Estimating the velocity of chemically-driven Janus colloids considering the anisotropic concentration field

The application of the active colloids is strongly related to their self-propulsion velocity, which is controlled by the generated anisotropic concentration field. We investigated the effect of this anisotropy on velocity induced by numerical treatments and size of Janus colloids. The far-field approximation is effective in estimating the velocity, even though it neglects the shape effect on the anisotropy of the concentration field. If the surface mobility contrast between the active and the inert part is moderate, the spherical approximation is feasible for sphere-like Janus colloids. Legendre expansion of the concentration field causes artificial anisotropy. Raising the order of the expansion can suppress this effect, but also distorts the concentration field at the top of active part. Thus, the order of the expansion should be chosen carefully depending on the goal of the study. Based on the verified Legendre expansion method and ionic-diffusiophoresis model, we show that due to the size-effect on both the concentration field and the surface mobility, increasing size of colloids can lower the self-propulsion velocity. Our finding is consistent with previous experimental observations without fitting parameter, shedding new light on the self-propulsion mechanism of chemically-driven active colloids. We further show a velocity reversal at high overall ζ potential induced by increasing size, providing a new way for controlling the dynamics of acitve colloids.