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.

Interfacial Behaviour in Ferroalloys: The Influence of Sulfur in FeMn and SiMn Systems

The present study has investigated the influence of sulfur content in synthetic FeMn and SiMn from 0 to 1.00 wt pct on interfacial properties between these ferroalloys and slags. The effect of experimental parameters such as temperature and holding time was evaluated. Interfacial interaction between ferroalloys and slags was characterized by interfacial tension and apparent contact angle between metal and slag, measured based on the Young–Laplace equation and an inverse modelling approach developed in OpenFOAM. The results show that sulfur has a significant influence on both interfacial tension and apparent contact angle, decreasing both values and promoting the formation of a metal-slag mixture. Despite the fact that sulfur was added only to the ferroalloys, most of sulfur is distributed into slag after reactions with the metal phase. Increasing the maximum experimental temperature in the sessile drop furnace also resulted in a decrease of both interfacial properties, resulting in higher mass transfer rates and intensive reactions between metal and slag. The effect of holding time demonstrated that after reaching equilibrium in FeMn-slag and SiMn-slag systems (both with and without sulfur), interfacial tension and apparent contact angle remain constant.

A Porous Media Leakage Model of Contact Mechanical Seals Considering Surface Wettability

The fluid leakage channel found in contact mechanical seals belongs to the microchannel category. Thus, upon further inspection, the influence of surface wettability and other factors neglected in previous studies becomes obvious. The porous leakage model of contact mechanical seals considering the surface wettability presented in this paper was based on the Cassie model and slip theory. The variations of the microchannel slip length and the velocity under various wettability conditions were studied and the relationship between the slip length and the apparent contact angle was established. Moreover, using porous media theory, the theoretical model of the leakage rate in contact mechanical seals considers the surface wettability depending on various parameters. The observed parameters included the surface contact angle, sealing medium pressure, viscosity coefficient, fractal dimension, and maximum pore diameter. The simulation results obtained using the proposed model have shown that the leakage rate increases with the increase of the apparent contact angle. Particularly when the contact pressure is small, the influence of the surface wettability is more significant. Furthermore, the leakage rate results obtained via the proposed model were compared to those of existing models. The comparison confirmed that the proposed model is applicable and that the necessity of considering wettability significantly affects the leakage rate calculation accuracy. The proposed model lays a foundation for further improving the calculation accuracy, making it easier for both the researchers and practitioners to suppress the leakage in contact mechanical seals.

The Effect of Patterned Micro-Structure on the Apparent Contact Angle and Three-Dimensional Contact Line

The measurement of the apparent contact angle on structured surfaces is much more difficult to obtain than on smooth surfaces because the pinning of liquid to the roughness has a tremendous influence on the three phase contact line. The results presented here clearly show an apparent contact angle variation along the three phase contact line. Accordingly, not only one value for the apparent contact angle can be provided, but a contact angle distribution or an interval has to be given to characterize the wetting behavior. For measuring the apparent contact angle distribution on regularly structured surfaces, namely micrometric pillars and grooves, an experimental approach is presented and the results are provided. A short introduction into the manufacturing process of such structured surfaces, which is a combination of Direct LASER Writing (DLW) lithography, electroforming and hot embossing shows the high quality standard of the used surfaces.

Apparent Contact Angle of Droplets on Liquid Infused Surfaces: Geometric Interpretation

We theoretically investigate the apparent contact angle of droplets on liquid infused surfaces as a function of the relative size of the wetting ridge and the deposited droplet. We provide...