Emergent clusters in strongly confined systems

TL;DR

This study reveals that strong confinement can induce large-scale density fluctuations in driven colloidal suspensions of microrollers, driven by long-range hydrodynamic recirculation from distant boundaries. Using experiments and GPU-accelerated force-coupling simulations, the authors show that pattern formation is non-monotonic with vertical confinement: patterns appear at intermediate heights due to a system-spanning recirculation zone that requires lateral walls, and disappear at very small heights where the recirculation breaks into particle-scale structures. The work provides a quantitative link between confinement geometry, flow topology, and mesoscale structure, demonstrating that remote boundaries can qualitatively alter suspension organization even when confinement is strong. These insights have implications for microfluidic design and confinement-aware control of active-like suspensions in applied settings.

Abstract

Driven suspensions, where energy is input at a particle scale, are a framework for understanding general principles of out-of-equilibrium organization. A large number of simple interacting units can give rise to non-trivial structure and hierarchy. Rotationally driven colloidal particles are a particularly nice model system for exploring this pattern formation, as the dominant interaction between the particles is hydrodynamic. Here, we use experiments and large-scale simulations to explore how strong confinement alters dynamics and emergent structure at the particle scale in these driven suspensions. Surprisingly, we find that large-scale (many times the particle size) density fluctuations emerge as a result of confinement, and that these density fluctuations sensitively depend on the degree of confinement. We extract a characteristic length scale for these fluctuations, demonstrating that the simulations quantitatively reproduce the experimental pattern. Moreover, we show that these density fluctuations are a result of the large-scale recirculating flow generated by the rotating particles inside a sealed chamber. This surprising result shows that even when system boundaries are far away, they can cause qualitative changes to mesoscale structure and ordering.

Figures (7)

• Figure 1: (a) Illustration of a roller suspension $(\phi=0.32)$ at the experimental scale with the pink square showing the smaller scale used in simulations. The domain is strongly confined vertically by a bottom and top cover slip. Inset: SEM image of the microrollers; magnetic core is highlighted in red. (b) Magnification of the smaller simulation domain. Pink walls indicate location of lateral confinement in the simulation. Inset: high-resolution simulation of the velocity field generated by a microroller.
• Figure 2: (a) Cross-sectional geometry of the commercial channels used (all lengths are in dimensionless units of particle radii). (b,c): PIV measurements of the flow velocity in channels of (b) $h^* =10$ and (c) $h^* = 100$. In strong confinement (b), the velocity is highly heterogeneous, while in the absence of confinement (c) the velocity is nearly uniform. (d) MSD of the particles in (b) and (c). The unconfined ($h^* = 100$) system shows ballistic motion (MSD $\sim t^2$), while the strongly confined system ($h^* = 10$) is diffusive (MSD $\sim t$). (e) Experimental measurements of the suspension velocity distribution. As confinement is increased, the bimodal distribution becomes a unimodal distribution centered about zero.
• Figure 3: (a) Experimental image showing the pattern formation we observe in a highly confined sample ($h^* = 10,$$\phi = 0.32$); image shows the center of the channel. (b,c) Numerical simulations ($l^*=500$) of the experimental system with (b) periodic boundaries and (c) fixed lateral boundaries (as illustrated in Fig. \ref{['fig:colloid_config']}). All images show the system after it has evolved to a steady state starting from an initially uniform distribution.
• Figure 4: The normalized power spectral density for the simulation and experiment, the peaks correspond to wavenumbers $0.014 \: \upmu m^{-1}$ ($71 \: \upmu m$) and $0.011 \: \upmu m^{-1}$ ($90 \: \upmu m$) respectively. Insets show the absolute value of the Fourier amplitude spectra for (left) experiment and (right) simulation.
• Figure 5: Images: Steady-state particle distributions resulting from simulation runs for $h^*= 6, 8, 10$ and 16 (fixed boundaries, $l^* = 500$). Graph shows the resulting power spectral density for each $h^*$, with a periodic simulation for $h^* = 10$ shown for reference. There is a clear peak, corresponding to the appearance of a large scale pattern for $h^* = 8, 10$ and 16, but no peak (and only particle-scale clustering) at $h^* = 6$, as well as the periodic simulation at $h^* = 10$.