discuss the behavior of the extended sound modes of a dense binary hard-sphere mixture. In a dense simple hard-sphere fluid the Enskog theory predicts a gap in the sound propagation at large wave vectors. In a binary mixture the gap is only present for low concentrations of one of the two species. At intermediate concentrations sound modes are always propagating. This behavior is not affected by the mass difference of the two species, but it only depends on the packing fractions. The gap is absent when the packing fractions are comparable and the mixture structurally resembles a metallic glass.Comment: Published; withdrawn since ordering in archive gives misleading impression of new publicatio

Structure in cohesive powders studied with spin-echo small angle\ud neutron scattering

Extracting structure and ordering information from the bulk of granular materials is a challenging task. Here we present Spin-Echo Small Angle Neutron Scattering Measurements in combination with computer simulations on a fine powder of silica, before and after uniaxial compression. The cohesive powder packing is modeled by using molecular dynamics simulations and the structure, in terms of the density–density correlation function, is calculated from the simulation and compared with experiment. In the dense case, both quantitative and qualitative agreement between measurement and simulations is observed, thus creating the desired link between experiment and computer simulation. Further simulations with appropriate attractive potentials and adequate preparation procedures are needed in order to capture the very loose-packed cohesive powders.\u

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n>2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses.Comment: A less ambiguous mathematical notation for cumulants was adopted and several passages were reformulated and clarified. 40 pages, 1 figure. Accepted by J. Stat. Phy

Domination and Cut Problems on Chordal Graphs with Bounded Leafage

The leafage of a chordal graph G is the minimum integer l such that G can berealized as an intersection graph of subtrees of a tree with l leaves. Weconsider structural parameterization by the leafage of classical domination andcut problems on chordal graphs. Fomin, Golovach, and Raymond [ESA 2018,Algorithmica 2020] proved, among other things, that Dominating Set on chordalgraphs admits an algorithm running in time $2^{O(l^2)} n^{O(1)}$. We present aconceptually much simpler algorithm that runs in time $2^{O(l)} n^{O(1)}$. Weextend our approach to obtain similar results for Connected Dominating Set andSteiner Tree. We then consider the two classical cut problems MultiCut withUndeletable Terminals and Multiway Cut with Undeletable Terminals. We provethat the former is W[1]-hard when parameterized by the leafage and complementthis result by presenting a simple $n^{O(l)}$-time algorithm. To our surprise,we find that Multiway Cut with Undeletable Terminals on chordal graphs can besolved, in contrast, in $n^{O(1)}$-time.<br