Water–propylene glycol sessile droplet shapes and migration: Marangoni mixing and separation of scales

New light is shed on morphological features of water–propylene glycol sessile droplets evaporating into ambient air at not too high relative humidity. Such droplets adopt a Marangoni-contracted shape even on perfectly wetting substrates, an effect well known since Cira et al. (Nature, 519, 2015). We here highlight a strong separation of scales normally occurring for such droplets. Namely, there is a narrow high-curvature zone localized at the foot of the droplet, where the apparent contact angle is formed, while the core of the droplet merely adheres to the classical (capillary–gravity) static shape. Experimentally, we rely upon interferometry to discern such fine key details. We detect a maximum of the droplet slope profile in the foot region, which amounts to the apparent contact angle. Theoretically, a local description of the foot region is devised. We indicate a crucial role of convective mixing by the solutal Marangoni flow, here accounted for by the Taylor dispersion, which proves to underlie the separation of scales and ensure self-consistency of the local model. Migration of such droplets in a humidity gradient is also approached within the same experimental and theoretical framework. It is considered that the resulting back–front asymmetry of the apparent contact angles drives the motion similarly to a wettability gradient, although the drag (‘Cox–Voinov’) factor is here found to be different. The predictions, comparing well with the measurements (our own and from the literature), are based on rigorous models, isothermal and as reduced as possible, without any fitting parameters or microphysics effects.

Molecular Origin of Fast Evaporation at the Solid–water–vapor Line in a Sessile Droplet

By analyzing the behaviors of water molecules at the solid–water–vapor contact line, we explore the molecular origins of large evaporation rates at the contact line and find new ways to...

Modelling Sessile Droplet Profile Using Asymmetrical Ellipses

Modelling the profile of a liquid droplet has been a mainstream technique for researchers to study the physical properties of a liquid. This study proposes a facile modelling approach using an elliptic model to generate the profile of sessile droplets, with MATLAB as the simulation environment. The concept of the elliptic method is simple and easy to use. Only three specific points on the droplet are needed to generate the complete theoretical droplet profile along with its critical parameters such as volume, surface area, height, and contact radius. In addition, we introduced fitting coefficients to accurately determine the contact angle and surface tension of a droplet. Droplet volumes ranging from 1 to 300 µL were chosen for this investigation, with contact angles ranging from 90° to 180°. Our proposed method was also applied to images of actual water droplets with good results. This study demonstrates that the elliptic method is in excellent agreement with the Young–Laplace equation and can be used for rapid and accurate approximation of liquid droplet profiles to determine the surface tension and contact angle.

Equivalence of sessile droplet dynamics under periodic and steady electric fields

The electrohydrodynamics of a sessile droplet under the influence of periodic and steady electric fields in microgravity conditions is theoretically investigated using an inertial lubrication model. Previous studies have revealed that a freely suspended spherical droplet with unequal conductivity and permittivity ratios exhibits distinct dynamics under periodic and equivalent steady forcing in the root mean-square sense. However, it is unclear when (if at all) such distinct dynamics occur for periodic and equivalent steady forcing in the case of sessile droplets. The equivalence between periodic and steady forcing is shown to be governed by the interfacial charge buildup, which further depends on the competition between the charge relaxation and forcing timescales. A circulation-deformation map is introduced for the sessile droplet that acts as a guideline to achieve electric field-induced wetting or dewetting as the case may be. We also demonstrate that a droplet may be rendered either more or less wetting solely by tuning the forcing frequency.

Evaporation of a liquid sessile droplet subjected to forced convection

Experiments on measuring the rate of evaporation of liquid sessile droplets into air show that the rate of evaporation increases in the presence of forced convection flows. However, data on the effect of convection on evaporation are often contradictory and should be clarified. The paper presents a numerical analysis of evaporation from the surface of a water droplet subjected to forced convection in the gas phase. The drop is located on a smooth horizontal isothermal substrate; the mode with constant contact angle is considered. The shape of the drop has axial symmetry, the same for the velocities and pressure. Forced convection compatible with the symmetry conditions are represented by flows directed downward along the axis of the system and diverging along the sides near the drop and the substrate. The mathematical model is constructed for evaporation controlled by diffusion in the gas phase and takes into account surface tension, gravity, and viscosity in both media, buoyancy and Marangoni convection. The results indicate the existence of the mutual influence of liquid and gaseous media. Thus, a drop vibrates under the influence of movements in the atmosphere, which generates a density wave in the gas: the drop «sounds». The magnitude of the velocity in a liquid is 50 times less than the characteristic velocity in air. It is found that the evaporation rate does not change in the presence of forced convection flows, which contradicts most of the experimental works. The reason for the discrepancies is supposed to be the appearance of nonequilibrium conditions at the boundary of the condensed phase: under these conditions, the evaporation regime ceases to be diffusional.