Trapping of deformable active particles by a periodic background potential

The dynamic behaviors, specifically trapping and sorting, of active particles interacting with periodic substrates have garnered significant attention. This study investigates numerically the trapping of soft, deformable particles on a periodic potential substrate, which can be experimentally verified through optical tweezers. The research demonstrates that multiple factors, including the relative size of traps, self-propelled velocity, shape parameters, ratio of particles to traps, and translational diffusion, can influence the trapping effect. Within certain parameter boundaries, it is shown that all particles can be consistently trapped. The research reveals that stable trapping typically occurs at median values of the relative trap size. An increase in the self-propelled velocity, the shape parameter, and the translational diffusion coefficient tends to facilitate the escapement of the particles from the traps. It is noteworthy that particles with larger shape parameters can escape even when the restoring force exceeds the self-propelled force. In addition, as the ratio of particles to traps grows, the fraction of trapped particles steadily reduces. Notably, rigid particles are consistently divided and trapped by traps closely approximating an integer multiple of the particles' area, up until the ratio reaches the aforesaid integer value. These findings can potentially enhance the understanding of the interactive effects between active deformable particles and periodic substrates. Moreover, this work suggests a different experimental approach to sort active particles based on rigidity disparities.

Figure 1

(a) Illustration of the active deformable particles featuring repulsive interaction. (b) Contour plot showcasing the periodic potential substrate resembling an egg-carton shape.

Figure 2

(a) Contour plot illustrating the potential of the substrate, $U\left(x,y\right)$, over a period for $B=0.025$. (b) Contour plot showcasing the restoring force field derived from (a). (c) Contour plot illustrating the potential of the substrate, $U\left(x,y\right)$, over a period for $B=0.475$. (d) Contour plot showcasing the restoring force field derived from (c). The other parameters are $V_0=0.33, C=5.0$, and $\lambda =3.68$.

Figure 3

(a) The self-diffusivity $D_s$ as a function of the parameter $B$ for different shape parameter $A/A_v$ at $v_0=0.55$ and $N/N_{\mathrm{trap}}=1$. (b) The MSD of the centers of mass of the particles for different $B$ at $A/A_v=1.16$.

Figure 4

The fraction of trapped particles (FTP) as a function of the parameter $B$ for different shape parameter $A/A_v$ at $v_0=0.55$ and $N/N_{\mathrm{trap}}=1$.

Figure 5

Typical snapshots of the dynamic behaviors of the active deformable particles for different parameter $B$: (a),(b) at $A/A_v=1.16$ and (c)–(f) at $A/A_v=1.10$. The other parameters are $v_0=0.55$ and $N/N_{\mathrm{trap}}=1$.

Figure 6

(a) The self-diffusivity $D_s$ as a function of the self-propelled velocity $v_0$ for different shape parameter $A/A_v$ at $B=0.25$ and $N/N_{\mathrm{trap}}=1$. (b) The MSD of the centers of mass of the particles for different $v_0$ at $A/A_v=1.16$.

Figure 7

The FTP as a function of the self-propelled velocity $v_0$ for different shape parameter $A/A_v$ at $B=0.25$ and $N/N_{\mathrm{trap}}=1$.

Figure 8

(a) The self-diffusivity $D_s$ as a function of the shape parameter $A/A_v$ for different self-propelled velocity $v_0$ at $B=0.25$ and $N/N_{\mathrm{trap}}=1$. (b) The MSD of the centers of mass of the particles for different $A/A_v$ at $v_0=0.55$.

Figure 9

The FTP as a function of the shape parameter $A/A_v$ for different self-propelled velocity $v_0$ at $B=0.25$ and $N/N_{\mathrm{trap}}=1$.

Figure 10

Contour plots of (a) the potential and (b) the derived restoring force field over a period at $B=0.25$. Other parameters are $V_0=0.33, C=5.0$, and $\lambda =3.68$.

Figure 11

Phase diagram of the FTP in the $v_0-A/A_v$ representation at $B=0.25$ and $N/N_{\mathrm{trap}}=1$. The background represents the value of FTP according to the color bar on the right.

Figure 12

(a) The self-diffusivity $D_s$ as a function of the ratio of the number of particles to traps $N/N_{\mathrm{trap}}$ for different shape parameter $A/A_v$ at $B=0.25$ and $v_0=0.55$. (b) The MSD of the centers of mass of the particles for different $N/N_{\mathrm{trap}}$ at $A/A_v=1.05$.

Figure 13

The FTP as a function of the ratio of the number of particles to traps, $N/N_{\mathrm{trap}}$, for different shape parameter $A/A_v$ at $B=0.25$ and $v_0=0.55$.

Figure 14

(a) The self-diffusivity $D_s$ as a function of the translational diffusion coefficient $D_t$ for different shape parameter $A/A_v$ at $B=0.25$ and $v_0=0.55$. (b) The MSD of the centers of mass of the particles for different $D_t$ at $A/A_v=1.16$.

Figure 15

The FTP as a function of the translational diffusion coefficient $D_t$ for different shape parameter $A/A_v$ at $B=0.25$ and $v_0=0.55$.

Figure 16

The FTP as a function of simulation time for different shape parameter $A/A_v$ at $B=0.25$ and $v_0=0.55$.