The Greek aperitif Ouzo is not only famous for its specific anise-flavoured taste, but also for its ability to turn from a transparent miscible liquid to a milky-white coloured emulsion when water is ...added. Recently, it has been shown that this so-called Ouzo effect, i.e. the spontaneous emulsification of oil microdroplets, can also be triggered by the preferential evaporation of ethanol in an evaporating sessile Ouzo drop, leading to an amazingly rich drying process with multiple phase transitions (Tan et al., Proc. Natl Acad. Sci. USA, vol. 113 (31), 2016, pp. 8642–8647). Due to the enhanced evaporation near the contact line, the nucleation of oil droplets starts at the rim which results in an oil ring encircling the drop. Furthermore, the oil droplets are advected through the Ouzo drop by a fast solutal Marangoni flow. In this article, we investigate the evaporation of mixture droplets in more detail, by successively increasing the mixture complexity from pure water over a binary water–ethanol mixture to the ternary Ouzo mixture (water, ethanol and anise oil). In particular, axisymmetric and full three-dimensional finite element method simulations have been performed on these droplets to discuss thermal effects and the complicated flow in the droplet driven by an interplay of preferential evaporation, evaporative cooling and solutal and thermal Marangoni flow. By using image analysis techniques and micro-particle-image-velocimetry measurements, we are able to compare the numerically predicted volume evolutions and velocity fields with experimental data. The Ouzo droplet is furthermore investigated by confocal microscopy. It is shown that the oil ring predominantly emerges due to coalescence.
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We extended a mathematical model for the drying of sessile droplets, based on the lubrication approximation, to binary mixture droplets. This extension is relevant for e.g. inkjet ...printing applications, where ink consisting of several components are used. The extension involves the generalization of an established vapor diffusion-limited evaporation model to multi-component mixtures. The different volatilities of the liquid components generate a composition gradient at the liquid-air interface. The model takes the composition-dependence of the mass density, viscosity, surface tension, mutual diffusion coefficient and thermodynamic activities into account. This leads to a variety of effects ranging from solutal Marangoni flow over deviations from the typical spherical cap shape to an entrapped residual amount of the more volatile component at later stages of the drying. These aspects are discussed in detail on the basis of the numerical results for water-glycerol and water-ethanol droplets. The results show good agreement with experimental findings. Finally, the accuracy of the lubrication approximation is assessed by comparison with a finite element method.
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Thermal Marangoni flow in evaporating sessile water droplets is much weaker in experiments than predicted theoretically. Often this is attributed to surfactant contamination, but ...there have not been any in-depth analyses that consider the full fluid and surfactant dynamics. It is expected that more insight into this problem can be gained by using numerical models to analyze the interplay between thermal Marangoni flow and surfactant dynamics in terms of dimensionless parameters.
Two numerical models are implemented: one dynamic model based on lubrication theory and one quasi-stationary model, that allows for arbitrary contact angles.
It is found that insoluble surfactants can suppress the thermal Marangoni flow if their concentration is sufficiently large and evaporation and diffusion are sufficiently slow. Soluble surfactants, however, either reduce or increase the interfacial velocity, depending on their sorption kinetics. Furthermore, insoluble surfactant concentrations that cause an order 0.1% surface tension reduction are sufficient to reduce the spatially averaged tangential flow velocity at the interface by a factor 100. For larger contact angles and smaller droplets this required concentration is larger (typically <1% surface tension reduction). The numerical models are mutually validated by comparing their results in cases where both are valid.
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Soluble surfactants in evaporating sessile droplets can cause a circulatory Marangoni flow. However, it is not straightforward to predict for what cases this vortical flow arises. It ...is hypothesized that the occurrence of Marangoni circulation can be predicted from the values of a small number of dimensionless parameters.
A numerical model for the drop evolution is developed using lubrication theory. Surfactant transport is implemented by means of convection–diffusion-adsorption equations. Results are compared to literature.
It is shown that stronger evaporation, slower adsorption kinetics and lower solubility of the surfactants all tend to increasingly suppress Marangoni circulation. These results are found to be consistent with both experimental and numerical results from literature and can explain qualitative differences in flow behavior of surfactant-laden droplets. Furthermore, diffusion also tends to counteract Marangoni flow, where bulk diffusion has a more significant influence than surface diffusion. Also, the formation of micelles is found to slightly suppress Marangoni circulation. Experimental results from literature, however, show that in some cases circulatory behavior is enhanced by micelles, possibly even resulting in qualitative changes in the flow. Potential explanations for these differences are given and extensions to the model are suggested to improve its consistency with experiments.
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► We developed an extended physical model for the drying of inkjet-printed droplets. ► We compared the results with experimental results. ► We applied the lubrication approximation. ► ...We examined the influence of the precursor film and the Kelvin effect. ► We examined the influence of the contact line conditions.
