Anomalous Diffusion of Deformable Particles in a Honeycomb Network

Transport of deformable particles in a honeycomb network is studied numerically. It is shown that the particle deformability has a strong impact on their distribution in the network. For sufficiently soft particles, we observe a short memory behavior from one bifurcation to the next, and the overall behavior consists in a random partition of particles, exhibiting a diffusionlike transport. On the contrary, stiff enough particles undergo a biased distribution whereby they follow a deterministic partition at bifurcations, due to long memory. This leads to a lateral ballistic drift in the network at small concentration and anomalous superdiffusion at larger concentration, even though the network is ordered. A further increase of concentration enhances particle-particle interactions which shorten the memory effect, turning the particle anomalous diffusion into a classical diffusion. We expect the drifting and diffusive regime transition to be generic for deformable particles.

Figure 1

(a) A snapshot showing the simulation system. The particles flow in a hexagonal network, where each segment of the channel has length $L$ and width $W$. The hollow arrows show the flow directions in the channels. (b) Schematic trajectories of a rigid sphere (black), a rigid nonspherical particle (magenta), and a soft particle (blue) in the network. (c) Trajectories of a single particle in the network for different reduced area and capillary numbers. The particle shapes in the center of the feeding channel are plotted for the corresponding parameters.

Figure 2

(a) Deviation of the particle mass center from channel centerline ($\mathrm{\Delta }X$) versus deformation $a/b$ measured at the midpoint of the feeding channel for different Ca. The bifurcation of $\mathrm{\Delta }X$ shows that the single particle starts to erratically enter the branch when Ca is approximately larger than 12.5. (b),(c) The time series of particle configurations at a bifurcation are given for (b) $\mathrm{Ca}=2.5$ and (c) $\mathrm{Ca}=25$.

Figure 3

(a) and (b) The time evolution of particle positions under the condition of (a) $\mathrm{Ca}=20$ and (b) $\mathrm{Ca}=2$. (c) and (d) The concentration profile along the lateral direction ($X$) at different times, corresponding to the configurations shown in (a) and (b).

Figure 4

(a) Lateral mean squared displacement (in $X$ direction) of the particles for two capillary numbers ($\mathrm{Ca}=2$ and $\mathrm{Ca}=20$) with five implementations (shown by different symbols). (b) Lateral MSD for various Ca. The inset shows the scaling exponent $\alpha$ as a function of Ca.

Figure 5

(a) and (b) Lateral MSD for various $\varphi$ with (a) $\mathrm{Ca}=2$ and (b) $\mathrm{Ca}=16$. (c) The scaling exponent of MSD as a function of $\varphi$.