Modeling the time evolution of a camphor rotor perturbed by a stationary camphor source

TL;DR

This paper evaluates the Hamiltonian modeling approach for camphor rotors, finding it qualitatively different from experiments in certain cases and suggesting improvements for more realistic simulations.

Contribution

It critically assesses the applicability of Hamiltonian models to camphor rotor dynamics and proposes enhancements for better experimental agreement.

Findings

Hamiltonian approach yields qualitatively different results from experiments for a single rotor.

Including hydrodynamic friction improves model realism.

Adding an equation for camphor surface concentration enhances simulation accuracy.

Abstract

A self-propelled motion resulting from the dissipation of camphor molecules on the water surface has been attracting scientific attention for more than 200 years. A generally accepted description of the phenomenon includes equations for the object motion coupled with the hydrodynamics of Marangoni flows and the time evolution of camphor surface concentration. The solution of such equations is a numerically complex problem. In recent publications, an alternative approach based on Hamiltonian including the potential term representing Marangoni interactions has been applied to simulate the time evolution of camphor rotors. Such a model represents a significant numerical simplification if compared to the standard description. Here, we comment on the applicability of Hamiltonian approach by applying it to a single camphor rotor perturbed by a camphor disk fixed on the water surface. We demonstrate that in such a case, the approach leads to the results qualitatively different from the experimental ones. Therefore, we doubt in its applicability to describe the time evolution of interacting camphor rotors. We also show that the approximation of the Marangoni forces by a potential gives more realistic results if used together with the equation of motion that includes the hydrodynamic friction. Still, a better agreement with experiments can be obtained by considering an additional equation for the time evolution of camphor surface concentration.