199 research outputs found
Pair Interaction of Catalytically Active Colloids: From Assembly to Escape
The dynamics and pair trajectory of two self-propelled colloids are reported.
The autonomous motions of the colloids are due to a catalytic chemical reaction
taking place asymmetrically on their surfaces that generates a concentration
gradient of interactive solutes around the particles and actuate particle
propulsion. We consider two spherical particles with symmetric catalytic caps
extending over the local polar angles and
from the centers of active sectors in an otherwise quiescent fluid. A combined
analytical-numerical technique was developed to solve the coupled mass transfer
equation and the hydrodynamics in the Stokes flow regime. The ensuing pair
trajectory of the colloids is controlled by the reacting coverages
and their initial relative orientation with respect to each
other. Our analysis indicates two possible scenarios for pair trajectories of
catalytic self-propelled particles: either the particles approach, come into
contact and assemble or they interact and move away from each other (escape).
For arbitrary motions of the colloids, it is found that the direction of
particle rotations is the key factor in determining the escape or assembly
scenario. Based on the analysis, a phase diagram is sketched for the pair
trajectory of the catalytically active particles as a function of active
coverages and their initial relative orientations. We believe this study has
important implications in elucidation of collective behaviors of
auotophoretically self-propelled colloids
Curvature Capillary Migration of Microspheres
We address the question: How does capillarity propel microspheres along
curvature gradients? For a particle on a fluid interface, there are two
conditions that can apply at the three phase contact line: Either the contact
line adopts an equilibrium contact angle, or it can be pinned by kinetic
trapping, e.g. at chemical heterogeneities, asperities or other pinning sites
on the particle surface. We formulate the curvature capillary energy for both
scenarios for particles smaller than the capillary length and far from any
pinning boundaries. The scale and range of the distortion made by the particle
are set by the particle radius; we use singular perturbation methods to find
the distortions and to rigorously evaluate the associated capillary energies.
For particles with equilibrium contact angles, contrary to the literature, we
find that the capillary energy is negligible, with the first contribution
bounded to fourth order in the product of the particle radius and the
deviatoric curvature. For pinned contact lines, we find curvature capillary
energies that are finite, with a functional form investigated previously by us
for disks and microcylinders on curved interfaces. In experiments, we show
microsphere migrate along deterministic trajectories toward regions of maximum
deviatoric curvature with curvature capillary energies ranging from . These data agree with the curvature capillary
energy for the case of pinned contact lines. The underlying physics of this
migration is a coupling of the interface deviatoric curvature with the
quadrupolar mode of nanometric disturbances in the interface owing to the
particle's contact line undulations. This work is an example of the major
implications of nanometric roughness and contact line pinning for colloidal
dynamics.Comment: 9 pages, 8 figure
Capillary Assembly of Colloids: Interactions on Planar and Curved Interfaces
In directed assembly, small building clocks are assembled into an organized
structures under the influence of guiding fields. Capillary interactions
provide a versatile route for structure formation. Colloids adsorbed on fluid
interfaces distort the interface, which creates an associated energy field.
When neighboring distortions overlap, colloids interact to minimize interfacial
area. Contact line pinning, particle shape and surface chemistry play important
roles in structure formation. Interface curvature acts like an external field;
particles migrate and assemble in patterns dictated by curvature gradients. We
review basic analysis and recent findings in this rapidly evolving literature.
Understanding the roles of assembly is essential for tuning the mechanical,
physical, and optical properties of the structure.Comment: 14 pages, 9 figure
Reply to the Comments on "Curvature capillary migration of microspheres" by P. Galatola and A. Wurger
We have studied microparticle migration on curved fluid interfaces in
experiment and derived an expression for the associated capillary energy
for two cases, i.e., pinned contact lines and equilibrium contact lines, which
differ from expressions derived by others in the literature. In this problem, a
particle of radius makes a disturbance in a large domain characterized by
principal radii of curvature and . Since is smaller than all
associated geometric and physico-chemical length scales, analysis calls for a
singular perturbation approach. We recapitulate these concepts, identify
conceptual errors in the Comments about our work, and provide evidence from
experiment and simulation that supports our view.Comment: 6 pages, 2 figure
Self-Diffusiophoretic Colloidal Propulsion Near a Solid Boundary
We study the diffusiophoretic self-propulsion of a colloidal catalytic
particle due to a surface chemical reaction in a vicinity of a solid wall.
Diffusiophoresis is a chemico-mechanical transduction mechanism in which a
concentration gradient of an interacting solute produces an unbalanced force on
a colloidal particle and drives it along the gradient. We consider a spherical
particle with an axisymmetric reacting cap covering the polar angle range in the presence of a repulsive solute, near an infinite
planar wall, and solve the coupled solute concentration and Stokes equations,
using a mixture of numerical and analytic arguments. The resulting particle
trajectory is determined by and the initial orientation of the
symmetry axis with respect to the plane. At normal incidence the particle
initially moves away from or towards the wall, depending on whether the cap
faces towards or away, respectively, but even in the latter case the particle
never reaches the wall due to hydrodynamic lubrication resistance. For other
initial orientations, when the particle either
moves away immediately or else rotates along its trajectory so as to cause the
active side to face the wall and the particle to rebound. For higher coverage
we find trajectories where the particle skims along the wall at constant
separation or else comes to rest. We provide a phase diagram giving the nature
of the trajectory (repulsion, rebound, skimming or stationary) as a function of
and the initial orientation
Capillary Interactions on Fluid Interfaces: Opportunities for Directed Assembly
A particle placed in soft matter distorts its host and creates an energy
landscape. This can occur, for example, for particles in liquid crystals, for
particles on lipid bilayers or for particles trapped at fluid interfaces. Such
energies can be used to direct particles to assemble with remarkable degrees of
control over orientation and structure. These notes explore that concept for
capillary interactions, beginning with particle trapping at fluid interfaces,
addressing pair interactions on planar interfaces and culminating with
curvature capillary migration. Particular care is given to the solution of the
associated boundary value problems to determine the energies of interaction.
