Simulating Microswimmers Under Confinement With Dissipative Particle (Hydro) Dynamics

Abstract

In this work we study microwimmers, whether colloids or polymers, embedded in bulk or in confinement. We explicitly consider hydrodynamic interactions and simulate the swimmers via an implementation inspired by the squirmer model. Concerning the surrounding fluid, we employ a Dissipative Particle Dynamics scheme. Differently from the Lattice-Boltzmann technique, on the one side this approach allows us to properly deal not only with hydrodynamics but also with thermal fluctuations. On the other side, this approach enables us to study microwimmers with complex shapes, ranging from spherical colloids to polymers. To start with, we study a simple spherical colloid. We analyze the features of the velocity fields of the surrounding solvent, when the colloid is a pusher, a puller or a neutral swimmer either in bulk or confined in a cylindrical channel. Next, we characterise its dynamical behaviour by computing the mean square displacement and the long time diffusion when the active colloid is in bulk or in a channel (varying its radius) and analyze the orientation autocorrelation function in the latter case. While the three studied squirmer types are characterised by the same bulk diffusion, the cylindrical confinement considerably modulates the diffusion and the orientation autocorrelation function. Finally, we focus our attention on a more complex shape: an active polymer. We first characterise the structural features computing its radius of gyration when in bulk or in cylindrical confinement, and compare to known results obtained without hydrodynamics. Next, we characterise the dynamical behaviour of the active polymer by computing its mean square displacement and the long time diffusion. On the one hand, both diffusion and radius of gyration decrease due to the hydrodynamic interaction when the system is in bulk. On the other hand, the effect of confinement is to decrease the radius of gyration, disturbing the motion of the polymer and thus reducing its diffusion.

Minimal numerical ingredients describe chemical microswimmers’ 3-D motion

“…By extending the DPD numerical framework described in 55 to include the effects of mass and shape asymmetries, we have demonstrated that hydrodynamic interactions, gravity, and thermal fluctuations are sufficient to capture the dynamics of a range of experimental chemically active colloidal systems. 17,18,20,64 Promisingly, the use of DPD particles to build the overall structure of the microswimmer enables us to access to a range of more complex shapes than those described here, whose formulation would otherwise be either intractable or highly challenging when using other numerical modelling frameworks, or explicitly including chemical fields.…”

“…1b (ref. 55)), properly aligned along the x-and y-axes to ensure a flat repulsive potential interacting with both the solvent and colloid particles via the DPD soft conservative force with a large amplitude F c = 100. 49 The microswimmers motility originates from one central "thruster" particle, which generates the squirmer-type force field experienced by the solvent particles in the spherical shell between the outer surface of the microswimmer (dashed black Nanoscale Paper circle) and R H=4 (dashed black circle and dotted black circle respectively, see Fig.…”

“…1b (ref. 55)), properly aligned along the x - and y -axes to ensure a flat repulsive potential interacting with both the solvent and colloid particles via the DPD soft conservative force with a large amplitude F c = 100. 49…”

“…For these reasons, a DPD framework capturing the hydrodynamic interactions of microswimmers in the presence of confining boundaries – by applying tangential solvent forces around the swimmer – was recently developed by some of the authors. 55 As DPD is already implemented in the open-access molecular dynamics program Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), 56 this provides the opportunity to exploit a range of in-built functions to extend previous studies, with the goal of mimicking the behaviour of chemical microswimmers above a substrate.…”

“…Here, we further develop this model to consider the influence of mass and shape asymmetries on the dynamics of spherical microswimmers in the presence of a bounding substrate, mirroring common experimental conditions for chemical active colloids. 55,[57][58][59] The strength of our approach lies in its modularity, which allows the simple inclusion of these asymmetries that may have otherwise presented significant complications when considering other numerical schemes. We find that the interplay between hydrodynamic interactions, gravity, bottom-heaviness, and shape is sufficient to qualitatively capture the 2-and 3-D physics of a range of catalytic (and photo-catalytic) Janus microswimmer systems, 17,18,20 i.e.…”