Spreading Law of Evaporative Droplets

Droplet spreading is ubiquitous and plays a significant role in applications such as spray cooling, inkjet printing, and micro-flow devices. While the spreading of non-volatile droplets can be described by the competition between capillary and viscous dissipation, namely the Tanner's law, R(t)~t1/10, the spreading and flow transition in volatile droplets remains elusive due to the complexity added by interfacial phase change. Here we show, using both theoretical modeling and experiments, that the wetting dynamics of volatile droplets can be scaled by the spatial temporal interplay between capillary, evaporation, and thermal Marangoni effects. We quantify these complex interactions using phase diagrams based on detailed theoretical and experimental analyses. We further illustrate the spreading law of droplets by generalizing the Tanner's law to a full range of liquids with saturation vapor pressure spanning from 101 to 104 Pa and on substrates with thermal conductivity spanning from 10-1 to 103W/m/K. Our conclusions enable a unifying explanation to a series of individual works including the criterion of flow reversal and the state of dynamic wetting, making it possible to control liquid transport in diverse application scenarios

How does blood regulate cerebral temperatures during hypothermia?

AbstractMacro-modeling of cerebral blood flow can help determine the impact of thermal intervention during instances of head trauma to mitigate tissue damage. This work presents a bioheat model using a 3D fluid-porous domain coupled with intersecting 1D arterial and venous vessel trees. This combined vascular porous (VaPor) model resolves both cerebral blood flow and energy equations, including heat generated by metabolism, using vasculature extracted from MRI data and is extended using a tree generation algorithm. Counter-current flows are expected to increase thermal transfer within the brain and are enforced using either the vascular structure or flow reversal, represented by a flow reversal constant, C R . These methods exhibit larger average brain cooling (from 0.56 °C ± &lt;0.01 °C to 0.58 °C ± &lt;0.01 °C) compared with previous models (0.39 °C) when scalp temperature is reduced. An greater reduction in core brain temperature is observed (from 0.29 °C ± &lt;0.01 °C to 0.45 °C ± &lt;0.01 °C) compared to previous models (0.11 °C) due to the inclusion of counter-current cooling effects. The VaPor model also predicts that a hypothermic average temperature (&lt;36 °C) can be reached in core regions of neonatal models using scalp cooling alone.</jats:p

Ultraefficient reduced model for countercurrent two-layer flows

International audienceWe investigate the dynamics of two superposed layers with density contrast flowing countercurrent inside a channel, when the lower layer is much thinner than the wavelength of interfacial waves. We apply a low-dimensional film model to the bottom (heavier) layer and introduce a fast and efficient method to predict the onset of flow reversal in this phase. We study three vertical scenarios with different applied pressure gradients and compare the temporal growth rates of linear and weakly nonlinear waves to the Orr-Sommerfeld problem and to the weakly nonlinear theory, respectively. At the loading point, i.e., when a large wave hump stands at the interface, our spatiotemporal analysis shows that the system is absolutely unstable. We then present profiles of nonlinear saturated waves, pressure field, and streamline distribution in agreement with direct numerical simulation. The reduced model presented here allows us to explore the effect of the upper-layer speed on the wave pattern, showing that the wave profile is very sensitive when the mean film thickness, rather than the liquid flow rate, is maintained constant in the simulation. In addition, we show the strong effect of surface tension on both the maximum wave hump and the crest steepness before the loading point. Finally, we reveal how the nonlinear wave speed affects the vortex distribution within the lower layer by analyzing the stream function under different scenarios

Semicrystalline Polymer Micro/Nanostructures Formed by Droplet Evaporation of Aqueous Poly(ethylene oxide) Solutions: Effect of Solution Concentration

[Image: see text] Deposits formed after evaporation of sessile droplets, containing aqueous solutions of poly(ethylene oxide), on hydrophilic glass substrates were studied experimentally and mathematically as a function of the initial solution concentration. The macrostructure and micro/nanostructures of deposits were studied using stereo microscopy and atomic force microscopy. A model, based on thin-film lubrication theory, was developed to evaluate the deposit macrostructure by estimating the droplet final height. Moreover, the model was extended to evaluate the micro/nanostructure of deposits by estimating the rate of supersaturation development in connection with the driving force of crystallization. Previous studies had only described the macrostructure of poly(ethylene oxide) deposits formed after droplet evaporation, whereas the focus of our study was the deposit micro/nanostructures. Our atomic force microscopy study showed that regions close to the deposit periphery were composed of predominantly semicrystalline micro/nanostructures in the form of out-of-plane lamellae, which require a high driving force of crystallization. However, deposit central areas presented semicrystalline micro/nanostructures in the form of in-plane terraces and spirals, which require a lower driving force of crystallization. Increasing the initial concentration of solutions led to an increase in the lengths and thicknesses of the out-of-plane lamellae at the deposits’ periphery and enhanced the tendency to form spirals in the central areas. Our numerical study suggested that the rate of supersaturation development and thus the driving force of crystallization increased from the center toward the periphery of droplets, and the supersaturation rate was lower for solutions with higher initial concentrations at each radius. Therefore, periphery areas of droplets with lower initial concentrations were suitable for the formation of micro/nanostructures which require higher driving forces, whereas central areas of droplets with higher initial concentration were desirable for the formation of micro/nanostructures which require lower driving forces. These numerical results were in good qualitative agreement with the experimental findings

Droplet Motion on Contrasting Striated Surfaces

Liquid droplets move readily under the influence of surface tension gradients on their substrates. Substrates decorated with parallel microgrooves, or striations, presenting the advantage of homogeneous chemical properties yet varying the topological characteristics on either side of a straight-line boundary, are considered in this study. The basic type of geometry consists of hydrophobic micro-striations/rails perpendicular to the boundary, with the systematic variation of the width to spacing ratio, thus changing the solid–liquid contact fraction and inducing a well-defined wettability contrast across the boundary. Droplets in the Cassie–Baxter state, straddling the boundary, move along the wettability contrast in order to reduce the overall surface free energy. The results show the importance of the average solid fraction and contrasting fraction in a wide range of given geometries across the boundary on droplet motion. A unified criterion for contrasting striated surfaces, which describes the displacement and the velocity of the droplets, is suggested, providing guidelines for droplet manipulation on micro-striated/railed surfaces. The authors would like to acknowledge the support of the European Space Agency through ESA Contract No. 4000129506/20/NL/PG and the support received from the Engineering and Physical Sciences Research Council (EPSRC) through Grant No. EP/P005705/1. The authors also acknowledge the EC-RISE-ThermaSMART project, which received funding from the European Union's Horizon 2020 research and innovation program under Marie Skłodowska-Curie Grant Agreement No. 778104