1,773 research outputs found
Passive swimming in low Reynolds number flows
The possibility of microscopic swimming by extraction of energy from an
external flow is discussed, focusing on the migration of a simple trimer across
a linear shear flow. The geometric properties of swimming, together with the
possible generalization to the case of a vesicle, are analyzed.The mechanism of
energy extraction from the flow appears to be the generalization to a discrete
swimmer of the tank-treading regime of a vesicle. The swimmer takes advantage
of the external flow by both extracting energy for swimming and "sailing"
through it. The migration velocity is found to scale linearly in the stroke
amplitude, and not quadratically as in a quiescent fluid. This effect turns out
to be connected with the non-applicability of the scallop theorem in the
presence of external flow fields.Comment: 4 pages, 4 figure
Efficiency of surface-driven motion: nano-swimmers beat micro-swimmers
Surface interactions provide a class of mechanisms which can be employed for
propulsion of micro- and nanometer sized particles. We investigate the related
efficiency of externally and self-propelled swimmers. A general scaling
relation is derived showing that only swimmers whose size is comparable to, or
smaller than, the interaction range can have appreciable efficiency. An upper
bound for efficiency at maximum power is 1/2. Numerical calculations for the
case of diffusiophoresis are found to be in good agreement with analytical
expressions for the efficiency
Pair diffusion, hydrodynamic interactions, and available volume in dense fluids
We calculate the pair diffusion coefficient D(r) as a function of the
distance r between two hard-sphere particles in a dense monodisperse
suspension. The distance-dependent pair diffusion coefficient describes the
hydrodynamic interactions between particles in a fluid that are central to
theories of polymer and colloid dynamics. We determine D(r) from the
propagators (Green's functions) of particle pairs obtained from discontinuous
molecular dynamics simulations. At distances exceeding 3 molecular diameters,
the calculated pair diffusion coefficients are in excellent agreement with
predictions from exact macroscopic hydrodynamic theory for large Brownian
particles suspended in a solvent bath, as well as the Oseen approximation.
However, the asymptotic 1/r distance dependence of D(r) associated with
hydrodynamic effects emerges only after the pair distance dynamics has been
followed for relatively long times, indicating non-negligible memory effects in
the pair diffusion at short times. Deviations of the calculated D(r) from the
hydrodynamic models at short distances r reflect the underlying many-body fluid
structure, and are found to be correlated to differences in the local available
volume. The procedure used here to determine the pair diffusion coefficients
can also be used for single-particle diffusion in confinement with spherical
symmetry.Comment: 6 pages, 5 figure
Analytical solution of Stokes flow inside an evaporating sessile drop: Spherical and cylindrical cap shapes
Exact analytical solutions are derived for the Stokes flows within
evaporating sessile drops of spherical and cylindrical cap shapes. The results
are valid for arbitrary contact angle. Solutions are obtained for arbitrary
evaporative flux distributions along the free surface as long as the flux is
bounded at the contact line. The field equations, E^4(Psi)=0 and Del^4(Phi)=0,
are solved for the spherical and cylindrical cap cases, respectively. Specific
results and computations are presented for evaporation corresponding to uniform
flux and to purely diffusive gas phase transport into an infinite ambient.
Wetting and non-wetting contact angles are considered with the flow patterns in
each case being illustrated. For the spherical cap with evaporation controlled
by vapor phase diffusion, when the contact angle lies in the range
0<theta_c<pi, the mass flux of vapor becomes singular at the contact line. This
condition required modification when solving for the liquid phase transport.
Droplets in all of the above categories are considered for the following two
cases: the contact lines are either pinned or free to move during evaporation.
