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 τ 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 F_a is found to follow (D - D₀) ∝ (μ₀F_a)²τ where D₀ depicts the Brownian diffusivity. When the nanoswimmer suspension is under the external force F_e, the balance between the downward migration and upward active diffusion yields the sedimentation length δ = D/(μ₀F_e), which no longer obeys δ₀ = k_BT/F_e obtained from the Einstein-Smoluchowski relationship, D₀ = μ₀k_BT. 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 F_e/F_a. 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.