Self-propelled colloidal particle near a planar wall: A Brownian dynamics study

Abstract

Miniaturized, self-propelled locomotors use chemo-mechanical transduction mechanisms to convert fuel in the environment to autonomous motion. Recent experimental and theoretical studies demonstrate that these autonomous engines can passively follow the contours of solid boundaries they encounter. Boundary guidance, however, is not necessarily stable: Mechanical disturbances can cause the motor to hydrodynamically depart from the passively guided pathway. Furthermore, given the scaled-down size of micromotors (typically 100 nm -10 µm), Brownian thermal fluctuation forces are necessarily important and these stochastic forces can randomize passively-steered trajectories.Here we examine theoretically the stability of boundary guided motion of micromotors along infinite planar walls to mechanical disturbances and to Brownian forces. Our aim is to understand under what conditions this passively guided motion is stable. We choose a locomotor design in which spherical colloids are partially coated with a catalytic cap that reacts with solute to produce a product. The product is repelled from the particle surface, causing the particle to move with the inert face at the front (autonomous motion via self-diffusiophoresis). When propelled towards a planar wall, deterministic hydrodynamic studies demonstrate that these locomotors can exhibit, for large enough cap sizes, steady trajectories in which the particle either skims unidirectionally along the surface at a constant distance from the wall, or becomes stationary. We first investigate the linear hydrodynamic stability of these states by expanding the equations of motion about the states, and find that linear perturbations decay exponentially in time. We then study the effects of thermal fluctuations by formulating a Langevin equation for the particle motion which includes the Brownian stochastic force. The Pećlet number scales the ratio of deterministic to Brownian forces, where Pe = πµa 2ṽ c /k B T and a denotes the colloid radius, µ the continuous phase viscosity,ṽ c the characteristic diffusiophoretic velocity and k B T the thermal energy. The skimming and stationary states are found to persist for Pe above 10 3 . At Pe below 200, the trajectory of a locomotor approaching the wall is unpredictable. We present representative individual trajectories along with probability distributions for statistical ensembles of particles, quantifying the effects of thermal fluctuations and illustrating the transition from unpredictable to passively guided motion. *

Swimming trajectories of a three-sphere microswimmer near a wall

“…Simplistic two-sphere nearwall models of bacterial motion have revealed that the dynamics of a bead swimmer can be surprisingly rich, including circular motion in contact with the wall, swimming away from the wall, and a non-trivial steady circulation at a finite distance from the interface 90 . This diverse phase behavior has also been corroborated in systems of chemically powered autophoretic particles [91][92][93][94][95][96][97][98] , leading to a phase di-agram also includes trapping, escape, and a steady hovering state. Swimming near a boundary has been addressed using a two-dimensional singularity model combined with a complex variable approach 99 , a resistive force theory 100 , and a multipole expansion technique 101 .…”

Hydrodynamics can determine the optimal route for microswimmer navigation

“…To fill this gap, in the present work, we systematically explore the optimal microswimmer navigation problem in the presence of walls or obstacles, where hydrodynamic microswimmer-wall interactions are well known to occur [41][42][43][44][45][46][47][48][49] , but whose impact on optimal microswimmer navigation is essentially unknown. Combining an analytical approach with numerical simulations, we find that in the presence of remote obstacles or walls, the shortest path is not fastest for microswimmers, even in the complete absence of external force or flow fields.…”

State diagram of a three-sphere microswimmer in a channel

“…As seen already in simplistic models involving two linked spheres near a wall 91 , a surprisingly rich behavior emerges, with the presence of trapping states, escape from the wall and non-trivial steady trajectories above the surface. This behavior has also been seen in an analogous system of self-phoretic active Janus particles [92][93][94][95][96][97][98][99][100] , where a complex phase diagram has been found, based on the initial orientation and the distance separating the swimmer from the wall. Additional investigations have considered the hydrodynamic interactions between two squirmers near a boundary 101 , the dynamics of active particles near a fluid interface [102][103][104] , swimming in a confining microchannel [105][106][107][108][109][110][111][112][113][114][115][116] , inside a spherical cavity [117][118][119] , near a curved obstacle 120,121 and in a liquid film [122][123][124] .…”