The present viscous flow behavior is compared to the inviscid flow behavior
previously reported. It is seen that the streamlines for viscous flow lie
farther from the substrate than the corresponding inviscid ones.Comment: Revised version; in review in Physics of Fluid
Self-diffusion in two-dimensional hard ellipsoid suspensions
We studied the self-diffusion of colloidal ellipsoids in a monolayer near a
flat wall by video microscopy. The image processing algorithm can track the
positions and orientations of ellipsoids with sub-pixel resolution. The
translational and rotational diffusions were measured in both the lab frame and
the body frame along the long and short axes. The long-time and short-time
diffusion coefficients of translational and rotational motions were measured as
functions of the particle concentration. We observed sub-diffusive behavior in
the intermediate time regime due to the caging of neighboring particles. Both
the beginning and the ending times of the intermediate regime exhibit power-law
dependence on concentration. The long-time and short-time diffusion
anisotropies change non-monotonically with concentration and reach minima in
the semi-dilute regime because the motions along long axes are caged at lower
concentrations than the motions along short axes. The effective diffusion
coefficients change with time t as a linear function of (lnt)/t for the
translational and rotational diffusions at various particle densities. This
indicates that their relaxation functions decay according to 1/t which provides
new challenges in theory. The effects of coupling between rotational and
translational Brownian motions were demonstrated and the two time scales
corresponding to anisotropic particle shape and anisotropic neighboring
environment were measured
Finite-size effects in intracellular microrheology
We propose a model to explain finite-size effects in intracellular
microrheology observed in experiments. The constrained dynamics of the
particles in the intracellular medium, treated as a viscoelastic medium, is
described by means of a diffusion equation in which interactions of the
particles with the cytoskeleton are modelled by a harmonic force. The model
reproduces the observed power-law behavior of the mean-square displacement in
which the exponent depends on the ratio between
particle-to-cytoskeleton-network sizes.Comment: 6 pages 2 figures. To appear in the Journal of Chemical Physic
Hydrodynamic friction of fakir-like super-hydrophobic surfaces
A fluid droplet located on a super-hydrophobic surface makes contact with the
surface only at small isolated regions, and is mostly in contact with the
surrounding air. As a result, a fluid in motion near such a surface experiences
very low friction, and super-hydrophobic surfaces display strong drag-reduction
in the laminar regime. Here we consider theoretically a super-hydrophobic
surface composed of circular posts (so called fakir geometry) located on a
planar rectangular lattice. Using a superposition of point forces with suitably
spatially-dependent strength, we derive the effective surface slip length for a
planar shear flow on such a fakir surface as the solution to an infinite series
of linear equations. In the asymptotic limit of small surface coverage by the
posts, the series can be interpreted as Riemann sums, and the slip length can
be obtained analytically. For posts on a square lattice, our analytical results
are in excellent quantitative agreement with previous numerical computations
Which canonical algebras are derived equivalent to incidence algebras of posets?
We give a full description of all the canonical algebras over an
algebraically closed field that are derived equivalent to incidence algebras of
finite posets. These are the canonical algebras whose number of weights is
either 2 or 3.Comment: 8 pages; slight revision; to appear in Comm. Algebr
Simulating Brownian suspensions with fluctuating hydrodynamics
Fluctuating hydrodynamics has been successfully combined with several
computational methods to rapidly compute the correlated random velocities of
Brownian particles. In the overdamped limit where both particle and fluid
inertia are ignored, one must also account for a Brownian drift term in order
to successfully update the particle positions. In this paper, we present an
efficient computational method for the dynamic simulation of Brownian
suspensions with fluctuating hydrodynamics that handles both computations and
provides a similar approximation as Stokesian Dynamics for dilute and
semidilute suspensions. This advancement relies on combining the fluctuating
force-coupling method (FCM) with a new midpoint time-integration scheme we
refer to as the drifter-corrector (DC). The DC resolves the drift term for
fluctuating hydrodynamics-based methods at a minimal computational cost when
constraints are imposed on the fluid flow to obtain the stresslet corrections
to the particle hydrodynamic interactions. With the DC, this constraint need
only be imposed once per time step, reducing the simulation cost to nearly that
of a completely deterministic simulation. By performing a series of
simulations, we show that the DC with fluctuating FCM is an effective and
versatile approach as it reproduces both the equilibrium distribution and the
evolution of particulate suspensions in periodic as well as bounded domains. In
addition, we demonstrate that fluctuating FCM coupled with the DC provides an
efficient and accurate method for large-scale dynamic simulation of colloidal
dispersions and the study of processes such as colloidal gelation
No many-scallop theorem: Collective locomotion of reciprocal swimmers
To achieve propulsion at low Reynolds number, a swimmer must deform in a way
that is not invariant under time-reversal symmetry; this result is known as the
scallop theorem. We show here that there is no many-scallop theorem. We
demonstrate that two active particles undergoing reciprocal deformations can
swim collectively; moreover, polar particles also experience effective
long-range interactions. These results are derived for a minimal dimers model,
and generalized to more complex geometries on the basis of symmetry and scaling
arguments. We explain how such cooperative locomotion can be realized
experimentally by shaking a collection of soft particles with a homogeneous
external field
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