10 research outputs found
Understanding the Frequency Distribution of Mechanically Stable Disk Packings
Relative frequencies of mechanically stable (MS) packings of frictionless
bidisperse disks are studied numerically in small systems. The packings are
created by successively compressing or decompressing a system of soft purely
repulsive disks, followed by energy minimization, until only infinitesimal
particle overlaps remain. For systems of up to 14 particles most of the MS
packings were generated. We find that the packings are not equally probable as
has been assumed in recent thermodynamic descriptions of granular systems.
Instead, the frequency distribution, averaged over each packing-fraction
interval , grows exponentially with increasing . Moreover,
within each packing-fraction interval MS packings occur with frequencies
that differ by many orders of magnitude. Also, key features of the frequency
distribution do not change when we significantly alter the packing-generation
algorithm--for example frequent packings remain frequent and rare ones remain
rare. These results indicate that the frequency distribution of MS packings is
strongly influenced by geometrical properties of the multidimensional
configuration space. By adding thermal fluctuations to a set of the MS
packings, we were able to examine a number of local features of configuration
space near each packing including the time required for a given packing to
break to a distinct one, which enabled us to estimate the energy barriers that
separate one packing from another. We found a positive correlation between the
packing frequencies and the heights of the lowest energy barriers .
We also examined displacement fluctuations away from the MS packings to
correlate the size and shape of the local basins near each packing to the
packing frequencies.Comment: 21 pages, 20 figures, 1 tabl
Lubrication approximation for micro-particles moving along parallel walls
Lubrication expressions for the friction coefficients of a spherical particle
moving in a fluid between and along two parallel solid walls are explicitly
evaluated in the low-Reynolds-number regime. They are used to determine
lubrication expression for the particle free motion under an ambient Poiseuille
flow. The range of validity and the accuracy of the lubrication approximation
is determined by comparing with the corresponding results of the accurate
multipole procedure. The results are applicable for thin, wide and long
microchannels, or quasi-two-dimensional systems.Comment: 4 pages, 5 figure
High-frequency viscosity of a dilute suspension of elongated particles in a linear shear flow between two walls
International audienceA general expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in linear shear flow between two parallel walls is derived in terms of the induced stresslets on particles. This formula is applied to N-bead rods and to prolate spheroids with the same length, aspect ratio and volume. The effective viscosity of non-Brownian particles in a periodic shear flow is considered here. The oscillating frequency is high enough for the particle orientation and centre-of-mass distribution to be practically frozen, yet small enough for the flow to be quasi-steady. It is known that for spheres, the intrinsic viscosity [μ] increases monotonically when the distance H between the walls is decreased. The dependence is more complex for both types of elongated particles. Three regimes are theoretically predicted here: (i) a ‘weakly confined’ regime (for H>l, where l is the particle length), where [μ] is slightly larger for smaller H; (ii) a ‘semi-confined’ regime, when H becomes smaller than l, where [μ] rapidly decreases since the geometric constraints eliminate particle orientations corresponding to the largest stresslets; (iii) a ‘strongly confined’ regime when H becomes smaller than 2–3 particle widths d, where [μ] rapidly increases owing to the strong hydrodynamic coupling with the walls. In addition, for sufficiently slender particles (with aspect ratio larger than 5–6) there is a domain of narrow gaps for which the intrinsic viscosity is smaller than that in unbounded fluid
Near-wall dynamics of concentrated hard-sphere suspensions: comparison of evanescent wave DLS experiments, virial approximation and simulations
In this article we report on a study of the near-wall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of ϕ ≈ 0.25 which provides us with a fast and non-costly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall
An Adaptive Mesh Algorithm for Evolving Surfaces: Simulations of Drop Breakup and Coalescence
Near-wall dynamics of concentrated hard-sphere suspensions: comparison of evanescent wave DLS experiments, virial approximation and simulations
State diagram of a three-sphere microswimmer in a channel
Geometric confinements are frequently encountered in soft matter systems and
in particular significantly alter the dynamics of swimming microorganisms in
viscous media. Surface-related effects on the motility of microswimmers can
lead to important consequences in a large number of biological systems, such as
biofilm formation, bacterial adhesion and microbial activity. On the basis of
low-Reynolds-number hydrodynamics, we explore the state diagram of a
three-sphere microswimmer under channel confinement in a slit geometry and
fully characterize the swimming behavior and trajectories for neutral swimmers,
puller- and pusher-type swimmers. While pushers always end up trapped at the
channel walls, neutral swimmers and pullers may further perform a gliding
motion and maintain a stable navigation along the channel. We find that the
resulting dynamical system exhibits a supercritical pitchfork bifurcation in
which swimming in the mid-plane becomes unstable beyond a transition channel
height while two new stable limit cycles or fixed points that are symmetrically
disposed with respect to the channel mid-height emerge. Additionally, we show
that an accurate description of the averaged swimming velocity and rotation
rate in a channel can be captured analytically using the method of hydrodynamic
images, provided that the swimmer size is much smaller than the channel height.Comment: 19 pages, 9 figures. Article contributed to the Topical Issue of the
Journal of Physics: Condensed Matter, entitled "Transport in Narrow Channels"
edited by Paolo Malgaretti, Gleb Oshanin, and Julian Talbo