Power law observed in the motion of an asymmetric camphor boat under viscous conditions

We investigated the velocity of an asymmetric camphor boat moving on aqueous solutions with glycerol. The viscosity was controlled by using several concentrations of glycerol into the solution. The velocity decreased with an increase in the glycerol concentration. We proposed a phenomenological model, and showed that the velocity decreased with an increase in the viscosity according to power law. Our experimental result agreed with the one obtained from our model. The results provided an approximation that the characteristic decay length of the camphor concentration profile at the front of the boat was sufficiently shorter than that at the rear of the boat, which was difficult to measure directly.