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Marangoni-flow-driven hysteresis and azimuthal symmetry breaking in evaporating binary droplets
Published online by Cambridge University Press: 29 August 2025
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. Continuity of the fluid 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 with the bulk. The return flow therefore creates a positive feedback loop, further reducing surface tension in the perturbed region and enhancing the instability. This study investigates bistable quasi-stationary solutions in evaporating binary droplets with negative Marangoni numbers (e.g. water–ethanol) and examines symmetry breaking across a range of Marangoni numbers and contact angles. Bistable domains exhibit hysteresis. Remarkably, flat droplets (small contact angles) show instabilities at much 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, as in wells. Finally, through a Lyapunov exponent analysis, we confirm the chaotic nature of flows in droplets with a negative Marangoni number. We emphasise that the numerical models are intentionally simplified to isolate and clarify the underlying mechanisms, rather than to quantitatively predict specific experimental outcomes; in particular, the model becomes increasingly limited in regimes of rapid evaporation.
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Rocha et al. supplementary movie 1
Numerical solution of ethanol liquid and vapour mass fraction in transient (left) and quasi-stationary (right) simulations under the same conditions.
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Rocha et al. supplementary movie 2
Numerical solution of ethanol vapour mass fraction and liquid’s velocity magnitude in transient (left) and quasi-stationary (right) simulations under the same conditions.
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Rocha et al. supplementary movie 3
Numerical solution of water vapour mass fraction and temperature field in both phase in transient simulations.
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Rocha et al. supplementary movie 4
Lyaponov exponents in evaporating negative Marangoni flat droplet, with a Marangoni number Ma=-10000. Here, a transient lubrication model is used for the calculation, where the average mass fraction of each component in the droplet is kept fixed over time.
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786.6 KB