Hydrodynamic Synchronisation of Model Microswimmers

Abstract

We define a model microswimmer with a variable cycle time, thus allowing the possibility of phase locking driven by hydrodynamic interactions between swimmers. We find that, for extensile or contractile swimmers, phase locking does occur, with the relative phase of the two swimmers being, in general, close to 0 or pi, depending on their relative position and orientation. We show that, as expected on grounds of symmetry, self T-dual swimmers, which are time-reversal covariant, do not phase-lock. We also discuss the phase behaviour of a line of tethered swimmers, or pumps. These show oscillations in their relative phases reminiscent of the metachronal waves of cilia.Comment: 17 pages, 8 figure

Hydrodynamic synchronization of colloidal oscillators

“…This leads to swimming trajectories with sharp turns, analogous to the run-and-tumble mechanism used by bacteria (30). Our system can be used to gain more insight into this phenomenon, which would also be relevant in artificial swimmers (7,8). The model studied here can stabilize inphase motion with slight variations (21) and we expect this to be relevant in determining the conditions necessary to obtain inphase synchronization.…”

“…Coordinated motion is crucial for the effective functioning of cilia and flagella, the elements of eukaryotic cells implicated in generating fluid flows and motility (4). Hydrodynamic coupling is also important in natural and artificial microfluidic conditions (5,6) and low Reynolds number (Re) "microbot" swimmers (7,8). At the relevant scales and temperatures, it has the same magnitude as the random thermal forces; nevertheless, the synchronized states of e.g.…”

Synchronization and Collective Dynamics in a Carpet of Microfluidic Rotors

“…For a collection of free swimmers, such as microorganisms [8], hydrodynamic interactions have been shown to lead to instabilities [9,10] that can result in complex dynamical behaviors [10,11]. In the context of simple microswimmer models where hydrodynamic interactions coupled to internal degrees of freedom can be studied with minimal complexity, it has been shown that the coupling could result in complex dynamical behaviors such as oscillatory bound states between two swimmers [12], and collective many-body swimming phases [13,14].A particularly interesting aspect of such hydrodynamic coupling is the possibility of synchronization between different objects with cyclic motions [4,5,[15][16][17][18][19][20][21]. This effect has mostly been studied in simple systems such as two interacting objects or linear arrays and very little is known about possible many-body emergent behaviors of a large number of active objects with hydrodynamic coupling.…”

Energetics of synchronization in coupled oscillators rotating on circular trajectories

“…In this context, the swimming efficiency [33] of a Stokes swimmer [34][35][36][37] as a simple model of such propulsion with additional motional-degrees of freedom of a body of the microorganism beyond those of flagella would be worthy of further investigation. Developing the concise description of energy dissipation for more complicated collective dynamics, e.g., hydrodynamic synchronization of microswimmers [38] and cilia in metachronal coordination [9,39,40], will also be interesting. To this end, extensions of our theory so that it includes radial flexibility [19] with general orbital shapes [13,14] and the formulation for many-body systems will be required to achieve a more general formulation of the energetics of synchronization in coupled oscillators.…”