Can you imagine a beautiful phenomenon that only lasts a fraction of a second? That’s what happens when an ethanol-water droplet is gently placed on a layer of water.
First, a thin film spreads quickly from the drop across the water surface, with the lighter drop floating at the centre. This film becomes unstable at its edges, forming evenly spaced, flower petal-like structures known as ‘plumes’ around its periphery. Shortly after these plumes appear, the film stops spreading and retracts. Finally, the drop in the centre mixes with the water within less than 0.6 seconds! Amazing, right?
This happens due to a phenomenon called Marangoni spreading, where a liquid with lower surface tension spreads out on another liquid with higher surface tension because of differences in surface tension between two fluids. A simple demonstration of this is the “soap boat” experiment: if you place a small boat made of lightweight material on water and add a drop of soap at the back, the boat will move forward as the soap reduces the surface tension behind it. Surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible.
Marangoni spreading has applications in many fields, such as mimicking the spreading of drugs on mucus layers in the human body, controlling oil spills in seas, coating processes, and ink-jet printing.
The spreading behaviour is well-understood in immiscible (liquids that do not mix) and non-volatile (liquids that do not evaporate) films. Examples include oil slicks on water and using solvents and surfactants (compounds that reduce surface tension between different substances). In these cases, the spreading follows a rule where the distance the film spreads, ‘l’, varies with time, ‘t’, as l ~ t^(3/4).
However, for miscible (liquids that mix) and volatile (evaporating) films, like those made with toluene or xylene, the spreading follows a different rule: the radius of the spreading region grows as t^(1/2), not t^(3/4).
Several theories have tried to explain this difference, but until now, there hasn’t been a model to predict the t^(1/2) scaling law.
In this study, Dr. Anurag Pant and Prof. Baburaj A. Puthenveettil from the Indian Institute of Technology Madras, India, performed a scaling analysis to explain this variation for the first time.
They measured the radii (r_o) and velocities (U_o) of the outer edge of ethanol-water films over time for different ethanol concentrations and drop sizes. They found that as the stable film expanded with a radius (r_f), it created an unstable region at its edges with equally spaced, radially growing plumes of length (l_p).
The outer edge radius (r_o) is the sum of the film radius (r_f) and the plume length (l_p), so: r_o = r_f + l_p.
Using this, they derived scaling relationships for the mean outer edge radius (r_o) and its expansion velocity (U_o) as functions of time and the properties of the droplet and the surface.
These relationships matched their experimental measurements, confirming their model.
Prof. Kirti Sahu, from the Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Telangana, India, described the significance and importance of this study in a nutshell as follows: “This fundamental experimental study reveals that the outer tip radius of a fast-spreading ethanol-water film over a deep water pool exhibits complex and unique scaling behaviour for its radius and velocity. These findings offer new insights into miscible, volatile film-spreading dynamics driven by Marangoni flow, showcasing novel dynamics and elucidating previously unexplained behaviours of the outer spreading radius and velocity.”
Article by Akshay Anantharaman
Click here for the original link to the paper
