65 research outputs found
Synchronous versus asynchronous transport of a paramagnetic particle in a modulated ratchet potential
We present a combined experimental and theoretical study describing the
dynamical regimes displayed by a paramagnetic colloidal particle externally
driven above a stripe-patterned magnetic garnet film. A circularly polarized
rotating magnetic field modulates the stray field of the garnet film and
generates a translating periodic potential which induces particle motion.
Increasing the driving frequency, we observe a transition from a phase-locked
motion with constant speed to a sliding dynamics characterized by a lower speed
due to the loss of synchronization with the traveling potential. We explain the
experimental findings with an analytically tractable theoretical model and
interpret the particle dynamics in the presence of thermal noise. The model is
in good quantitative agreement with the experiments.Comment: 6 pages, 3 figures, published in Europhysics Letters (EPL
Superexponential droplet fractalization as a hierarchical formation of dissipative compactons
We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hilliard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate that a primitive element in the appearing hierarchical structure is a dissipative compacton. Both direct simulations and the analysis of a self-similar solution show that the compactons appear at superexponentially decreasing scales, which means vanishing dimension of the fractal
Bubble dynamics atop an oscillating substrate: Interplay of compressibility and contact angle hysteresis
We consider a sessile hemispherical bubble sitting on the transversally oscillating bottom of a deep liquid layer and focus on the interplay of the compressibility of the bubble and the contact angle hysteresis. In the presence of contact angle hysteresis, the compressible bubble exhibits two kinds of terminal oscillations: either with the stick-slip motion of the contact line or with the completely
immobile contact line. For the stick-slip oscillations, we detect a double resonance, when the external frequency is close to eigenfrequencies of both the breathing mode and shape oscillations. For the regimes evolving to terminal oscillations with the fixed contact line, we find an
unusual transient resembling modulated oscillations
Langevin equations and a geometric integration scheme for the overdamped limit of homogeneous rotational Brownian motion
The translational motion of anisotropic and self-propelled colloidal
particles is closely linked with the particle's orientation and its rotational
Brownian motion. In the overdamped limit, the stochastic evolution of the
orientation vector follows a diffusion process on the unit sphere and is
characterised by an orientation-dependent ("multiplicative") noise. As a
consequence, the corresponding Langevin equation attains different forms
depending on whether It\=o's or Stratonovich's stochastic calculus is used. We
clarify that both forms are equivalent and derive them from a geometric
construction of Brownian motion on the unit sphere, based on infinitesimal
random rotations. Our approach suggests further a geometric integration scheme
for rotational Brownian motion, which preserves the normalisation constraint of
the orientation vector exactly. We show that a simple implementation of the
scheme converges weakly at order 1 of the integration time step, and we outline
an advanced variant of the scheme that is weakly exact for an arbitrarily large
time step. The discussion is restricted to time-homogeneous rotational Brownian
motion (i.e., constant rotational diffusion tensor), which is relevant for
chemically anisotropic spheres such as self-propelled Janus particles.Comment: 8 page
Transport and selective chaining of bidisperse particles in a travelling wave potential
We combine experiments, theory and numerical simulation to investigate the dynamics of a binary suspension of paramagnetic colloidal particles dispersed in water and transported above a stripe-patterned magnetic garnet film. The substrate generates a one-dimensional periodic energy landscape above its surface. The application of an elliptically polarized rotating magnetic field causes the landscape to translate, inducing direct transport of paramagnetic particles placed above the film. The ellipticity of the applied field can be used to control and tune the interparticle interactions, from net repulsive to net attractive. When considering particles of two distinct sizes, we find that, depending on their elevation above the surface of the magnetic substrate, the particles feel effectively different potentials, resulting in different mobilities. We exploit this feature to induce selective chaining for certain values of the applied field parameters. In particular, when driving two types of particles, we force only one type to condense into travelling parallel chains. These chains confine the movement of the other non-chaining particles within narrow colloidal channels. This phenomenon is explained by considering the balance of pairwise magnetic forces between the particles and their individual coupling with the travelling landscape
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