Simulating active agents under confinement with Dissipative Particles (hydro)Dynamics

TL;DR

This work develops a dissipative particle dynamics (DPD) framework to model active swimmers under confinement with explicit hydrodynamics and thermal fluctuations, enabling simulations of both simple colloids and flexible polymers. By prescribing axisymmetric, shell-based propulsion forces and enforcing momentum conservation, the authors reproduce flow fields and quantify transport properties across bulk and cylindrical confinement, spanning diverse Reynolds and Peclet numbers. Key findings include pronounced confinement-induced modifications to diffusion and reorientation for pushers versus pullers, nontrivial radius-of-gyration and diffusion behavior for active polymers under hydrodynamics, and the emergence of regime-dependent scaling that blends Rouse and Zimm-like dynamics. The approach provides a scalable, thermally fluctuating, shape-flexible platform for studying dense active suspensions and confining geometries, with open-source implementation potential in LAMMPS for broader adoption.

Abstract

We study active agents embedded in bulk or in confinement explicitly considering hydrodynamics and simulating the swimmers via an implementation inspired by the squirmer model. We develop a Dissipative Particle Dynamics scheme for the solvent. 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 active agents 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.

Figures (11)

• Figure 1: a: A raspberry-like active colloid composed of 18 filler particles and one thruster particles at the center. Note that in these figures the filler particle radius is scaled down to $1$ for better visibility, but in all simulations we use $r_c^\text{sf}=2$ as the solvent-filler DPD cutoff in order to obtain a more spherical colloid and to prevent the solvent particles from stepping into the colloid. b: An active polymer composed of 20 beads. c: An active colloids in a cylindrical confinement. d: An active polymer in a cylindrical confinement. Red: thruster particles. Gray: filler particles. Blue: wall particles composing the confining channel. Yellow: solvent particles.
• Figure 2: Examples of 2D hydrodynamic redistribution force fields for all the studied cases: a pusher (panel a) with $\beta=-5$, a puller (panel b) with $\beta=5$, a neutral squirmer (panel c) with $\beta=0$ and a monomer of the active polymer (panel d). These correspond to a section of the 3D field passing through the equator of the redistribution sphere. The arrow inside the central colloid indicates the direction of the propulsion force $F_p$, with magnitude indicated in each panel. Here, the hydrodynamic region $\Gamma_H$ would be the area contained between the solid and dashed circles.
• Figure 3: Sections of the velocity fields in the lab frame (bottom row) and moving with the colloid (top row), for the pusher (a, d), neutral (b, e) and puller (c, f) squirmer. surrounded by $\sim 10^4$ fluid particles and swimming to the right. The colour of the background is the averaged density of fluid particles, the colour of the arrows shows the fields magnitude. Here the colloid radius is $R_c=3$ and $F_p=100$ in order to obtain a clearer flow field. These values produce $\mathrm{Pe}\approx\{818,\,655,\,573\}$ and $\mathrm{Re}\approx\{25,\,20,\,17\}$ for the pusher, neutral and puller squirmers respectively.
• Figure 4: Solvent flow fields of the colloid confined in an cylindrical channel ($R_\text{cyl}=3.5$) in the lab frame (bottom row) and moving with the colloid (top row), for the pusher (a, d), neutral (b, e) and puller (c ,f) squirmer. Here the colloid radius is $R_c=2$ and $F_p=50$. These values produce $\mathrm{Pe}\approx\{90,\,76,\,61\}$ and $\mathrm{Re}\approx\{3.9,\,3.3,\,2.7\}$ for the pusher, neutral and puller squirmer respectively.
• Figure 5: MSDs for the three squirmer types studied. Left column: pusher (panels a, d and g). Center column: neutral (panels b, e and h). Right column: puller (panels c, f and i). Top row: bulk (panels a, b and c). Center row: in cylindrical confinement for different $\mathrm{Pe}$'s for the smallest channel radius $R_\text{cyl}=3.5$ (panels d, e and f). Bottom row: for different channel radii for the highest Péclet numbers available corresponding to the highest thrust force $F_p=50$ (panels g, h and i).