Frozen water might appear opaque since gas bubbles can get trapped in the ice during the freezing process. They nucleate and then grow near the advancing solidification front, due to the formation of a gas supersaturation region in its vicinity. A delicate interplay between the rate of mass transfer and the rate of freezing dictates the final shapes and sizes of the entrapped gas bubbles. In this work, we experimentally and numerically investigate the initial growth of such gas bubbles that nucleate and grow near the advancing ice front. We show that the initial growth of these bubbles is governed by diffusion and is enhanced due to a combination of the presence of the background gas concentration gradient and the motion of the approaching front. Additionally, we recast the problem into that of mass transfer to a moving spherical object in a homogeneous concentration field, finding good agreement between our experimental data and the existing scaling relations for that latter problem. Lastly, we address how fluid flow around the bubble might further affect this growth and qualitatively explore this through numerical simulations.

Evaporation of multicomponent droplets is important, albeit complex, in a wide range of applications, and requires a careful investigation. We investigate experimentally and numerically the evaporation characteristics of spherical, ethanol–water droplets with different initial concentration ratios in the acoustic levitation field. Imaging techniques and infrared thermometry are used for acquiring volume and surface temperature variations of droplets, reflecting their mass and heat transfer characteristics. Numerical simulations are conducted using modified parameters based on a theoretical model to consider the effect of the acoustic field. The calculation results show good agreement with the experimental data. The concentration and temperature distribution within the droplet is further investigated based on the numerical results.

Evaporation of multi-component liquid mixtures in confined geometries, such as capillaries, is crucial in applications such as microfluidics, two-phase cooling devices and inkjet printing. Predicting the behaviour of such systems becomes challenging because evaporation triggers complex spatio-temporal changes in the composition of the mixture. These changes in composition, in turn, affect evaporation. In the present work, we study the evaporation of aqueous glycerol solutions contained as a liquid column in a capillary tube. Experiments and direct numerical simulations show three evaporation regimes characterised by different temporal evolutions of the normalised mass transfer rate (or Sherwood number $Sh$), namely $Sh (\tilde{t} ) = 1$, $Sh \sim 1/\sqrt {\tilde{t} }$ and $Sh \sim \exp (-\tilde{t} )$, where $\tilde {t}$ is a normalised time. We present a simplistic analytical model that shows that the evaporation dynamics can be expressed by the classical relation $Sh = \exp ( \tilde{t} )\,\mathrm {erfc} ( \sqrt {\tilde{t} })$. For small and medium $\tilde{t}$, this expression results in the first and second of the three observed scaling regimes, respectively. This analytical model is formulated in the limit of pure diffusion and when the penetration depth $\delta (t)$ of the diffusion front is much smaller than the length $L(t)$ of the liquid column. When $\delta \approx L$, finite-length effects lead to $Sh \sim \exp (-\tilde{t} )$, i.e. the third regime. Finally, we extend our analytical model to incorporate the effect of advection and determine the conditions under which this effect is important. Our results provide fundamental insights into the physics of selective evaporation from a multi-component liquid column.

Microfluidic flow focusing is a versatile method for the production of monodisperse microbubbles for biomedical applications involving ultrasound. Existing studies propose several theoretical models to predict bubble size and production rate as a function of the liquid and gas flow rate. Yet, they typically do not include physical fluid parameters such as density, viscosity and surface tension. Here, we present an exhaustive experimental and numerical investigation of the influence of physical properties of the gas and liquid, and of the channel geometry on bubble size and production rate. We find a particularly strong effect of (i) gas density on the production rate and (ii) liquid viscosity on the bubble size. We further discuss our findings within the context of existing theoretical models to reflect on gaps in our current understanding of the fluid mechanics of bubble formation by flow focusing.

