Shape matters: Geometry-driven Marangoni instability in evaporating binary droplets*

When sessile glycerol-water droplets evaporate, the solutal Marangoni flow remains stable and axisymmetric, whereas e.g. ethanol-water droplets usually exhibit highly non-axisymmetric chaotic flow scenarios.

This behavior, known as Marangoni instability, is attributed to an interplay of solutal Marangoni flow at the free surface and replenishing flow from the bulk due to continuity. In the case of an ethanol-water mixture, any spot on the interface with a slightly enhanced ethanol concentration drives Marangoni flow directed tangentially outward, which is replenished by even more ethanol-rich bulk fluid. Thereby, the evaporating interface becomes unstable.

While an analytical linear stability analysis is available for flat interfaces between two containers in the seminal work by Sternling and Scriven [AIChE J. 5, 514-523, (1959)], it cannot be transferred to droplets due to the nontrivial geometry and the contact-angle dependent profile of the evaporation rate.

We derive a quasi-stationary minimal model to numerically investigate the stability of evaporating binary droplets as function of the Marangoni number and the contact angle. We provide a phase diagram of different hysteretic solutions and numerically assess the axisymmetric and azimuthal stability.

Interestingly, droplets with low contact angles undergo such symmetry-breaking Marangoni instabilities already for small Marangoni numbers, although the solutal bulk gradient required within the classical theory is absent. By applying lubrication theory, we show that the geometric confinement and the different height exponents of Marangoni flow (h^2) and pressure-driven refill (h^3) map the dynamics of the instability to the lateral plane. We also reveal the chaotic nature of these flows by calculating Lyapunov exponents and show how this geometrically confined Marangoni instability can destabilize e.g. glycerol-water mixtures in a well.