Effects of hydrodynamic interactions on rectified transport of self-propelled particles

Directed transport of self-propelled particles is numerically investigated in a three-dimensional asymmetric potential. Beside the steric repulsive forces, hydrodynamic interactions between particles have been taken into account in an approximate way. From numerical simulations, we find that hydrodynamic interactions can strongly affect the rectified transport of self-propelled particles. Hydrodynamic interactions enhance the performance of the rectified transport when particles can easily pass across the barrier of the potential, and reduce the rectified transport when particles are mainly trapped in the potential well.

Figure 1

Scaled average velocity $V_s$ when hydrodynamic interactions are included (with HIs) or neglected (without HIs). (a) $V_s$ as a function of the asymmetric parameter $\mathrm{\Delta }$ at $f_0=3.0$. (b) $V_s$ as a function of the asymmetric parameter $\mathrm{\Delta }$ at $f_0=5.0$. (c) $V_s$ as a function of the rotational diffusion coefficient $D_r$ at $f_0=3.0$. (d) $V_s$ as a function of the rotational diffusion coefficient $D_r$ at $f_0=5.0$. The inset of (a) describes the profile of $x$ direction potential for $\mathrm{\Delta }>0$. The other parameter are $N=10$, $\mathrm{\Delta }=-1.5$, $D_r=0.01$, and $U_0=5.0$.

Figure 2

(a) Scaled average velocity $V_s$ as a function of the potential height $U_0$ when hydrodynamic interactions are included (with HIs) or neglected (without HIs). (b) Scaled average velocity $V_s$ as a function of the self-propulsion force $f_0$ when hydrodynamic interactions are included (with HIs) or neglected (without HIs). The other parameters are $N=10$, $D_r=0.01$, and $\mathrm{\Delta }=-1.5$.

Figure 3

Scaled average velocity $V_s$ as a function of particle number $N$ for both with HIs and without HIs at $f_0=3.0$, $U_0=5.0$, $D_r=0.01$, and $\mathrm{\Delta }=-1.5$.