Marangoni flow driven hysteresis and azimuthal symmetry breaking in evaporating binary droplets

TL;DR

This study investigates how Marangoni flows cause symmetry breaking and hysteresis in evaporating binary droplets, revealing different behaviors based on the sign of the Marangoni number and droplet geometry.

Contribution

It uncovers the mechanisms of instability and symmetry breaking in binary droplets with negative Marangoni numbers, including the role of contact angle and interface shape.

Findings

Negative Marangoni number induces instabilities and chaos.

Low contact angle droplets destabilize at lower Marangoni numbers.

Azimuthal instabilities can occur even in positive Marangoni number mixtures.

Abstract

The non-uniform evaporation rate at the liquid-gas interface of binary droplets induces solutal Marangoni flows. In glycerol-water mixtures (positive Marangoni number, where the more volatile fluid has higher surface tension), these flows stabilise into steady patterns. Conversely, in water-ethanol mixtures (negative Marangoni number, where the less volatile fluid has higher surface tension), Marangoni instabilities emerge, producing seemingly chaotic flows. This behaviour arises from the opposing signs of the Marangoni number. Perturbations locally reducing surface tension at the interface drive Marangoni flows away from the perturbed region. Incompressibility enforces a return flow, drawing fluid from the bulk towards the interface. In mixtures with a negative Marangoni number, preferential evaporation of the lower-surface-tension component leads to a higher concentration of the higher-surface-tension component at the interface as compared to the bulk. The return flow therefore creates a positive feedback loop, further reducing surface tension and enhancing the instability. We investigate bistable quasi-stationary solutions in evaporating binary droplets with negative Marangoni numbers and we examine symmetry breaking across a range of Marangoni number and contact angles. Remarkably, droplets with low contact angle show instabilities at lower critical Marangoni numbers than droplets with larger contact angles. Our numerical simulations reveal that interactions between droplet height profiles and non-uniform evaporation rates trigger azimuthal Marangoni instabilities in flat droplets. This geometrically confined instability can even destabilise mixtures with positive Marangoni numbers, particularly for concave liquid-gas interfaces. Finally, through Lyapunov exponent analysis, we confirm the chaotic nature of flows in droplets with a negative Marangoni number.