When an immiscible oil drop is immersed in a stably stratified ethanol–water mixture, the Marangoni flow on the surface of the drop can experience an oscillatory instability, so that the drop undergoes a transition from levitating to bouncing. The onset of the instability and its mechanisms have been studied previously (Li et al., Phys. Rev. Lett., vol. 126, 2021, 124502; Li et al., J. Fluid Mech., vol. 932, 2022, A11), yet the bouncing motion of the drop itself, which is a completely different problem, has not yet been investigated. Here we study how the bouncing characteristics (jumping height, rising and sinking time) depend on the control parameters (drop radius, stratification strength, drop viscosity). We first record experimentally the bouncing trajectories of drops of different viscosities in different stratifications. Then a simplified dynamical analysis is performed to get the scaling relations of the jumping height and the rising and sinking times. The rising and sinking time scales are found to depend on the drag coefficient $C_D^S$ of the drop in the stratified liquid, which is determined empirically for the current parameter space (Zhang et al., J. Fluid Mech., vol. 875, 2019, 622–656). For low-viscosity (5 cSt) oil drops, the results on the drag coefficient match those from the literature (Yick et al., J. Fluid Mech., vol. 632, 2009, pp. 49–68; Candelier et al., J. Fluid Mech., vol. 749, 2014, pp. 184–200). For high-viscosity (100 cSt) oil drops, the parameter space had not been explored and the drag coefficients are not readily available. Numerical simulations are therefore performed to provide external verification for the drag coefficients, which well match with the experimental results.

We consider the time evolution of a sessile drop of volatile partially wetting liquid on a rigid solid substrate. The drop evaporates under strong confinement, namely, it sits on one of the two parallel plates that form a narrow gap. First, we develop an efficient mesoscopic long-wave description in gradient dynamics form. It couples the diffusive dynamics of the vertically averaged vapour density in the narrow gap to an evolution equation for the profile of the volatile drop. The underlying free energy functional incorporates wetting, interface and bulk energies of the liquid and gas entropy. The model allows us to investigate the transition between diffusion-limited and phase transition-limited evaporation for shallow droplets. Its gradient dynamics character allows for a long-wave as well as a full-curvature formulation. Second, we compare results obtained with the mesoscopic long-wave model to corresponding direct numerical simulations solving the Stokes equation for the drop coupled to the diffusion equation for the vapour as well as to selected experiments. In passing, we discuss the influence of contact line pinning.

Phase segregation triggered by selective evaporation can emerge in multicomponent systems, leading to complex physicochemical hydrodynamics. Recently, Li et al. (Phys. Rev. Lett., vol. 120, 2018, 224501) and Kim & Stone (J. Fluid Mech., vol. 850, 2018, pp. 769–783) reported a segregative behaviour (i.e. demixing) in an evaporating binary droplet. In this work, by means of experiments and theoretical analysis, we investigate the flow dynamics after the occurrence of the phase segregation. As example, we take the 1,2-hexanediol–water binary droplet system. First, we reveal experimentally the overall physicochemical hydrodynamics of the evaporation process, including the segregative behaviour and the resulting flow structure close to the substrate. By quantifying the evolution of the radial flow, we identify three successive life stages of the evaporation process. At Stage I, a radially outward flow is observed, driven by the Marangoni effect. At the transition to Stage II, the radial flow reverses partially, starting from the contact line. This flow breaks the axial symmetry and remarkably is driven by the segregation itself. Finally at Stage III, the flow decays as the evaporation ceases gradually. At this stage, the segregation has grown to the entire droplet, and the flow is again controlled by the Marangoni effect. The resulting Marangoni flow homogenizes the distribution of the entrapped volatile water over the whole droplet.

Interfacial stability is important for many processes involving heat and mass transfer across two immiscible phases. For the evaporation of a binary solution with one component more volatile than the other, gradients in surface tension can arise. These gradients can ultimately destabilize the liquid–gas interface. We study the evaporation of an ethanol–water solution, for which ethanol is more volatile. The solution is contained in a horizontal Hele-Shaw cell which is open from one end to allow for evaporation into air. A Marangoni instability is then triggered at the liquid–air interface. We study the temporal evolution of the instability through its effects on the bulk of the liquid. More specifically, the growth of convective cells is measured with confocal microscopy and the velocity field with microparticle image velocimetry. The results of numerical simulations based on quasi-two-dimensional equations satisfactorily compare with the experimental observations, even without consideration of evaporative cooling, although this cooling can play an extra role in experiments. Furthermore, a linear stability analysis applied to a simplified version of the quasi-two-dimensional equations showed reasonably good agreement with the results from simulations at early times, when the instability has just been triggered and before coarsening. In particular, we find a critical Marangoni number below which a regime of stability is predicted.

