PhD Defence Pim Dekker | Surface tension and evaporation of isolated and neighbouring droplets

Surface tension and evaporation of isolated and neighbouring droplets

Pim Dekker is a PhD student in the department Physics of Fluids. (Co)Promotors are prof.dr. D. Lohse and prof.dr. M.N. van der Linden from the faculty of Science & Technology (TNW), University of Twente.

This thesis, investigates the evaporation dynamics of pure water drops and binary water/1,2-hexanediol drops in several geometries and configurations, with a particular focus on the role of surface tension. A fundamental understanding of droplet evaporation is essential for optimizing and advancing various technological applications.

In chapter 2, we the investigated the evaporation dynamics for neighbouring binary water/1,2-hexanediol drops. we found that centres of the drop move consistently further apart, which is unexpected based on the literature. We identified that the key difference is the presence of solutes and particles, which are deposited more in regions where evaporation is higher. The higher solute deposition increases the probability that a drop will locally pin, resulting in pinning induced motion that moves the drops centres away from each other.

Additionally, using particle tracking velocimetry, we experimentally measured the flow in a drop and observed that it becomes asymmetric due to the presence of a neighbouring drop. We found good agreement when comparing the azimuthal dependence of the radial velocity with the local evaporative flux of a single component flat drop. Using numerical simulations, we found that thermal Marangoni flow hardly contributes when compositional gradients are present in the system.

In chapter 3, we continued to investigate internal flow in neighbouring evaporating binary drops using numerical simulations and theoretical analysis. To manage the complexity of the full three-dimensional droplet problem, we started with a two-dimensional model of neighbouring rivulets. We examined how the symmetry of flow, quantified by the position of the interfacial stagnation point of the flow, is affected by key parameters, namely the contact angle, the inter-droplet (or inter-rivulet) distance, and the Marangoni number.

Solving the complete transient equations for rivulets with pinned contact lines and fixed inter-rivulet distance revealed that the asymmetry diminishes over time. Using a validated quasi-stationary model, we found, with increasing contact angle and inter-rivulet distance, that the stagnation point migrates closer to the centre, yet it remains unaffected by the Marangoni number. A simplified lubrication model applied to droplets shows similar dependencies on contact angle and distance, although here the stagnation point appears to vary with the Marangoni number. We attributed this dependence to the additional azimuthal flow in droplets, leading to a non-linear evolution of the concentration and therefore a non-trivial dependence of the symmetry on the Marangoni number.

In chapter 4, we investigated the unusual segregation dynamics is observed in the evaporation of water/1,2-hexanediol, which shows the formation of 1,2-hexanediol rich spots, breaking axisymmetry. By ruling out any alternative mechanisms, we conclusively attributed the observed axisymmetry breaking the non-monotonic surface tension of water/1,2-hexanediol using numerical numerical simulations. Additionally, we developed a minimal model, which allowed us to predict when the symmetry breaking will occur, and that the number of spots scales as $m_\mathrm{crit} \sim \sqrt{\mathrm{Ma}}$.

In chapter 5, we we tried to answer the question: How much is the pendant drop method affected by evaporation? Experimentally we found that evaporative cooling has a profound effect on the measurement, significantly cooling down the drop, which in turn changes the surface tension measurement substantially. Using numerical simulations we further elucidated the role effect of evaporative cooling and of shape deformation on the measured surface tension. We found that the effect of evaporative cooling is the dominant effect of evaporation.

Additionally, we measured the surface tension of water/1,2-hexanediol and we found that it is indeed non-monotonic, as earlier predicted. Additionally, we measured the surface tension of aqueous mixtures with 1,2-butanediol, 1,2-pentanediol, 1,5-pentanediol, and glycerol.

In chapter 6, we studied the evaporation of pure water on a hydrophobic substrate. Experiments showed that buoyancy driven Rayleigh flow dominates the internal flow of the drop and that axisymmetry is broken, despite that numerical simulations predict that an axisymmetric thermal Marangoni flow will dominate the flow. We hypothesised that there are contaminants on the drop surface, responsible for this discrepancy.

Using numerical simulations we modelled the contaminants as a small amount of insoluble surfactants that exist only on the drop surface. Axisymmetric simulations showed that when these surfactants reduce the surface tension by mere 0.5$\%$ the flow would fully reverse the flow from thermal Marangoni flow direction (for a clean drop) to the Rayleigh flow direction (with the contaminants). Additionally, the azimuthal stability was analysed and we found that axisymmetry is broken for the experimental conditions. Although the match between experiments and numerical simulations is not perfect, we illustrated that the contaminants can induce a significant change in the internal flow.

In chapter 7, we reiterated the complexity and fascinating nature of the physics of evaporating drops. Additionally, this chapter is complementary to a video that is displayed on the Gallery of Fluid Motion https://doi.org/10.1103/APS.DFD.2024.GFM.V2685343 of APS Division of Fluid Dynamics.