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Register a new userRe-entrant bimodality in spheroidal chiral swimmers in shear flow
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We use a continuum model to report on the behavior of a dilute suspension of chiral swimmers subject to externally imposed shear in a planar channel. Swimmer orientation in response to the imposed shear can be characterized by two distinct phases of behavior, corresponding to unimodal or bimodal distribution functions for swimmer orientation along the channel. These phases indicate the occurrence (or not) of a population splitting phenomenon changing the swimming direction of a macroscopic fraction of active particles to the exact opposite of that dictated by the imposed flow. We present a detailed quantitative analysis elucidating the complexities added to the population splitting behavior of swimmers when they are chiral. In particular, the transition from unimodal to bimodal and vice versa are shown to display a re-entrant behavior across the parameter space spanned by varying the chiral angular speed. We also present the notable effects of particle aspect ratio and self-propulsion speed on system phase behavior and discuss potential implications of our results in applications such as swimmer separation/sorting.
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We present a quantitative analysis on the response of a dilute active suspension of self-propelled rods (swimmers) in a planar channel subjected to an imposed shear flow. To best capture the salient features of shear-induced effects, we consider the case of an imposed Couette flow, providing a constant shear rate across the channel. We argue that the steady-state behavior of swimmers can be understood in the light of a population splitting phenomenon, occurring as the shear rate exceeds a certain threshold, initiating the reversal of swimming direction for a finite fraction of swimmers from down- to upstream or vice versa, depending on swimmer position within the channel. Swimmers thus split into two distinct, statistically significant and oppositely swimming majority and minority populations. The onset of population splitting translates into a transition from a self-propulsion-dominated regime to a shear-dominated regime, corresponding to a unimodal-to-bimodal change in the probability distribution function of the swimmer orientation. We present a phase diagram in terms of the swim and flow Peclet numbers showing the separation of these two regimes by a discontinuous transition line. Our results shed further light on the behavior of swimmers in a shear flow and provide an explanation for the previously reported non-monotonic behavior of the mean, near-wall, parallel-to-flow orientation of swimmers with increasing shear strength.
We present a numerical study of the phase behavior of repulsively interacting active polar particles that align their active velocities nematically. The amplitude of the active velocity, and the noise in its orientational alignment control the active nature of the system. At high values of orientational noise, the structural fluid undergoes a continuous nematic-isotropic transition in active orientation. This transition is well separated from an active phase separation, characterized by the formation of high density hexatic clusters, observed at lower noise strengths. With increasing activity, the system undergoes a re-entrant fluid-phase separation-fluid transition. The phase coexistence at low activity can be understood in terms of motility induced phase separation. In contrast, the re-melting of hexatic clusters, and the collective motion at low orientational noise are dominated by flocking behavior. At high activity, sliding and jamming of polar sub-clusters, formation of grain boundaries, lane formation, and subsequent fragmentation of the polar patches mediate remelting.
We study the steady-state behavior of active, dipolar, Brownian spheroids in a planar channel subjected to an imposed Couette flow and an external transverse field, applied in the downward normal-to-flow direction. The field-induced torque on active spheroids (swimmers) is taken to be of magnetic form by assuming that they have a permanent magnetic dipole moment, pointing along their self-propulsion (swim) direction. Using a continuum approach, we show that a host of behaviors emerge over the parameter space spanned by the particle aspect ratio, self-propulsion and shear/field strengths, and the channel width. The cross-stream migration of the model swimmers is shown to involve a regime of linear response (quantified by a linear-response factor) in weak fields. For prolate swimmers, the weak-field behavior crosses over to a regime of full swimmer migration to the bottom half of the channel in strong fields. For oblate swimmers, a counterintuitive regime of reverse migration arises in intermediate fields, where a macroscopic fraction of swimmers reorient and swim to the top channel half at an acute `upward angle relative to the field axis. The diverse behaviors reported here are analyzed based on the shear-induced population splitting (bimodality) of the swim orientation, giving two distinct, oppositely polarized, swimmer subpopulations (albeit very differently for prolate/oblate swimmers) in each channel half. In strong fields, swimmers of both types exhibit net upstream currents relative to the laboratory frame. The onsets of full migration and net upstream current depend on the aspect ratio, enabling efficient particle separation strategies in microfluidic setups.
The Boltzmann equation for inelastic Maxwell models is considered to determine the velocity moments through fourth degree in the simple shear flow state. First, the rheological properties (which are related to the second-degree velocity moments) are {em exactly} evaluated in terms of the coefficient of restitution $alpha$ and the (reduced) shear rate $a^*$. For a given value of $alpha$, the above transport properties decrease with increasing shear rate. Moreover, as expected, the third-degree and the asymmetric fourth-degree moments vanish in the long time limit when they are scaled with the thermal speed. On the other hand, as in the case of elastic collisions, our results show that, for a given value of $alpha$, the scaled symmetric fourth-degree moments diverge in time for shear rates larger than a certain critical value $a_c^*(alpha)$ which decreases with increasing dissipation. The explicit shear-rate dependence of the fourth-degree moments below this critical value is also obtained.
The short-time motion of Brownian particles in an incompressible Newtonian fluid under shear, in which the fluid inertia becomes important, was investigated by direct numerical simulation of particulate flows. Three-dimensional simulations were performed, wherein external forces were introduced to approximately form Couette flows throughout the entire system with periodic boundary conditions. In order to examine the validity of the method, the mean square displacement of a single spherical particle in a simple shear flow was calculated, and these results were compared with a hydrodynamic analytical solution that includes the effects of the fluid inertia. Finally, the dynamical behavior of a monodisperse dispersion composed of repulsive spherical particles was examined on short time scales, and the shear-induced diffusion coefficients were measured for several volume fractions up to 0.50.
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