Stability of evaporating sessile droplets comprising of volatile binary mixtures

Abstract

This thesis investigates the evaporation dynamics and stability of evaporating sessile droplets comprised of volatile binary component mixtures. This is carried out by building, developing and utilising two new theoretical modelling linear stability analysis approaches on a lubrication model as well as implementing experimental approaches to analyse thin, volatile binary droplets. The primary focus is on understanding the influence of solutal Marangoni effects, surface tension and concentration gradients on droplet stability at the contact line. Firstly, the stability of thin volatile droplets comprising of binary mixtures deposited on a heated substrate is examined using a linear stability analysis approach under the quasi-steady state approximation (QSSA). A base state is first established using lubrication theory approximation on a one sided model. The QSSA analysis is performed by freezing the transient base state at an early time instance and applying small perturbations to the governing base state equations and boundary conditions. The results from the first theoretical modelling stability analysis approach indicate that the addition of a second component significantly destabilises the droplet, with high growth rates and wavenumbers revealing several competing modes of instability. Secondly, to gain further insight into the stability droplet dynamics, a transient growth linear stability analysis (TGA) is conducted, incorporating a time-dependent element to provide a comprehensive picture of the instabilities occurring in thin volatile binary component droplets. Results from the two stability analysis methods on our theoretical model highlight the concentration and surface tension as strong dominant destabilising factors, suggesting instabilities arise due to the increase in solutal Marangoni flows with the addition of another component in the droplet. Thirdly, experimental investigations are conducted to complement the initial theoretical modelling predictions. Experiments are performed examining the behaviour of thin droplets comprising of binary ethanol-water mixtures of varying concentrations on a very smooth heated hydrophilic glass substrate. Detached waves or ’spokes’ are identified and observed around the droplet contact line during spreading and evaporation, attributed to the presence of the second more volatile component, ethanol. These visual contact line instabilities are compared to the theoretical predictions observed from the two linear stability analysis approaches. This thesis demonstrates how combining linear stability modelling with thermal imaging experiments yields a holistic understanding of interfacial instability in volatile binary droplets. The results confirm the critical role of concentration gradients and surface tension gradients in destabilising the flow at the droplet contact line, offering qualitative agreement between experiments and theoretical modelling predictions. This shows that solutal Marangoni effects play a critical role in driving instability formation localised at the droplet edge contact line. The insights gained from this research offer a valuable foundation for further research and contribute to a deeper understanding of the complex behaviour of evaporation volatile binary droplets and their stability dynamics.This thesis investigates the evaporation dynamics and stability of evaporating sessile droplets comprised of volatile binary component mixtures. This is carried out by building, developing and utilising two new theoretical modelling linear stability analysis approaches on a lubrication model as well as implementing experimental approaches to analyse thin, volatile binary droplets. The primary focus is on understanding the influence of solutal Marangoni effects, surface tension and concentration gradients on droplet stability at the contact line.

Firstly, the stability of thin volatile droplets comprising of binary mixtures deposited on a heated substrate is examined using a linear stability analysis approach under the quasi-steady state approximation (QSSA). A base state is first established using lubrication theory approximation on a one sided model. The QSSA analysis is performed by freezing the transient base state at an early time instance and applying small perturbations to the governing base state equations and boundary conditions. The results from the first theoretical modelling stability analysis approach indicate that the addition of a second component significantly destabilises the droplet, with high growth rates and wavenumbers revealing several competing modes of instability.

Secondly, to gain further insight into the stability droplet dynamics, a transient growth linear stability analysis (TGA) is conducted, incorporating a time-dependent element to provide a comprehensive picture of the instabilities occurring in thin volatile binary component droplets. Results from the two stability analysis methods on our theoretical model highlight the concentration and surface tension as strong dominant destabilising factors, suggesting instabilities arise due to the increase in solutal Marangoni flows with the addition of another component in the droplet.

Thirdly, experimental investigations are conducted to complement the initial theoretical modelling predictions. Experiments are performed examining the behaviour of thin droplets comprising of binary ethanol-water mixtures of varying concentrations on a very smooth heated hydrophilic glass substrate. Detached waves or ’spokes’ are ideniii tified and observed around the droplet contact line during spreading and evaporation, attributed to the presence of the second more volatile component, ethanol. These visual contact line instabilities are compared to the theoretical predictions observed from the two linear stability analysis approaches.

This thesis demonstrates how combining linear stability modelling with thermal imaging experiments yields a holistic understanding of interfacial instability in volatile binary droplets. The results confirm the critical role of concentration gradients and surface tension gradients in destabilising the flow at the droplet contact line, offering qualitative agreement between experiments and theoretical modelling predictions. This shows that solutal Marangoni effects play a critical role in driving instability formation localised at the droplet edge contact line. The insights gained from this research offer a valuable foundation for further research and contribute to a deeper understanding of the complex behaviour of evaporation volatile binary droplets and their stability dynamics.