A Method to Measure Drag Coefficient of An Active Particle

The drag coefficient of an active particle is important because it reveals the energy cost of swimming of an active particle, i.e, micro-organisms or swimming colloids. We introduce a method to obtain the drag coefficient for an active particle by separately measuring diffusion and sedimentation. We test this method on an active Brownian particle (ABP) that is driven by induced-charge electrophoresis of Janus particles.
The diffusion is measured by tracking the single-particle motion and calculating the slope of mean squared displacement at long times. An effective temperature, T_eff1, can be calculated from diffusion. The particle density distribution in sedimentation is measured by counting the number of particles at different heights in the dilute region, where it obeys Boltzmann distribution with an effective temperature, T_eff2. With the assumption that the effective temperatures measured from the two methods are the same, the drag coefficient of ABP could be solved.