138 research outputs found
Liquid crystals boojum-colloids
Colloidal particles dispersed in a liquid crystal lead to distortions of the
director field. The distortions are responsible for long-range effective
colloidal interactions whose asymptotic behaviour is well understood. The short
distance behaviour of the interaction, however, is sensitive to the structure
and dynamics of the topological defects nucleated near the colloidal particles
in the strong anchoring regime. The full non-linear theory is required in order
to determine the interaction at short separations. Spherical colloidal
particles with sufficiently strong planar degenerate anchoring nucleate a pair
of antipodal surface topological defects, known as boojums. We use the
Landau-de Gennes formalism in order to resolve the mesoscopic structure of the
boojum cores and to determine the pairwise colloidal interaction. We compare
the results in three (3D) and two (2D) spatial dimensions. The corresponding
free energy functionals are minimized numerically using finite elements with
adaptive meshes. Boojums are always point-like in 2D, but acquire a rather
complex structure in 3D which depends on the combination of the anchoring
potential, the radius of the colloid, the temperature and the LC elastic
anisotropy. We identify three types of defect cores in 3D which we call single,
double and split core boojums, and investigate the associated structural
transitions. In the presence of two colloidal particles there are substantial
re-arrangements of the defects at short distances, both in 3D and 2D. These
re-arrangements lead to qualitative changes in the force-distance profile when
compared to the asymptotic quadrupole-quadrupole interaction. In line with the
experimental results, the presence of the defects prevents coalescence of the
colloidal particles in 2D, but not in 3D systems.Comment: 18 pages, 21 figure
Self-propulsion of a catalytically active particle near a planar wall: from reflection to sliding and hovering
Micron-sized particles moving through solution in response to self-generated
chemical gradients serve as model systems for studying active matter. Their
far-reaching potential applications will require the particles to sense and
respond to their local environment in a robust manner. The self-generated
hydrodynamic and chemical fields, which induce particle motion, probe and are
modified by that very environment, including confining boundaries. Focusing on
a catalytically active Janus particle as a paradigmatic example, we predict
that near a hard planar wall such a particle exhibits several scenarios of
motion: reflection from the wall, motion at a steady-state orientation and
height above the wall, or motionless, steady "hovering." Concerning the steady
states, the height and the orientation are determined both by the proportion of
catalyst coverage and the interactions of the solutes with the different
"faces" of the particle. Accordingly, we propose that a desired behavior can be
selected by tuning these parameters via a judicious design of the particle
surface chemistry
Interaction of colloids with a nematic-isotropic interface
The Landau-de Gennes free energy is used to calculate the interaction between
long cylindrical colloids and the nematic-isotropic (NI) interface. This
interaction has two contributions: one is specific of liquid crystals and
results from the deformation of the director field close to the particles or to
the interface, while the other is generic and results from wetting and surface
tension effects.
Deep in the nematic phase the director field of long cylindrical colloids,
with strong homeotropic anchoring, exhibits two half-integer defect lines. As
the colloid moves towards the interface, the director configuration changes
through a series of discontinuous transitions, where one or two of the defects
are annihilated. In addition, the NI interface bends towards the colloid in
order to minimize the elastic free energy in the nematic. In the isotropic
phase, the colloid is surrounded by a thin nematic layer that reduces the
surface free energy under favorable wetting conditions.
The interaction has a well-defined minimum near the interface. In this region
the director and interfacial structures are complex and cannot be described
analytically. Using the numerical results for the Landau-de Gennes free energy
in the harmonic region, we obtained simple scaling laws for the (linear) force
on the colloid
Diffusion-limited deposition with dipolar interactions: fractal dimension and multifractal structure
Computer simulations are used to generate two-dimensional diffusion-limited
deposits of dipoles. The structure of these deposits is analyzed by measuring
some global quantities: the density of the deposit and the lateral correlation
function at a given height, the mean height of the upper surface for a given
number of deposited particles and the interfacial width at a given height.
