Droplet dynamics under an impinging air jet

Abstract

Partially wetting droplets under an airflow can exhibit complex behaviours that arise from the coupling of surface tension, inertia of the external flow and contact-line dynamics. Recent experiments by Hooshanginejad et al. (J. Fluid Mech., vol. 901, 2020) revealed that a millimetric partially wetting water droplet under an impinging jet can oscillate in place, split or depin away from the jet, depending on the magnitude (i.e. $5\unicode{x2013}20\ {\rm m}\ {\rm s}^{-1}$ ) and position of the jet. To rationalise the experimental observations, we develop a two-dimensional lubrication model of the droplet that incorporates the external pressure of the impinging high-Reynolds-number jet, in addition to the capillary and hydrostatic pressures of the droplet. Distinct from the previous model by Hooshanginejad et al. (J. Fluid Mech., vol. 901, 2020), we simulate the motion of the contact line using precursor film and disjoining pressure, which allows us to capture a wider range of droplet behaviours, including the droplet dislodging to one side. Our simulations exhibit a comparable time-scale of droplet deformations and similar outcomes as the experimental observations. We also obtain the analytical steady-state solutions of the droplet shapes and construct the minimum criteria for splitting and depinning.

Influence of Surface Roughness on Droplet Evaporation and Absorption: Insights into Experiments from Lubrication-Theory-Based Models

“…Moreover, three-dimensionality leads to additional phenomena such as “pearling”, where smaller droplets break off the rear of a droplet sliding down an inclined substrate. Such wetting transitions can be qualitatively captured with lubrication-theory-based models, which predict that substrate permeability and external stresses (e.g., by air flowing over the droplet) can cause significant changes to these transitions in the absence of surface topography. , Incorporating three-dimensional topography into the models discussed here can readily be done by (i) allowing for droplet height and solute concentration variations in both directions parallel to the substrate and (ii) using an appropriate expression for the function describing the surface topography (η). In principle, η could be obtained from experimental measurements and input into the governing equations.…”

“…Moreover, three-dimensionality leads to additional phenomena such as “pearling”, where smaller droplets break off the rear of a droplet sliding down an inclined substrate. Such wetting transitions can be qualitatively captured with lubrication-theory-based models, which predict that substrate permeability and external stresses (e.g., by air flowing over the droplet) can cause significant changes to these transitions in the absence of surface topography. , …”