Importance of particle tracking and calculating the mean-squared displacement in distinguishing nanopropulsion from other processes

In this paper we show that processes such as Brownian motion, convection, sedimentation, and bacterial contamination can cause small particles to move through liquids in a fashion which may be mistaken as nanopropulsion. It is shown that particle tracking and subsequent statistical analysis is essential to ascertain if small particles actually propel themselves, or if they are propelled by another process. Specifically we find that it is necessary to calculate the mean-squared displacement of particles at both short and long time intervals, to show that the direction of propulsion changes coincident with rotation of the particle by Brownian motion, as this allows nanopropulsion to be differentiated from Brownian motion, convection and sedimentation. We also find that bacteria can attach themselves to particles and cause them to be propelled. This leads to motion which appears very similar to nanopropulsion and cannot be differentiated using particle tracking and therefore find that carefully designed control experiments must be performed. Finally, we suggest an experimental protocol which can be used to investigate the motion of small objects and prove if they move due to nanopropulsion.