For a small sessile or pendant droplet it is generally assumed that gravity does not play any role once the Bond number is small. This is even assumed for evaporating binary sessile or pendant droplets, in which convective flows can be driven due to selective evaporation of one component and the resulting concentration and thus surface tension differences at the air–liquid interface. However, recent studies have shown that in such droplets gravity indeed can play a role and that natural convection can be the dominant driving mechanism for the flow inside evaporating binary droplets (Edwards et al., Phys. Rev. Lett., vol. 121, 2018, 184501; Li et al., Phys. Rev. Lett., vol. 122, 2019, 114501). In this study, we derive and validate a quasi-stationary model for the flow inside evaporating binary sessile and pendant droplets, which successfully allows one to predict the prevalence and the intriguing interaction of Rayleigh and/or Marangoni convection on the basis of a phase diagram for the flow field expressed in terms of the Rayleigh and Marangoni numbers.

The evaporation of multicomponent droplets is relevant to various applications but challenging to study due to the complex physicochemical dynamics. Recently, Li etal. (Phys. Rev. Lett., vol. 120, 2018, 224501) reported evaporation-triggered segregation in 1,2-hexanediol–water binary droplets. In this present work, we added 0.5 wt % silicone oil to the 1,2-hexanediol–water binary solution. This minute silicone oil concentration dramatically modifies the evaporation process, as it triggers an early extraction of the 1,2-hexanediol from the mixture. Surprisingly, we observe that the segregation of 1,2-hexanediol forms plumes, rising up from the rim of the sessile droplet towards the apex during droplet evaporation. By orientating the droplet upside down, i.e. by studying a pendent droplet, the absence of the plumes indicates that the flow structure is induced by buoyancy, which drives a Rayleigh–Taylor instability (i.e. driven by density differences and gravitational acceleration). From micro particle image velocimetry measurement, we further prove that the segregation of the non-volatile component (1,2-hexanediol) hinders the evaporation near the contact line, which leads to a suppression of the Marangoni flow in this region. Hence, on long time scales, gravitational effects, rather than Marangoni flows, play the dominant role in the flow structure. We compare the measurement of the evaporation rate with the diffusion model of Popov (Phys. Rev., vol. 71, 2005, 036313), coupled with Raoult's law and the activity coefficient. This comparison indeed confirms that the silicone-oil-triggered segregation of the non-volatile 1,2-hexanediol significantly delays the evaporation. With an extended diffusion model, in which the influence of the segregation has been implemented, the evaporation can be well described.

Multicomponent liquid drops in a host liquid are very relevant in various technological applications. Their dissolution or growth dynamics is complex. Differences in solubility between the drop components combined with the solutal Marangoni effect and natural convection contribute to this complexity, which can be even further increased in combination with the ouzo effect, i.e. the spontaneous nucleation of microdroplets due to composition-dependent miscibilities in a ternary system. The quantitative understanding of this combined process is important for applications in industry, particularly for modern liquid–liquid microextraction processes. In this work, as a model system, we experimentally and theoretically explore water–ethanol drops dissolving in anethole oil. During the dissolution, we observed two types of microdroplet nucleation, namely water microdroplet nucleation in the surrounding oil at drop mid-height, and oil microdroplet nucleation in the aqueous drop, again at mid-height. The nucleated oil microdroplets are driven by Marangoni flows inside the aqueous drop and evolve into microdroplet rings. A one-dimensional multiphase and multicomponent diffusion model in combination with thermodynamic equilibrium theory is proposed to predict the behaviour of spontaneous emulsification, i.e. microdroplet nucleation, that is triggered by diffusion. A scale analysis together with experimental investigations of the fluid dynamics of the system reveals that both the solutal Marangoni flow inside the drop and the buoyancy-driven flow in the host liquid influence the diffusion-triggered emulsification process. Our work provides a physical understanding of the microdroplet nucleation by dissolution of a multicomponent drop in a host liquid.

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.