38 research outputs found

### Phase equilibria in stratified thin liquid films stabilized by colloidal particles

Phase equilibria between regions of different thickness in thin liquid films
stabilized by colloidal particles are investigated using a
quasi-two-dimensional thermodynamic formalism. Appropriate equilibrium
conditions for the film tension, normal pressure, and chemical potential of the
particles in the film are formulated, and it is shown that the relaxation of
these parameters occurs consecutively on three distinct time scales. Film
stratification is described quantitatively for a hard-sphere suspension using a
Monte-Carlo method to evaluate thermodynamic equations of state. Coexisting
phases are determined for systems in constrained- and full-equilibrium states
that correspond to different stages of film relaxation.Comment: 7 page

### Hydrodynamic crystals: collective dynamics of regular arrays of spherical particles in a parallel-wall channel

Simulations of over $10^3$ hydrodynamically coupled solid spheres are
performed to investigate collective motion of linear trains and regular square
arrays of particles suspended in a fluid bounded by two parallel walls. Our
novel accelerated Stokesian-dynamics algorithm relies on simplifications
associated with the Hele--Shaw asymptotic far-field form of the flow scattered
by the particles. The simulations reveal propagation of particle-displacement
waves, deformation and rearrangements of a particle lattice, propagation of
dislocation defects in ordered arrays, and long-lasting coexistence of ordered
and disordered regions.Comment: 4 pages 6 figure

### Hydrodynamic interactions of spherical particles in suspensions confined between two planar walls

Hydrodynamic interactions in a suspension of spherical particles confined
between two parallel planar walls are studied under creeping-flow conditions.
The many-particle friction matrix in this system is evaluated using our novel
numerical algorithm based on transformations between Cartesian and spherical
representations of Stokes flow. The Cartesian representation is used to
describe the interaction of the fluid with the walls and the spherical
representation is used to describe the interaction with the particles. The
transformations between these two representations are given in a closed form,
which allows us to evaluate the coefficients in linear equations for the
induced-force multipoles on particle surfaces. The friction matrix is obtained
from these equations, supplemented with the superposition lubrication
corrections. We have used our algorithm to evaluate the friction matrix for a
single sphere, a pair of spheres, and for linear chains of spheres. The
friction matrix exhibits a crossover from a quasi-two-dimensional behavior (for
systems with small wall separation H) to the three-dimensional behavior (when
the distance H is much larger than the interparticle distance L). The crossover
is especially pronounced for a long chain moving in the direction normal to its
orientation and parallel to the walls. In this configuration, a large pressure
buildup occurs in front of the chain for small values of the gapwidth H, which
results in a large hydrodynamic friction force. A standard wall superposition
approximation does not capture this behavior

### Correlated particle dynamics in concentrated quasi-two-dimensional suspensions

We investigate theoretically and experimentally how the hydrodynamically
correlated lateral motion of particles in a suspension confined between two
surfaces is affected by the suspension concentration. Despite the long range of
the correlations (decaying as 1/r^2 with the inter-particle distance r), the
concentration effect is present only at short inter-particle distances for
which the static pair correlation is nonuniform. This is in sharp contrast with
the effect of hydrodynamic screening present in unconfined suspensions, where
increasing the concentration changes the prefactor of the large-distance
correlation.Comment: 13 page

### Geometrical families of mechanically stable granular packings

We enumerate and classify nearly all of the possible mechanically stable (MS)
packings of bidipserse mixtures of frictionless disks in small sheared systems.
We find that MS packings form continuous geometrical families, where each
family is defined by its particular network of particle contacts. We also
monitor the dynamics of MS packings along geometrical families by applying
quasistatic simple shear strain at zero pressure. For small numbers of
particles (N < 16), we find that the dynamics is deterministic and highly
contracting. That is, if the system is initialized in a MS packing at a given
shear strain, it will quickly lock into a periodic orbit at subsequent shear
strain, and therefore sample only a very small fraction of the possible MS
packings in steady state. In studies with N>16, we observe an increase in the
period and random splittings of the trajectories caused by bifurcations in
configuration space. We argue that the ratio of the splitting and contraction
rates in large systems will determine the distribution of MS-packing
geometrical families visited in steady-state. This work is part of our
long-term research program to develop a master-equation formalism to describe
macroscopic slowly driven granular systems in terms of collections of small
subsystems.Comment: 18 pages, 23 figures, 5 table

### The intensity correlation function in evanescent wave scattering

As a first step toward the interpretation of dynamic light scattering with evanescent illumination from suspensions of interacting spheres, in order to probe their near wall dynamics, we develop a theory for the initial slope of the intensity autocorrelation function. An expression for the first cumulant is derived that is valid for arbitrary concentrations, which generalizes a well-known expression for the short-time, wave-vector dependent collective diffusion coefficient in bulk to the case where a wall is present. Explicit expressions and numerical results for the various contributions to the initial slope are obtained within a leading order virial expansion. The dependence of the initial slope on the components of the wave vector parallel and perpendicular to the wall, as well as the dependence on the evanescent-light penetration depth are discussed. For the hydrodynamic interactions between colloids and between the wall, which are essential for a correct description of the near-interface dynamics, we include both far-field and lubrication contributions. Lubrication contributions are essential to capture the dynamics as probed in experiments with small penetration depths. Simulations have been performed to verify the theory and to estimate the extent of the concentration range where the virial expansion is valid. The computer algorithm developed for this purpose will also be of future importance for the interpretation of experiments and to develop an understanding of near-interface dynamics, at high colloid concentrations

### A minimal model for kinetic arrest

To elucidate slow dynamics in glassy materials, we introduce the {\it
Figure-8 model} in which $N$ hard blocks undergo Brownian motion around a
circuit in the shape of a figure-8. This system undergoes kinetic arrest at a
critical packing fraction $\phi=\phi_g < 1$, and for $\phi\approx\phi_g$
long-time diffusion is controlled by rare, cooperative `junction-crossing'
particle rearrangements. We find that the average time between junction
crossings $\tau_{JC}$, and hence the structural relaxation time, does not
simply scale with the configurational volume \OmegaLow of transition states,
because $\tau_{JC}$ also depends on the time to complete a junction crossing.
The importance of these results in understanding cage-breaking dynamics in
glassy systems is discussed.Comment: 4 pages, 4 figure

### The Two Fluid Drop Snap-off Problem: Experiments and Theory

We address the dynamics of a drop with viscosity $\lambda \eta$ breaking up
inside another fluid of viscosity $\eta$. For $\lambda=1$, a scaling theory
predicts the time evolution of the drop shape near the point of snap-off which
is in excellent agreement with experiment and previous simulations of Lister
and Stone. We also investigate the $\lambda$ dependence of the shape and
breaking rate.Comment: 4 pages, 3 figure