Evidences are given that the fractal dimension of the deposits remains constant
as the deposition proceeds, independently of the dipolar strength. These same
deposits are used to obtain the growth probability measure through Monte Carlo
techniques. It is found that the distribution of growth probabilities obeys
multifractal scaling, i.e. it can be analyzed in terms of its
multifractal spectrum. For low dipolar strengths, the spectrum is
similar to that of diffusion-limited aggregation. Our results suggest that for
increasing dipolar strength both the minimal local growth exponent
and the information dimension decrease, while the fractal
dimension remains the same.Comment: 10 pages, 7 figure
Effective squirmer models for self-phoretic chemically active spherical colloids
Various aspects of self-motility of chemically active colloids in Newtonian
fluids can be captured by simple models for their chemical activity plus a
phoretic slip hydrodynamic boundary condition on their surface. For particles
of simple shapes (e.g., spheres) -- as employed in many experimental studies --
which move at very low Reynolds numbers in an unbounded fluid, such models of
chemically active particles effectively map onto the well studied so-called
hydrodynamic squirmers [S. Michelin and E. Lauga, J. Fluid Mech. \textbf{747},
572 (2014)]. Accordingly, intuitively appealing analogies of
"pusher/puller/neutral" squirmers arise naturally. Within the framework of
self-diffusiophoresis we illustrate the above mentioned mapping and the
corresponding flows in an unbounded fluid for a number of choices of the
activity function (i.e., the spatial distribution and the type of chemical
reactions across the surface of the particle). We use the central collision of
two active particles as a simple, paradigmatic case for demonstrating that in
the presence of other particles or boundaries the behavior of chemically active
colloids may be \textit{qualitatively} different, even in the far field, from
the one exhibited by the corresponding "effective squirmer", obtained from the
mapping in an unbounded fluid. This emphasizes that understanding the
collective behavior and the dynamics under geometrical confinement of
chemically active particles necessarily requires to explicitly account for the
dependence of the hydrodynamic interactions on the distribution of chemical
species resulting from the activity of the particles.Comment: 26 pages, 11 figure
Colloidal interactions in two dimensional nematics
The interaction between two disks immersed in a 2D nematic is investigated
(i) analitically using the tensor order parameter formalism for the nematic
configuration around isolated disks and (ii) numerically using finite element
methods with adaptive meshing to minimize the corresponding Landau-de Gennes
free energy. For strong homeotropic anchoring, each disk generates a pair of
defects with one-half topological charge responsible for the 2D quadrupolar
interaction between the disks at large distances. At short distance, the
position of the defects may change, leading to unexpected complex interactions
with the quadrupolar repulsive interactions becoming attractive. This short
range attraction in all directions is still anisotropic. As the distance
between the disks decreases their preferred relative orientation with respect
to the far-field nematic director changes from oblique to perpendicular.Comment: 7 pages, 7 figure
Effective interactions and equilibrium configurations of colloidal particles on a sessile droplet
We study the free energy landscapes of a pair of submicron spherical
particles floating at the surface of a sessile droplet. The particles are
subjected to radial external forces resulting in a deformation of the droplet
shape relative to the reference shape of a spherical cap. This deformation
leads to tangential forces on the particles. For small deformations and for the
contact angle at the substrate being equal to , the
corresponding linearized Young-Laplace equation is solved analytically. The
solution is constructed by employing the method of images from electrostatics,
where each of the particles plays the role of a capillary monopole and the
substrate is replaced by a virtual drop with image charges and by imposing the
conditions of fixed droplet volume and vanishing total force on the droplet.
The substrate boundary conditions determine the signs of the image capillary
charges and therefore also the strength of the tangential forces on the
particles. In the cases of an arbitrary contact angle these forces
are calculated numerically by employing a finite element method to find the
equilibrium shape of the droplet for those configurations in which the
particles are close to the local free energy minima.Comment: 23 pages, 8 figure
Complete Wetting of Pits and Grooves
For one-component volatile fluids governed by dispersion forces an effective
interface Hamiltonian, derived from a microscopic density functional theory, is
used to study complete wetting of geometrically structured substrates. Also the
long range of substrate potentials is explicitly taken into account. Four types
of geometrical patterns are considered: (i) one-dimensional periodic arrays of
rectangular or parabolic grooves and (ii) two-dimensional lattices of
cylindrical or parabolic pits. We present numerical evidence that at the
centers of the cavity regions the thicknesses of the adsorbed films obey
precisely the same geometrical covariance relation, which has been recently
reported for complete cone and wedge filling. However, this covariance does not
hold for the laterally averaged wetting film thicknesses. For sufficiently deep
cavities with vertical walls and close to liquid-gas phase coexistence in the
bulk, the film thicknesses exhibit an effective planar scaling regime, which as
function of undersaturation is characterized by a power law with the common
critical exponent -1/3 as for a flat substrate, but with the amplitude
depending on the geometrical features.Comment: 12 page
- …