Active particles in noninertial frames: How to self-propel on a carousel

Abstract

Typically the motion of self-propelled active particles is described in a quiescent environment establishing an inertial frame of reference. Here we assume that friction, self-propulsion and fluctuations occur relative to a non-inertial frame and thereby the active Brownian motion model is generalized to non-inertial frames. First, analytical solutions are presented for the overdamped case, both for linear swimmers and circle swimmers. For a frame rotating with constant angular velocity ("carousel"), the resulting noise-free trajectories in the static laboratory frame trochoids if these are circles in the rotating frame. For systems governed by inertia, such as vibrated granulates or active complex plasmas, centrifugal and Coriolis forces become relevant. For both linear and circling self-propulsion, these forces lead to out-spiraling trajectories which for long times approach a spira mirabilis. This implies that a self-propelled particle will typically leave a rotating carousel. A navigation strategy is proposed to avoid this expulsion, by adjusting the self-propulsion direction at wish. For a particle, initially quiescent in the rotating frame, it is shown that this strategy only works if the initial distance to the rotation centre is smaller than a critical radius Rc which scales with the self-propulsion velocity. Possible experiments to verify the theoretical predictions are discussed. arXiv:1904.12755v1 [cond-mat.soft]

Rototaxis: Localization of active motion under rotation

“…Here we also note that, for a givenμ, the limit of m → 0 corresponds to the overdamped dynamics considered in sec. 2, and indeed, we see that the domain size of the negative rototactic phase increases with decreasing m, and the presence of an asymmetry in the occurrence of negative rototaxis that favors smaller Rint and φint > 0, as we would expect given the result in (54) and the positively defined global rotation. Even more surprisingly, a closer examination of the numerical trajectories reveal that in addition to the epicyclic or rosette like trajectories also found in the overdamped scenario, there exists circular orbits (about the global rotational center) in the steady state that correspond to stable non-linear limit cycles (58), which we show examples of in Fig.…”

“…We note that in the absence of rotation ω, the overdamped limit of this model has recently been investigated for a mathematically equivalent phototactic torque T in a system of phototactically driven Janus particles and found experimentally to result in non-trivial trochoidal trajectories (18), which we subsequently also recover in this section. On the other hand, the zero-torque limit of this model has been studied in (54). Now, the radial and angular components of [5] explicitly readsṘ…”

“…In fact, notice that this emergent constant value of τ in the steady state plays the exact role of an internal torque M that is often placed by hand in various models of circle swimmers that we have thus far neglected, for which the circular orbit is a known solution to the inertial dynamics under a global rotation (54). It thus follows that the transition between overdamped epicyclic trajectories to circular limit cycles could possibly be understood as the onset of some instability of the circle solution itself.…”

Time-dependent inertia of self-propelled particles: the Langevin rocket

“…Future work should generalize the present model to external potentials like optical fields, disorder and confinement [39,[100][101][102][103] and to motion in noninertial rotating frames [104,105]. Furthermore, anisotropic particles which show out-of-plane orientations and positions relevant for active complex plasmas [106] should be considered in the future.…”

Designing circle Swimmers: Principles and strategies

“…Most synthetic motors are rotationally diffusive, which means that although the motors have an advective velocity controlled mainly by some chemical concentrations, their orientation is dictated by Brownian fluctuations. As a generic case of microswimmers, circular microswimmers moving in curved trajectories have been widely applied in cargo delivery [17,[41][42][43][44][45][46][47][48]. For instance, the spermflagella driven Micro-Bio-Robot (MBR) was reported to perform precise point-to-point closed-loop motion control under the influence of the controlled magnetic field lines with applications towards targeted drug delivery and microactuation [23][24][25].…”