Evaporation of water: evaporation rate and collective effects

Carrier, Odile; Shahidzadeh-Bonn, Noushine; Zargar, Rojman; Aytouna, Mounir; Habibi, Mehdi; Eggers, Jens; Bonn, Daniel

doi:10.1017/jfm.2016.356

Cited by 138 publications

(120 citation statements)

References 26 publications

(34 reference statements)

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“…In contrast, for gas bubbles the liquid and gas phases are of two different chemical natures; the driving physical mechanisms are the dissolution of the gas into the liquid to maintain equilibrium at its surface as quantified by Henry's law [8], and the slow diffusion of the dissolved gas into the liquid phase. Note that this second case presents many formal similarities with the dissolution process of droplets [22], their evaporation [23] or even dissolving solids [24].…”

Section: Introductionmentioning

confidence: 87%

Collective dissolution of microbubbles

2018

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A microscopic bubble of soluble gas always dissolves in finite time in an under-saturated fluid. This diffusive process is driven by the difference between the gas concentration near the bubble, whose value is governed by the internal pressure through Henry's law, and the concentration in the far field. The presence of neighbouring bubbles can significantly slow down this process by increasing the effective background concentration and reducing the diffusing flux of dissolved gas experienced by each bubble. We develop theoretical modelling of such diffusive shielding process in the case of small microbubbles whose internal pressure is dominated by Laplace pressure. We first use an exact semi-analytical solution to capture the case of two bubbles and analyse in detail the shielding effect as a function of the distance between the bubbles and their size ratio. While we also solve exactly for the Stokes flow around the bubble, we show that hydrodynamic effects are mostly negligible except in the case of almost-touching bubbles. In order to tackle the case of multiple bubbles, we then derive and validate two analytical approximate yet generic frameworks, first using the method of reflections and then by proposing a self-consistent continuum description. Using both modelling frameworks, we examine the dissolution of regular one-, two-and three-dimensional bubble lattices. Bubbles located at the edge of the lattices dissolve first, while innermost bubbles benefit from the diffusive shielding effect, leading to the inward propagation of a dissolution front within the lattice. We show that diffusive shielding leads to severalfold increases in the dissolution time which grows logarithmically with the number of bubbles in one dimensional lattices and algebraically in two and three dimensions, scaling respectively as its square root and 2/3-power. We further illustrate the sensitivity of the dissolution patterns to initial fluctuations in bubble size or arrangement in the case of large and dense lattices, as well as non-intuitive oscillatory effects.

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Section: Introductionmentioning

confidence: 87%

Collective dissolution of microbubbles

2018

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“…A more thorough study of vapour transport would therefore be an interesting direction for future work. This point is particularly relevant for water, for which it is thought that the effect of the atmosphere may be important [51][52][53].…”

Section: Discussionmentioning

confidence: 99%

Kinetic effects regularize the mass-flux singularity at the contact line of a thin evaporating drop

et al. 2017

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We consider the transport of vapour caused by the evaporation of a thin, axisymmetric, partially wetting drop into an inert gas. We take kinetic effects into account through a linear constitutive law that states that the mass flux through the drop surface is proportional to the difference between the vapour concentration in equilibrium and that at the interface. Provided that the vapour concentration is finite, our model leads to a finite mass flux in contrast to the contact-line singularity in the mass flux that is observed in more standard models that neglect kinetic effects. We perform a local analysis near the contact line to investigate the way in which kinetic effects regularize the mass-flux singularity at the contact line. An explicit expression is derived for the mass flux through the free surface of the drop. A matched-asymptotic analysis is used to further investigate the regularization of the mass-flux singularity in the physically relevant regime in which the kinetic timescale is much smaller than the diffusive one. We find that the effect of kinetics is limited to an inner region near the contact line, in which kinetic effects enter at leading order and regularize the mass-flux singularity. The inner problem is solved explicitly using the Wiener-Hopf method and a uniformly valid composite expansion is derived for the mass flux in this asymptotic limit.

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“…We have also compared the present findings with the analytical solutions of Carrier et al (2016). Their crude approximation of representing the vicinal droplets to super-drop fails for a sufficiently sparse (non-interacting) droplet arrangement and the scaling value overshoots to 2 (Figure 3(b)).…”

mentioning

confidence: 80%

“…This approach, however, does not quantify the droplet evaporation lifetime. Carrier et al (2016) formulated the droplet evaporation timescales by considering a group of interacting droplets as one flat superdrop. However, their asymptotic model loses its predictive capabilities under the limiting conditions of sufficiently sparse (lower vapor mediated interactions) distribution of sessile droplets.…”

mentioning

confidence: 99%

Cooperative evaporation in two-dimensional droplet arrays

et al. 2020

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Sessile droplets exposed to an incipient condition lead to an inevitable loss of mass, which is critical in many practical applications. By considering an arbitrarily configured two-dimensional array of droplets, here we provide a simple generalized theoretical limit to their lifetime in an evaporating state. Notwithstanding the geometrical and physical complexity of the effective confinement generated due to their cooperative interactions, we show that the consequent evaporation characteristics may be remarkably insensitive to the topographical details of the overall droplet organization, for a wide range of droplet-substrate combinations. With subsequent deployment of particle-laden droplets, however, our results lead to the discovery of a unique pathway towards tailoring the internal flows within the collective system by harnessing an exclusive topologically-driven symmetry breaking phenomenon, yielding a new strategy of patterning particulate matters around the droplet array. Evaporation of sessile droplets (Stauber et. al. 2014; Sáenz et. al. 2015; Schofield et. al. 2018; Ghasemi & Ward, 2010; Xu & Choi, 2012; Chen et al., 2012)is ubiquitous to our day-to-day experiences, including the formation of coffee-rings, ink-stains, as well as many commercial processes including spray painting, ink-jet printing, crop spraying, coating of seeds or tablets, spray cooling and spray drying. In most of these practical scenarios, the droplet arrangement can be best represented by topologically varying two-dimensional structures (2D arrays), resulting in obvious complexities in describing their dynamical characteristics by appealing to a universal physical paradigm.The proximity of neighboring droplets in a multi-dimensional droplet array creates localized regions of vapor accumulation by saturating the interstitial voids. Consequently, an 'effective' vapor mediated confinement is established around the individual droplets. The distribution and extent of vapor accumulation leads to further modifications in the flow dynamics in and around the droplet, culminating in alterations in the global rate of evaporation, thereby influencing the evaporation dynamics of the droplet array in an intriguing manner (Dugas et. al. 2005). Laghezza et. al. (2016), through experiments and numerical simulations, showed that a system of interacting droplets results in increase in the dissolution lifetime of the central droplet. However, their formulation could not predict the droplet dissolution lifetime increment as a function of the droplet array configuration. Toledano et al. (2005)

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Evaporation of water: evaporation rate and collective effects

Cited by 138 publications

References 26 publications

Collective dissolution of microbubbles

Collective dissolution of microbubbles

Kinetic effects regularize the mass-flux singularity at the contact line of a thin evaporating drop

Cooperative evaporation in two-dimensional droplet arrays

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