Induced polar order in sedimentation equilibrium of rod-like nanoswimmers

The active diffusion and sedimentation equilibrium of rod-like nanoswimmers with length L are investigated by dissipative particle dynamics. In the absence of propulsion, the nanorod has the rotational correlation time τθ and mobility μ0, which vary with L. On the basis of the mean squared displacement, the diffusive behavior of rod-like nanoswimmers subject to active force Fa is found to follow (D - D0) ∝ (μ0Fa)(2)τθ, where D0 depicts the Brownian diffusivity. When the nanoswimmer suspension is under the external force Fe, the balance between the downward migration and upward active diffusion yields the sedimentation length δ = D/(μ0Fe), which no longer obeys δ0 = kBT/Fe obtained from the Einstein-Smoluchowski relationship, D0 = μ0kBT. Different from the suspension of passive rods, the polar order is clearly seen for active rods. The local polar order is essentially constant within the distance of about 2δ from the bottom wall but decays as the distance is further increased. In this work, the active Peclet number is small compared to unity and the maximum polar order grows linearly with Fe/Fa. The polar order arises because it is easier for the nanoswimmer with the swimming direction opposite to the external force to escape from the bottom wall.