78 research outputs found
Active and driven hydrodynamic crystals
Motivated by the experimental ability to produce monodisperse particles in
microfluidic devices, we study theoretically the hydrodynamic stability of
driven and active crystals. We first recall the theoretical tools allowing to
quantify the dynamics of elongated particles in a confined fluid. In this
regime hydrodynamic interactions between particles arise from a superposition
of potential dipolar singularities. We exploit this feature to derive the
equations of motion for the particle positions and orientations. After showing
that all five planar Bravais lattices are stationary solutions of the equations
of motion, we consider separately the case where the particles are passively
driven by an external force, and the situation where they are self-propelling.
We first demonstrate that phonon modes propagate in driven crystals, which are
always marginally stable. The spatial structure of the eigenmodes depend solely
on the symmetries of the lattices, and on the orientation of the driving force.
For active crystals, the stability of the particle positions and orientations
depends not only on the symmetry of the crystals but also on the perturbation
wavelengths and on the crystal density. Unlike unconfined fluids, the stability
of active crystals is independent of the nature of the propulsion mechanism at
the single particle level. The square and rectangular lattices are found to be
linearly unstable at short wavelengths provided the volume fraction of the
crystals is high enough. Differently, hexagonal, oblique, and face-centered
crystals are always unstable. Our work provides a theoretical basis for future
experimental work on flowing microfluidic crystals.Comment: 10 pages, 10 figure
Implicit and explicit solvent models for the simulation of a single polymer chain in solution: Lattice Boltzmann vs Brownian dynamics
We present a comparative study of two computer simulation methods to obtain
static and dynamic properties of dilute polymer solutions. The first approach
is a recently established hybrid algorithm based upon dissipative coupling
between Molecular Dynamics and lattice Boltzmann (LB), while the second is
standard Brownian Dynamics (BD) with fluctuating hydrodynamic interactions.
Applying these methods to the same physical system (a single polymer chain in a
good solvent in thermal equilibrium) allows us to draw a detailed and
quantitative comparison in terms of both accuracy and efficiency. It is found
that the static conformations of the LB model are distorted when the box length
L is too small compared to the chain size. Furthermore, some dynamic properties
of the LB model are subject to an finite size effect, while the BD
model directly reproduces the asymptotic behavior. Apart from
these finite size effects, it is also found that in order to obtain the correct
dynamic properties for the LB simulations, it is crucial to properly thermalize
all the kinetic modes. Only in this case, the results are in excellent
agreement with each other, as expected. Moreover, Brownian Dynamics is found to
be much more efficient than lattice Boltzmann as long as the degree of
polymerization is not excessively large.Comment: 11 figures, submitted to J. Chem. Phy
The long-time dynamics of two hydrodynamically-coupled swimming cells
Swimming micro-organisms such as bacteria or spermatozoa are typically found
in dense suspensions, and exhibit collective modes of locomotion qualitatively
different from that displayed by isolated cells. In the dilute limit where
fluid-mediated interactions can be treated rigorously, the long-time
hydrodynamics of a collection of cells result from interactions with many other
cells, and as such typically eludes an analytical approach. Here we consider
the only case where such problem can be treated rigorously analytically, namely
when the cells have spatially confined trajectories, such as the spermatozoa of
some marine invertebrates. We consider two spherical cells swimming, when
isolated, with arbitrary circular trajectories, and derive the long-time
kinematics of their relative locomotion. We show that in the dilute limit where
the cells are much further away than their size, and the size of their circular
motion, a separation of time scale occurs between a fast (intrinsic) swimming
time, and a slow time where hydrodynamic interactions lead to change in the
relative position and orientation of the swimmers. We perform a multiple-scale
analysis and derive the effective dynamical system - of dimension two -
describing the long-time behavior of the pair of cells. We show that the system
displays one type of equilibrium, and two types of rotational equilibrium, all
of which are found to be unstable. A detailed mathematical analysis of the
dynamical systems further allows us to show that only two cell-cell behaviors
are possible in the limit of , either the cells are attracted to
each other (possibly monotonically), or they are repelled (possibly
monotonically as well), which we confirm with numerical computations
Actively crosslinked microtubule networks: mechanics, dynamics and filament sliding
Cytoskeletal networks are foundational examples of active matter and central
to self-organized structures in the cell. In vivo, these networks are active
and heavily crosslinked. Relating their large-scale dynamics to properties of
their constituents remains an unsolved problem. Here we study an in vitro
system made from microtubules and XCTK2 kinesin motors, which forms an aligned
and active gel. Using photobleaching we demonstrate that the gel's aligned
microtubules, driven by motors, continually slide past each other at a speed
independent of the local polarity. This phenomenon is also observed, and
remains unexplained, in spindles. We derive a general framework for coarse
graining microtubule gels crosslinked by molecular motors from microscopic
considerations. Using the microtubule-microtubule coupling, and force-velocity
relationship for kinesin, this theory naturally explains the experimental
results: motors generate an active strain-rate in regions of changing polarity,
which allows microtubules of opposite polarities to slide past each other
without stressing the material
Periodic and Quasiperiodic Motion of an Elongated Microswimmer in Poiseuille Flow
We study the dynamics of a prolate spheroidal microswimmer in Poiseuille flow
for different flow geometries. When moving between two parallel plates or in a
cylindrical microchannel, the swimmer performs either periodic swinging or
periodic tumbling motion. Although the trajectories of spherical and elongated
swimmers are qualitatively similar, the swinging and tumbling frequency
strongly depends on the aspect ratio of the swimmer. In channels with reduced
symmetry the swimmers perform quasiperiodic motion which we demonstrate
explicitely for swimming in a channel with elliptical cross section
Lattice Boltzmann simulations of soft matter systems
This article concerns numerical simulations of the dynamics of particles
