Accumulation of Microswimmers near a Surface Mediated by Collision and Rotational Brownian Motion

Abstract

In this letter we propose a kinematic model to explain how collisions with a surface and rotational Brownian motion give rise to accumulation of micro-swimmers near a surface. In this model, an elongated microswimmer invariably travels parallel to the surface after hitting it from an oblique angle. It then swims away from the surface, facilitated by rotational Brownian motion. Simulations based on this model reproduce the density distributions measured for the small bacteria E. coli and Caulobacter crescentus, as well as for the much larger bull spermatozoa swimming between two walls.Swimming aids the function of microorganisms, such as enhancing the formation of biofilms on surfaces [1]. Swimming also helps transport sperms toward eggs for fertilization [2]. The density of cells as a function of distance from a surface has been measured for swimming E. coli [3] and bull spermatozoa [4], showing interestingly in both cases values much higher near the surface than far away. This near surface accumulation has mainly been attributed to the hydrodynamic attraction between the cells and the surface [4,5]. Recently, Berke et al. [3] combined the effects of the hydrodynamic attraction and the translational Brownian motion of the cells to predict the distribution of E. coli as a function of distance. As noted by the authors [3], however, this interpretation is not applicable to cells within 10 μm from the surface, where the cell density is the highest. The hydrodynamic interaction among the microswimmers has been shown to be important only at high cell concentrations [6,7].In this letter we present a different account for the near surface accumulation. We ignore the hydrodynamic attraction but emphasize the role of collision with a surface at a low Reynolds number [8], an interaction that deflects the swimming direction, and the role of rotational Brownian motion of individual microswimmers in a confined environment. We show that a typical microswimmer with an elongated shape tends to swim parallel to a surface after hitting it at an oblique angle and therefore accumulate near the surface. Rotational Brownian motion [9] then relaxes the accumulation by randomly changing the swimming direction so that the cells have chances to swim away from the surface. In the extreme case of no rotational Brownian motion, all the cells would end up swimming in close proximity with the surface. In the opposite extreme of very fast rotational Brownian motion, the cells will quickly change to any possible swimming direction and subsequently would be found anywhere with equal probability. In reality, a microswimmer randomly changes its swimming direction with a finite rotational diffusion constant, resulting in a distribution in between the two extremes, that is, more cells stay near the surface and fewer far away.We used the bacterium C. crescentus strain CB15 SB3860 to examine the near surface swimming and accumulation. Swarmer cells of this mutant swim forward only and do not *Jay_Tang@brown.edu. . We noted that although this ...

Batchelor Prize Lecture Fluid dynamics at the scale of the cell

“…One of the prominent early observations was that of Rothschild (1963) who found this in the case of sperm cells, and more recent work on bacteria discovered a similar phenomenon (Berke et al 2008) and attributed the effect to long-range hydrodynamic interactions between the swimmers (viewed as pusher stresslets) and the no-slip wall. An opposing point of view advocated by Li & Tang (2009), but actually first mentioned by Rothschild (1963), is that the accumulation is associated with what has come to be called 'inelastic scattering' of cells by surfaces. That is, rather than the kind of elastic reflection one might see with a ball bouncing off the surface, with equal incident and final angles with respect to the surface normal, here nearly all incident angles result in the same outgoing orientation, nearly parallel to the surface.…”

Influence of swimming strategy on microorganism separation by asymmetric obstacles

“…The accumulation for swimmers s 3 is consistent with experimental results shown in Refs. [12,13] for E. coli.…”

“…These agents range from cancer [3][4][5], fibroblasts [6], and stem cells [7] to self-propelled bacteria [8,9], human spermatozoa [10], and microbots [11]. Each self-propelled agent has a specific propulsion mechanism and interacts in its own characteristic way with the confining walls [12][13][14]. A strong motivation for the study of these systems is the possibility to sort out, concentrate, and manipulate the movement and distribution of the swimmers or even to harvest their energy by using suitably designed microarchitectures [2,[4][5][6][7][8][9][10][14][15][16].…”

Hydrodynamic Trapping of Swimming Bacteria by Convex Walls

“…The second mechanism involves hydrodynamic torques that arise in anisotropic bodies swimming in close contact with the wall and leading to swimming at a finite angle with the wall surface [22]. More recently, the role of hydrodynamic interactions has been questioned [24,25], suggesting that steric repulsion and rotational Brownian motion are enough to reproduce the observed accumulation of bacteria in the proximity of solid walls. Despite the extensive theoretical and numerous experimental works on the hydrodynamics of bacterial swimming, a straightforward, unambiguous, and direct identification of a main mechanism responsible for wall entrapment is still lacking.…”