Experimental exploration of these interactions on planar and curved interfaces
is described. Theory and experiment are compared. These interactions provide a
rich toolkit for directed assembly of materials, and, owing to their close
analogy to related systems, pave the way to new explorations in materials
science.Comment: 37 pages, 28 figure
Capillary migration of microdisks on curved interfaces
The capillary energy landscape for particles on curved fluid interfaces is
strongly influenced by the particle wetting conditions. Contact line pinning
has now been widely reported for colloidal particles, but its implications in
capillary interactions have not been addressed. Here, we present experiment and
analysis for disks with pinned contact lines on curved fluid interfaces. In
experiment, we study microdisk migration on a host interface with zero mean
curvature; the microdisks have contact lines pinned at their sharp edges and
are sufficiently small that gravitational effects are negligible. The disks
migrate away from planar regions toward regions of steep curvature with
capillary energies inferred from the dissipation along particle trajectories
which are linear in the deviatoric curvature. We derive the curvature capillary
energy for an interface with arbitrary curvature, and discuss each contribution
to the expression. By adsorbing to a curved interface, a particle eliminates a
patch of fluid interface and perturbs the surrounding interface shape. Analysis
predicts that perfectly smooth, circular disks do not migrate, and that
nanometric deviations from a planar circular, contact line, like those around a
weakly roughened planar disk, will drive migration with linear dependence on
deviatoric curvature, in agreement with experiment
Films of bacteria at interfaces: three stages of behaviour
Bacterial attachment to a fluid interface can lead to the formation of a film
with physicochemical properties that evolve with time. We study the time
evolution of interface (micro)mechanics for interfaces between oil and
bacterial suspensions by following the motion of colloidal probes trapped by
capillarity to determine the interface microrheology. Initially, active
bacteria at and near the interface drive superdiffusive motion of the colloidal
probes. Over timescales of minutes, the bacteria form a viscoelastic film which
we discuss as a quasi-two-dimensional, active, glassy system. To study late
stage mechanics of the film, we use pendant drop elastometry. The films, grown
over tens of hours on oil drops, are expanded and compressed by changing the
drop volume. For small strains, by modeling the films as 2D Hookean solids, we
estimate the film elastic moduli, finding values similar to those reported in
the literature for the bacteria themselves. For large strains, the films are
highly hysteretic. Finally, from wrinkles formed on highly compressed drops, we
estimate film bending energies. The dramatic restructuring of the interface by
such robust films has broad implications, e.g. in the study of active colloids,
in understanding the community dynamics of bacteria, and in applied settings
including bioremediation
Curvature capillary repulsion
Directed assembly of colloids is an exciting field in materials science to
form structures with new symmetries and responses. Fluid interfaces have been
widely exploited to make densely packed ordered structures. We have been
studying how interface curvature can be used in new ways to guide structure
formation. On a fluid interface, the area of the deformation field around
adsorbed microparticles depends on interface curvature; particles move to
minimize the excess area of the distortions that they make in the interface.
For particles that are sufficiently small, this area decreases as particles
move along principle axes to sites of high deviatoric curvature. We have
studied this migration for microparticles on a curved host interface with zero
mean curvature created by pinning an oil-water interface around a micropost.
Here, on a similar interface, we demonstrate capillary curvature repulsion,
that is, we identify conditions in which microparticles migrate away from high
curvature sites. Using theory and experiment, we discuss the origin of these
interactions and their relationship to the particle's undulated contact line.
We discuss the implications of this new type of interaction in various contexts
from materials science to microrobotics.Comment: 9 pages, 7 figure
Curvature-driven migration of colloids on lipid bilayers
Colloids and proteins alike can bind to lipid bilayers and move laterally in
these two-dimensional fluids. Inspired by proteins that generate membrane
curvature, sense the underlying membrane geometry, and migrate to high
curvature sites, we explore the question: Can colloids, adhered to lipid
bilayers, also sense and respond to membrane geometry? We report the curvature
migration of Janus microparticles adhered to giant unilamellar vesicles
elongated to present well defined curvature fields. However, unlike proteins,
which migrate to minimize membrane bending energy, colloids migrate by an
entirely different mechanism. By determining the energy dissipated along a
trajectory, the energy field mediating these interactions is inferred to be
linear in the local deviatoric curvature, as reported previously for colloids
trapped at curved interfaces between immiscible fluids. In this latter system,
however, the energy gradients are far larger, so particles move
deterministically, whereas the colloids on vesicles move with significant
fluctuations in regions of weak curvature gradient. By addressing the role of
Brownian motion, we show that the observed curvature migration of colloids on
bilayers is indeed a case of curvature capillary migration, with membrane
tension playing the role of interfacial tension. Furthermore, since this motion
is mediated by membrane tension and shape, it can be modulated, or even turned
"on" and "off", by simply varying these parameters. While particle-particle
interactions on lipid membranes have been considered in many contributions, we
report here an exciting and previously unexplored modality to actively direct
the migration of colloids to desired locations on lipid bilayers.Comment: 24 pages, 12 figure
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