immersed in a continuum solvent. As prototypical systems, we consider colloidal
dispersions of spherical particles and solutions of uncharged polymers. After a
brief explanation of the concept of hydrodynamic interactions, we give a
general overview over the various simulation methods that have been developed
to cope with the resulting computational problems. We then focus on the
approach we have developed, which couples a system of particles to a lattice
Boltzmann model representing the solvent degrees of freedom. The standard D3Q19
lattice Boltzmann model is derived and explained in depth, followed by a
detailed discussion of complementary methods for the coupling of solvent and
solute. Colloidal dispersions are best described in terms of extended particles
with appropriate boundary conditions at the surfaces, while particles with
internal degrees of freedom are easier to simulate as an arrangement of mass
points with frictional coupling to the solvent. In both cases, particular care
has been taken to simulate thermal fluctuations in a consistent way. The
usefulness of this methodology is illustrated by studies from our own research,
where the dynamics of colloidal and polymeric systems has been investigated in
both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures,
76 page
Origin of Polar Order in Dense Suspensions of Phototactic Micro-Swimmers
A main question for the study of collective motion in living organisms is the origin of orientational polar order, i.e., how organisms align and what are the benefits of such collective behaviour. In the case of micro-organisms swimming at a low Reynolds number, steric repulsion and long-range hydrodynamic interactions are not sufficient to explain a homogeneous polar order state in which the direction of motion is aligned. An external symmetry-breaking guiding field such as a mechanism of taxis appears necessary to understand this phonemonon. We have investigated the onset of polar order in the velocity field induced by phototaxis in a suspension of a motile micro-organism, the algae Chlamydomonas reinhardtii, for density values above the limit provided by the hydrodynamic approximation of a force dipole model. We show that polar order originates from a combination of both the external guiding field intensity and the population density. In particular, we show evidence for a linear dependence of a phototactic guiding field on cell density to determine the polar order for dense suspensions and demonstrate the existence of a density threshold for the origin of polar order. This threshold represents the density value below which cells undergoing phototaxis are not able to maintain a homogeneous polar order state and marks the transition to ordered collective motion. Such a transition is driven by a noise dominated phototactic reorientation where the noise is modelled as a normal distribution with a variance that is inversely proportional to the guiding field strength. Finally, we discuss the role of density in dense suspensions of phototactic micro-swimmers
Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions
The venerable theory of electrokinetic phenomena rests on the hypothesis of a dilute solution of point-like ions in quasi-equilibrium with a weakly charged surface, whose potential relative to the bulk is of order the thermal voltage (kT/e ≈ 25 mV at room temperature). In nonlinear electrokinetic phenomena, such as AC or induced-charge electro-osmosis (ACEO, ICEO) and induced-charge electrophoresis (ICEP), several V ≈ 100 kT/e are applied to polarizable surfaces in microscopic geometries, and the resulting electric fields and induced surface charges are large enough to violate the assumptions of the classical theory. In this article, we review the experimental and theoretical literatures, highlight discrepancies between theory and experiment, introduce possible modifications of the theory, and analyze their consequences. We argue that, in response to a large applied voltage, the “compact layer” and “shear plane” effectively advance into the liquid, due to the crowding of counterions. Using simple continuum models, we predict two general trends at large voltages: (i) ionic crowding against a blocking surface expands the diffuse double layer and thus decreases its differential capacitance, and (ii) a charge-induced viscosity increase near the surface reduces the electro-osmotic mobility; each trend is enhanced by dielectric saturation. The first effect is able to predict high-frequency flow reversal in ACEO pumps, while the second may explain the decay of ICEO flow with increasing salt concentration. Through several colloidal examples, such as ICEP of an uncharged metal sphere in an asymmetric electrolyte, we show that nonlinear electrokinetic phenomena are generally ion-specific. Similar theoretical issues arise in nanofluidics (due to confinement) and ionic liquids (due to the lack of solvent), so the paper concludes with a general framework of modified electrokinetic equations for finite-sized ions.National Science Foundation (U.S.) (contract DMS-0707641
Effect of flexibility on the growth of concentration fluctuations in a suspension of sedimenting fibers: Particle simulations
Three-dimensional numerical simulations are performed to study the stability of a sedimenting suspension of weakly flexible fibers. It is well known that a suspension of rigid rods sedimenting under gravity at low Reynolds number is unstable to concentration fluctuations owing to hydrodynamic interactions. Flexible fibers, however, reorient while settling and even weak flexibility can alter their collective dynamics. In our recent work [Manikantan et al., "The instability of a sedimenting suspension of weakly flexible fibres," J. Fluid Mech. 756, 935-964 (2014)], we developed a mean-field theory to predict the linear stability of such a system. Here, we verify these predictions using accurate and efficient particle simulations based on a slender-body model. We also demonstrate the mechanisms by which flexibility-induced reorientation alters suspension microstructure, and through it, its stability. Specifically, we first show that the anisotropy of the base state in the case of a suspension of flexible fibers has a destabilizing effect compared to a suspension of rigid rods. Second, a conflicting effect of flexibility is also shown to suppress particle clustering and slow down the growth of the instability. The relative magnitude of filament flexibility and rotational Brownian motion dictates which effect dominates, and our simulations qualitatively follow theoretically predicted trends. The mechanism for either effects is tied to the flexibility-induced reorientation of particles, which we illustrate using velocity and orientation statistics from our simulations. Finally, we also show that, in the case of an initially homogeneous and isotropic suspension, flexibility always acts to suppress the growth of the instability
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