In this paper we study the behavior of an inkjet-printed droplet of a solute dissolved in a solvent on a solid horizontal surface by numerical simulation. An extended model for drying of a droplet and the final distribution of the solute on an impermeable substrate is proposed. The model extends the work by Deegan, Fischer and Kuerten by taking into account convection, diffusion and adsorption of the solute in order to describe more accurately the surface coverage on the substrate. A spherically shaped droplet is considered such that the model can be formulated as an axially symmetric problem. The droplet dynamics is driven by the combined action of surface tension and evaporation. The fluid flow in the droplet is modeled by the Navier–Stokes equation and the continuity equation, where the lubrication approximation is applied. The rate of evaporation is determined by the distribution of vapor pressure in the air surrounding the droplet. Numerical results are compared with experimental results for droplets of various sizes.
•Development of scalable numerical algorithms for turbulent bubbly flows.•Accuracy investigation of curvature computation for colliding bubbles and wall collisions.•Detailed analysis of the parallel ...performance of the Navier–Stokes and the VOF solver.•Simulation of a channel flow loaded with a total of 10,000 deformable bubbles.
We present an efficient and highly scalable solver for direct numerical simulation (DNS) of dispersed gas-liquid flow, containing a large number of deformable bubbles. We apply this to O(104) bubbles in a turbulent flow. This was accomplished by a well-considered combination of state-of-the-art numerical methods, as well as fast and scalable numerical algorithms that have their origin in single-phase and two-phase flows. The features key-elements of the algorithm of curvature computation, bubble collision and variable-coefficient Poisson equation solver are presented. Resolution requirements for an accurate advection of a rising bubble have been established by comparison with the (Hysing, 2009) benchmark. The Generalized Height Function (GHF) method, was adopted for the curvature computations. We observed agreement with theoretical convergence rates, as well as a significant reduction of spurious velocities when employing GHF, compared to a finite difference approach. The main interaction mechanisms between bubbles and walls of the domain were analyzed, showing second order convergence of the underlying numerical methods.
A detailed analysis of the parallel performance of the Navier–Stokes (NS) solver and the solver for the gas volume fraction was carried out. The analysis revealed close to linear scaling up to ≈ 18000 cores on a computational grid with 1 billion cells for the NS solver, and an ideal scaling of the gas volume fraction solver up to O(103) bubbles. Beyond that, acceptable overhead for up to O(104) bubbles was found.
A simulation of a downflow configuration of a turbulent channel loaded with a total of 10000 bubbles illustrates the computational capabilities. First and second order statistics of the velocity field were computed as well as the profiles of the average gas volume fraction field in the statistically steady state. In the case considered, a 47% increase of the wall shear stress was observed, brought about by turbulence modification arising from the embedded bubbles. The interaction between turbulence and bubbles at high volume fraction resulted in a strong attenuation of the rms of the velocity fluctuations in a wide region of the core of the channel.
•New experimental setup enables quenching of surfaces moving at speeds up to 8 m/s.•Borescope is used to visualize the boiling regimes in the jet stagnation zone.•Heat flux decreases at increasing ...plate speed.•Heat flux estimations indicate boiling suppression due to boundary layer thinning.•Stagnation zone visualization confirms boiling suppression for increasing plate speed.
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Quench cooling of steel on the Run Out Table presents great complexity arising from the high speed of the steel slabs and the violent nature and short time scale that characterize the involved boiling regimes. Until now experimental studies on quenching of moving surfaces have reported surface speeds up to 1.6 m/s. This is far from the real Run Out Table operation conditions, where the steel slabs move between 2 and 22 m/s. In this study, a new experimental setup is presented that allows quenching of steel surfaces at speeds between 0 and 8 m/s. For the first time direct visualization of the boiling activity in the stagnation zone during quenching of a moving surface is presented and the effects of surface speed and water jet temperature are analyzed. The results show a change in the trend of the cooling history and boiling curves that depends on plate speed. This change is a consequence of the effect of surface motion on the viscous and thermal boundary layers. The direct visualization of the stagnation zone confirms that this change in trend corresponds to progressive suppression of boiling activity and enhancement of explosive boiling and film boiling with increasing surface speed.
We propose a point-particle model for two-way coupling of water droplets dispersed in the turbulent flow of a carrier gas consisting of air and water vapour. We adopt an Euler–Lagrangian formulation ...based on conservation laws for the mass, momentum and energy of the continuous phase and on empirical correlations describing momentum, heat and mass transfer between the droplet phase and the carrier gas phase. An incompressible flow formulation is applied for direct numerical simulation of differentially heated turbulent channel flow. The two-way coupling is investigated in terms of its effects on mass and heat transfer characteristics and the resulting droplet size distribution. Compared to simulations without droplets or those with solid particles with the same size and specific heat as the water droplets, a significant increase in Nusselt number is found, arising from the additional phase changes. The Nusselt number increases with increasing ambient temperature and is almost independent of the heat flux applied to the walls of the channel. The time-averaged droplet size distribution displays a characteristic dependence on position expressing the combined effect of turbophoresis and phase changes in turbulent wall-bounded flow. In the statistically steady state that is reached after a long time, the resulting flow exhibits a mean motion of water vapour from the warm wall to the cold wall, where it condenses on average, followed by a net mean mass transfer of droplets from the cold wall to the warm wall.
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