When a tiny drop of soapy water falls on a pool of liquid, its contents spread out over the pool’s surface. The dynamics of this spreading depends on the local concentration of soap at each point across the entire pool’s surface. But this varies in time, and its spread over the water surface is difficult to predict. Thomas Bickel of the University of Bordeaux in Talence and François Detcheverry of the University of Lyon (both in France) have now derived an exact time-dependent solution for these distributions. The solution revealed surprisingly rich behaviour in this everyday phenomenon. The work was published in a recent issue of Physical Review E.
The duo considered a surfactant-laden drop spreading over the surface of a deep pool of fluid. (A surfactant, or surface-active agent, is a substance such as soap that, when added to a liquid, reduces its surface tension, thereby increasing its spreading and wetting properties.) Earlier research showed that the transport of surfactant particles could be described by Burgers’ equation, which describes flows in turbulent fluids.
The researchers solved Burgers’ equation for their system for different initial conditions. They found that the time dependence of the spread was sensitive to the surfactant’s initial distribution on the pool’s surface, such that the higher the initial concentration, the quicker the spread. Also, the spreading of surfactants over a liquid surface does not always match what is expected for a simple diffusion process as other researchers had suggested earlier. Rather, the duo said, it is a rich and complex phenomenon. The duo hoped that experiments would bear out their predictions.
