Disorder-induced persistent random motion and trapping of microswimmers

Abstract

Microorganisms ofter move in confined, disordered environments, where hydrodynamic couplings can modify their transport behavior. Using extensive finite-element simulations, we investigate the dynamics of microswimmers -- modeled as squirmers -- in two-dimensional disordered porous media by resolving the full hydrodynamic interactions. We reveal that the deterministic coupling between activity, hydrodynamics, and disorder is sufficient to generate effective diffusive transport. Strong pushers and pullers become localised in the porous medium either by trapping at corners or dynamic trapping, depending on swimmer type and obstacle packing fraction. Squirmers can escape from dynamic traps, leading to a prominent ``hopping-and--trapping'' dynamics. Strikingly, we find a pusher-puller asymmetry in the trapping probability that can be reversed by short-range swimmer-obstacle interactions, highlighting the sensitivity of transport to near-field effects.

Figures (7)

• Figure 1: (Left) Representative trajectories of squirmers in a disordered porous medium. Four swimmers with different squirming parameters $\beta$ start at the same position and orientation (dark gray disk). The end of the trajectory is marked by the red stars. Here, we set the packing fraction to $\phi=0.45$ and use the cut-off $\delta = 1/20$. ( Inset) A trajectory transitioning between dynamic trapping phases and free swimming motion. (Right) Examples of dynamically trapped trajectories exhibiting quasi-periodic motion for $\beta=0$ (top) and $\beta=-4$ (bottom). In the former case, trapping is of topological origin, whereas in the latter it arises from hydrodynamic interactions. The shaded regions around the obstacles denote the effective disk radius, accounting for both the squirmer size and the short-range repulsive interaction.
• Figure 2: Exploring microswimmers. Mean-squared displacement $\langle |\Delta\boldsymbol{r}(t)|^2\rangle/a^2$ for agents exploring the disordered medium. The left and right panel show results for $\delta = 1/20$ and $\delta=1/4$, respectively. Further, $\phi$ denotes the packing fraction and $\beta$ is the squirming parameter. The triangle marks the crossover time $\tau=(R+a)/U$, corresponding to the time it takes the agent to move the center-to-center contact distance.
• Figure 3: Localized microswimmers. ( a) Trapping probability $P(\beta)$. Here, 's', 'd', and 't' denote static, dynamic, and total trapping events. ( b) Survival probability $S(t)$ as a function of time $t$ for different squirming parameters $\beta$. ( Inset) shows the rescaled median of the trapping time $\tilde{T}$. ( c) Histogram of the normalized confinement radius $\rho/(2(a+R))$. ( a-c) Different panels correspond to different packing fractions $\phi$ and repulsive potential strengths $\delta$.
• Figure 4: Velocity fields during a dynamic trapping event. Snapshots of a strong pusher ($\beta=-8$) and small cutoff ($\delta_{\text{cut}} = a/20$) illustrating dynamic trapping between two obstacles. The blue arrow denotes the squirmer' s orientation $\boldsymbol{p}$, while the red arrow indicates the direction of its instantaneous velocity $\boldsymbol{U}$. The small arrows indicate the fluid velocity direction.
• Figure 5: Left: Adaptive mesh refinement used to resolve steep gradients and hydrodynamic interactions in the phase-field formulation. Right: Flow field generated by a pusher ($\beta=-8$) in a confined geometry, rescaled by the free-space swimming speed.