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

TL;DR

This study explores how the velocity of an asymmetric camphor boat on viscous solutions decreases following a power law as viscosity increases, supported by experimental data and a phenomenological model.

Contribution

It introduces a phenomenological model linking viscosity and velocity in camphor boat motion, validated by experimental results showing a power-law relationship.

Findings

Velocity decreases with glycerol concentration.

Experimental data matches the power-law model.

Characteristic decay length is shorter at the front than at the rear.

Abstract

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.