Clustering instability of focused swimmers

Abstract

One of the hallmarks of active matter is its rich nonlinear dynamics and instabilities. Recent numerical simulations of phototactic algae showed that a thin jet of swimmers, obtained from hydrodynamic focusing inside a Poiseuille flow, was unstable to longitudinal perturbations with swimmers dynamically clustering (Jibuti et al., Phys. Rev. E, 90, 2014). As a simple starting point to understand these instabilities, we consider in this paper an initially homogeneous one-dimensional line of aligned swimmers moving along the same direction, and characterise its instability using both a continuum framework and a discrete approach. In both cases, we show that hydrodynamic interactions between the swimmers lead to instabilities in density for which we compute the growth rate analytically. Lines of pusher-type swimmers are predicted to remain stable while lines of pullers (such as flagellated algae) are predicted to always be unstable.

Physics driven behavioural clustering of free-falling paper shapes

“…Using these quantities allows the construction of a dimensionless parameter space in which different regions correspond to different falling behaviours. Similar approaches using other dimensionless quantities such as the Froude Fr or Strouhal St numbers have been used in the analysis of behavioural diversity in other systems [26, 46–49]. The benefit of this method is that it facilitates a quantitative method to differentiate between behaviours, while also exposing the underlying physical phenomena in the system.…”

Clustering of Magnetic Swimmers in a Poiseuille Flow

“…Examples of such systems include those with short range interactions and activity mechanisms that exhibit polar [3,4] and nematic [5][6][7][8][9][10] symmetry, as well as those with intrinsic mechanisms that mediate nonequilibrium long-range interactions such as phoretic swimmers [11][12][13]. On the other hand, external cues can guide individual microswimmers in nature by using different strategies to modulate their motility patterns, including chemotaxis [14][15][16][17], phototaxis [18][19][20], gyrotaxis [21][22][23], and magnetotaxis [24]. In the quest for understanding the full range of emergent properties of active matter systems, it is important to study the interplay between intrinsic mechanical activity, interactions, and external driving, including shear stresses [25].…”

“…In driven active suspensions through channels, such as phototactic algae exposed to a light source [18,19] and magnetotactic bacteria under the effect of an external magnetic field [24], the swimmers have been observed to accumulate at the center and exhibit clustering. While the clustering can be understood as a consequence of effectively attractive hydrodynamic interactions between pullers such as algae [20], for the magnetotactic bacteria studied in Ref. [24], which have the structural characteristics of pusher-type bacteria such as E. coli, the effect cannot be accounted for using hydrodynamic interactions.…”

“…Hydrodynamic interactions.-It is important to examine whether the above discussions are qualitatively modified if we incorporate hydrodynamic interaction between the swimmers, which can be repulsive or attractive depending on swimmer types [20,[40][41][42]. To account for this effect, we consider an active stress in the fluid (arising from the hydrodynamic activity of the swimmers) in the form of Σ a = Sρ e z e z − 1 3 , where S denotes the strength of the force dipoles exerted by the swimmers on the fluid (stresslet) [43] (S < 0 for pushers and S > 0 for pullers).…”

Effective squirmer models for self-phoretic chemically active spherical colloids

“…The squirmer model successfully captures many of the qualitative features exhibited by swimming microorganisms in unbounded fluids or near surfaces [33,[53][54][55][56]). Concepts such as "pullers" and "pushers" have emerged from this model and have turned out to be physically insightful concerning, e.g., the understanding of various behaviors exhibited by swimming microrganisms near boundaries [33,53,54,[56][57][58][59][60][61][62][63][64], the hydrodynamic interactions between microrganisms, [65][66][67], or the aggregation and ordering behavior in suspensions of squirmers [68][69][70][71]. In the context of artificial, man-made active particles, the effective mapping onto squirmers noted above has been explicitly carried out for a spherical "hot" colloid [72] or a spherical particle with spatially varying phoretic mobility [73,74] (see, c.f., Sec.…”