Hydrodynamic Interaction between Two Swimmers at Low Reynolds Number

Abstract

We investigate the hydrodynamic interactions between micro-organisms swimming at low Reynolds number. By considering simple model swimmers, and combining analytic and numerical approaches, we investigate the time-averaged flow field around a swimmer. At short distances the swimmer behaves like a pump. At large distances the velocity field depends on whether the swimming stroke is invariant under a combined time-reversal and parity transformation. We then consider two swimmers and find that the interaction between them consists of two parts: a passive term, independent of the motion of the second swimmer, and an active term resulting from the simultaneous swimming action of both swimmers. The swimmer-swimmer interaction is a complicated function of their relative displacement, orientation, and phase, leading to motion that can be attractive, repulsive, or oscillatory.

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.…”

“…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].…”

Swarming in viscous fluids: Three-dimensional patterns in swimmer- and force-induced flows

“…(1) describes hydrodynamic coupling under the period-averaged flow assumption. However, the phase difference of the microscopic strokes between two swimmers has been shown to actively affect the interaction in unexpected ways, leading to attraction, repulsion, or oscillations [91]. How these subtle swimmer-induced pairwise interactions [77,91] influence the collective behavior of swarms remains to be investigated.…”

Getting drowned in a swirl: Deformable bead-spring model microswimmers in external flow fields

“…Furthermore, the collective behavior of many such interacting particles has been explored [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Collections of self-propelled particles in liquid environment exhibit fascinating and complex nonequilibrium phenomena emerging from self-organization, where hydrodynamic interactions can play a significant role [11,[36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52].…”

“…form-stable) artificial microswimmers, several examples of microswimmers were identified that actively deform to achieve self-propulsion. Many biological microorganisms fall into this category [64][65][66], as well as several instances of proposed theoretical model microswimmers [40,[67][68][69][70][71]. Apart from that, microswimmers can be realized in the form of soft particles that are already de- * Electronic address: kuechler@thphy.uni-duesseldorf.de † Electronic address: menzel@thphy.uni-duesseldorf.de formable in their non-propelling passive state.…”