Marangoni-driven spreading of a droplet on a miscible thin liquid layer

The coalescence of droplets with liquid-gas interfaces of different surface tensions is common in nature and industrial applications, where the Marangoni-driven film spreading is an essential process. Unlike immiscible fluids governed by triple contact line dynamics, the mixing between two miscible fluids strongly couples with the film spreading process, which are expected to manifest distinct power-law relations for the temporal increase in the film radius.

We experimentally investigate the Marangoni-driven film spreading phenomenon for a droplet with lower surface tension dropping onto a miscible, thin liquid layer. The temporal growth of the film radius was detected by using a novel deep convolutional neural network, the U²-net method. Scaling analysis was performed to interpret the spreading dynamics of the film.

We find that the film radius exhibits a three-stage power-law relation over time, with the exponent varying from 1/2 to 1/8, and back to 1/2. The diffusion-affected Marangoni stresses in these three stages were derived, and two estimations of viscous stress were considered. Through estimating and balancing the viscous stress with the Marangoni stress, the three-stage power-law relation was derived and validated.