# Spreading dynamics of reactive surfactants driven by Marangoni convection

## TL;DR

This paper develops an exact model for the spreading of insoluble surfactants influenced by Marangoni convection, incorporating diffusion, reaction kinetics, and viscous effects, revealing linear variance growth and insights into camphor grain actuation.

## Contribution

It provides an exact solution to nonlinear transport equations for insoluble surfactants with Marangoni effects, advancing understanding of their spreading dynamics.

## Key findings

- Variance of surfactant distribution grows linearly with time
- Model explains enhanced diffusion observed experimentally
- Insights into camphor grain actuation at water-air interface

## Abstract

We consider the spreading dynamics of some insoluble surface-active species along an aqueous interface. The model includes both diffusion, Marangoni convection and first-order reaction kinetics. An exact solution of the nonlinear transport equations is derived in the regime of large Schmidt number, where viscous effects are dominant. We demonstrate that the variance of the surfactant distribution increases linearly with time, providing an unambiguous definition for the enhanced diffusion coefficient observed in the experiments. The model thus presents new insight regarding the actuation of camphor grains at the water-air interface.