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Register a new userActive Brownian motion in a narrow channel
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Added by
Pulak Kumar Ghosh Dr.
Publication date
2014
fields
Physics
and research's language is
English
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We review recent advances in rectification control of artificial microswimmers, also known as Janus particles, diffusing along narrow, periodically corrugated channels. The swimmer self-propulsion mechanism is modeled so as to incorporate a nonzero torque (propulsion chirality). We first summarize the effects of chirality on the autonomous current of microswimmers freely diffusing in channels of different geometries. In particular, left-right and upside-down asymmetric channels are shown to exhibit different transport properties. We then report new results on the dependence of the diffusivity of chiral microswimmers on the channel geometry and their own self-propulsion mechanism. The self-propulsion torque turns out to play a key role as a transport control parameter.
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We study the transport of Brownian particles under a constant driving force and moving in channels that present a varying centerline but have constant aperture width. We investigate two types of channels, {it solid} channels in which the particles are geometrically confined between walls and {em soft} channels in which the particles are confined by a periodic potential. We consider the limit of narrow, slowly-varying channels, i.e., when the aperture and the variation in the position of the centerline are small compared to the length of a unit cell in the channel (wavelength). We use the method of asymptotic expansions to determine both the average velocity (or mobility) and the effective diffusion coefficient of the particles. We show that both solid and soft-channels have the same effects on the transport properties up to $O(epsilon^2)$. We also show that the mobility in a solid-channel at $O(epsilon^4)$ is smaller than that in a soft-channel. Interestingly, in both cases, the corrections to the mobility of the particles are independent of the Peclet number and, as a result, the Einstein-Smoluchowski relation is satisfied. Finally, we show that by increasing the solid-channel width from $w(x)$ to $sqrt{6/pi}w(x)$, the mobility of the particles in the solid-channel can be matched to that in the soft-channel up to $O(epsilon^4)$.
Combining experiments on active colloids, whose propulsion velocity can be controlled via a feedback loop, and theory of active Brownian motion, we explore the dynamics of an overdamped active particle with a motility that depends explicitly on the particle orientation. In this case, the active particle moves faster when oriented along one direction and slower when oriented along another, leading to an anisotropic translational dynamics which is coupled to the particles rotational diffusion. We propose a basic model of active Brownian motion for orientation-dependent motility. Based on this model, we obtain analytic results for the mean trajectories, averaged over the Brownian noise for various initial configurations, and for the mean-square displacements including their anisotropic non-Gaussian behavior. The theoretical results are found to be in good agreement with the experimental data. Our findings establish a methodology to engineer complex anisotropic motilities of active Brownian particles, with potential impact in the study of the swimming behavior of microorganisms subjected to anisotropic driving fields.
We consider the active Brownian particle (ABP) model for a two-dimensional microswimmer with fixed speed, whose direction of swimming changes according to a Brownian process. The probability density for the swimmer evolves according to a Fokker-Planck equation defined on the configuration space, whose structure depends on the swimmers shape, center of rotation and domain of swimming. We enforce zero probability flux at the boundaries of configuration space. We derive a reduced equation for a swimmer in an infinite channel, in the limit of small rotational diffusivity, and find that the invariant density depends strongly on the swimmers precise shape and center of rotation. We also give a formula for the mean reversal time: the expected time taken for a swimmer to completely reverse direction in the channel. Using homogenization theory, we find an expression for the effective longitudinal diffusivity of a swimmer in the channel, and show that it is bounded by the mean reversal time.
We derive a mode-coupling theory (MCT) to describe the dynamics of tracer particles in dense systems of active Brownian particles (ABPs) in two spatial dimensions. The ABP undergo translational and rotational Brownian dynamics, and are equipped with a fixed self-propulsion speed along their orientational vector that describes their active motility. The resulting equations of motion for the tagged-particle density correlation functions describe the various cases of tracer dynamics close to the glass transition: that of a passive colloidal particle in a suspension of ABP, that of a single active particle in a glass-forming passive host suspensions, and that of active tracers in a bath of active particles. Numerical results are presented for these cases assuming hard-sphere interactions among the particles. The qualitative and quantitative accuracy of the theory is tested against event-driven Brownian dynamics (ED-BD) simulations of active and passive hard disks. Simulation and theory are found in quantitative agreement, provided one adjusts the overall density (as known from the passive description of glassy dynamics), and allows for a rescaling of self-propulsion velocities in the active host system. These adjustments account for the fact that ABP-MCT generally overestimates the tendency for kinetic arrest. We also confirm in the simulations a peculiar feature of the transient and stationary dynamical density correlation functions regarding their lack of symmetry under time reversal, demonstrating the non-equilibrium nature of the system and how it manifests itself in the theory.
Active particles may happen to be confined in channels so narrow that they cannot overtake each other (Single File conditions). This interesting situation reveals nontrivial physical features as a consequence of the strong inter-particle correlations developed in collective rearrangements. We consider a minimal model for active Brownian particles with the aim of studying the modifications introduced by activity with respect to the classical (passive) Single File picture. Depending on whether their motion is dominated by translational or rotational diffusion, we find that active Brownian particles in Single File may arrange into clusters which are continuously merging and splitting ({it active clusters}) or merely reproduce passive-motion paradigms, respectively. We show that activity convey to self-propelled particles a strategic advantage for trespassing narrow channels against external biases (e.g., the gravitational field).
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