Self-Propelled Rods near Surfaces

We study the behavior of self-propelled nanoand micro-rods in three dimensions, confined between two parallel walls, by simulations and scaling arguments. Our simulations include thermal fluctuations and hydrodynamic interactions, which are both relevant for the dynamical behavior at nanoto micrometer length scales. In order to investigate the importance hydrodynamic interactions, we also perform Brownian-dynamics-like simulations. In both cases, we find that self-propelled rods display a strong surface excess in confined geometries. An analogy with semi-flexible polymers is employed to derive scaling laws for the dependence on the wall distance, the rod length, and the propulsive force. The simulation data confirm the scaling predictions. Introduction. – Both in soft matter and in biology, there are numerous examples of swimmers and selfpropelled particles. With a typical size in the range of a few nanoto several micro-meters, both low-Reynoldsnumber hydrodynamics [1] and thermal fluctuations are essential to determine their dynamics. Well-known biological examples are sperm cells which are propelled by a snake-like motion of their tail [2], bacteria like E. coli which move forward by a rotational motion of their spiralshaped flagella [3], and listeria which are propelled by local actin polymerization at their surface [4, 5]. In soft matter systems, synthetic self-propelled particles have been designed to perform directed motion. Examples are bimetallic nanorods which are driven by different chemical reactions at the two types of surfaces [6–8], or connected chains of magnetic colloidal particles on which a snake-like motion is imposed by an external magnetic field [9]. Both in soft matter and in biological systems, surfaces and walls are ubiquitous. For example, bacteria in wet soil, near surfaces or in microfluidic devices [10, 11], or sperm in the female reproductive tract find themselves in strongly confined geometries. Already in 1963, Rothschild found that sperm accumulate at surfaces [12]. Thus surfaces strongly affect the dynamics of swimmers and selfpropelled particles. Typically, these particles live in an aqueous environment. Therefore, hydrodynamics plays an (a)e-mail:[email protected] (b)e-mail:[email protected] important role in determining their behavior. The longrange hydrodynamic interactions (at distances from the wall much larger than the particle size, so that the particle can be approximated by a force dipole) induce a parallel orientation and effective attraction to the wall [13,14]. At short distances from the wall, the details of the propulsion mechanism become relevant. For example, it has been shown for E. coli that corkscrew motion of the flagella leads to hydrodynamic attraction [15]. We study here the dynamics of self-propelled rod-like particles confined between two planar walls. Such particles capture the elongated geometry of most of the swimmers mentioned above. In the vicinity of a wall, the rod-like geometry of the particles is important, since it favors parallel orientation — both with and without hydrodynamic interactions. We consider rods which are small enough for thermal fluctuations to play an important role. Thermal fluctuations induce a persistent-random-walk behavior of the trajectories in the bulk, and an entropic repulsion near the wall. In order to study these effects, we employ a particlebased mesoscale hydrodynamics technique, in which hydrodynamic interactions (HI) can be switched on and off easily. In the absence of hydrodynamic interactions, the effect of the fluid on the self-propelled particle corresponds to a Stokes friction and thermal fluctuations, as described by Brownian dynamics (BD). Our main result is that selfpropelled rods accumulate at surfaces, both with Brownian dynamics and full hydrodynamics. Note that this