Evaporation of a Droplet: From physics to applications

In this paper, we develop a first principles model that connects respiratory droplet physics with the evolution of a pandemic such as the ongoing Covid-19. The model has two parts. First, we model the growth rate of the infected population based on a reaction mechanism. The advantage of modeling the pandemic using the reaction mechanism is that the rate constants have sound physical interpretation. The infection rate constant is derived using collision rate theory and shown to be a function of the respiratory droplet lifetime. In the second part, we have emulated the respiratory droplets responsible for disease transmission as salt solution droplets and computed their evaporation time, accounting for droplet cooling, heat and mass transfer, and finally, crystallization of the dissolved salt. The model output favourably compares with the experimentally obtained evaporation characteristics of levitated droplets of pure water and salt solution, respectively, ensuring fidelity of the model. The droplet evaporation/desiccation time is, indeed, dependent on ambient temperature and is also a strong function of relative humidity. The multi-scale model thus developed and the firm theoretical underpinning that connects the two scales-macro-scale pandemic dynamics and micro-scale droplet physics-thus could emerge as a powerful tool in elucidating the role of environmental factors on infection spread through respiratory droplets.

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Modeling the role of respiratory droplets in Covid-19 type pandemics

One of the many unresolved questions that revolves around the Covid-19 pandemic is whether local outbreaks can depend on ambient conditions like temperature and relative humidity. In this paper, we develop a model that tries to explain and describe the temperature and relative humidity sensitivity of respiratory droplets and their possible connection in determining viral outbreaks. The model has two parts. First, we model the growth rate of the infected population based on a reaction mechanism - the final equations of which are similar to the well-known SIR model. The advantage of modeling the pandemic using the reaction mechanism is that the rate constants have sound physical interpretation. The infection rate constant is derived using collision rate theory and shown to be a function of the respiratory droplet lifetime. In the second part, we have emulated the respiratory droplets responsible for disease transmission as salt solution droplets and computed their evaporation time accounting for droplet cooling, heat and mass transfer and finally crystallization of the salt. The model output favourably compares with the experimentally obtained evaporation characteristics of levitated droplets of pure water and salt solution, respectively, ensuring fidelity of the model. Droplet evaporation/desiccation time is indeed dependent on ambient temperature and relative humidity, considered at both outdoor and indoor conditions. Since the droplet evaporation time determines the infection rate constant, ambient temperature and relative humidity are shown to impact the outbreak growth rates.

Modeling ambient temperature and relative humidity sensitivity of respiratory droplets and their role in Covid-19 outbreaks

Controlling dropwise condensation is fundamental to water-harvesting systems, desalination, thermal power generation, air conditioning, distillation towers, and numerous other applications. For any of these, it is essential to design surfaces that enable droplets to grow rapidly and to be shed as quickly as possible. However, approaches based on microscale, nanoscale or molecular-scale textures suffer from intrinsic trade-offs that make it difficult to optimize both growth and transport at once. Here we present a conceptually different design approach—based on principles derived from Namib desert beetles, cacti, and pitcher plants—that synergistically combines these aspects of condensation and substantially outperforms other synthetic surfaces. Inspired by an unconventional interpretation of the role of the beetle’s bumpy surface geometry in promoting condensation, and using theoretical modelling, we show how to maximize vapour diffusion fluxat the apex of convex millimetric bumps by optimizing the radius of curvature and cross-sectional shape. Integrating this apex geometry with a widening slope, analogous to cactus spines, directly couples facilitated droplet growth with fast directional transport, by creating a free-energy profile that drives the droplet down the slope before its growth rate can decrease. This coupling is further enhanced by a slippery, pitcher-plant-inspired nanocoating that facilitates feedback between coalescence-driven growth and capillary-driven motion on the way down. Bumps that are rationally designed to integrate these mechanisms are able to grow and transport large droplets even against gravity and overcome the effect of an unfavourable temperature gradient. We further observe an unprecedented sixfold-higher exponent of growth rate, faster onset, higher steady-state turnover rate, and a greater volume of water collected compared to other surfaces. We envision that this fundamental understanding and rational design strategy can be applied to a wide range of water-harvesting and phase-change heat-transfer applications.

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Condensation on Slippery Asymmetric Bumps

An asymptotic model is derived for the competitive diffusion-limited evaporation of multiple thin sessile droplets under the assumption that the droplets are well separated. Exact solutions of the model are obtained for a pair of and for a polygonal array of identical droplets, and the model is found to perform well even outside its formal range of validity, up to and including the limit of touching droplets. The shielding effect of droplets on each other is demonstrated, and the model is used to investigate the effect of this shielding on droplet evolutions and lifetimes, as well as on the coffee-ring effect. The theoretical predictions of the model are found to be in good agreement with recent experimental results for seven relatively closely spaced droplets, suggesting that the model could be a useful tool for studying a wide range of other droplet configurations.

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Competitive evaporation of multiple sessile droplets

Coffee ring patterns in drying sessile droplets are undesirable in various practical applications. Here, we experimentally demonstrate that on hydrophobic substrates, the coffee ring can be suppressed just by increasing the particle diameter. Particles with larger size flocculate within the evaporation timescale, leading to a significant gravimetric settling (for Pe > 1) triggering a uniform deposit. Interestingly, the transition to a uniform deposit is found to be independent of the internal flow field and substrate properties. Flocculation of particles also alters the particle packing at the nanoscale resulting in order to disorder transitions. In this letter, we exhibit a physical exposition on how particle size affects morphodynamics of the droplet drying at macro-nano length scales. Published by AIP Publishing.

Suppression of coffee ring: (Particle) size matters

Droplet evaporation under confinement is ubiquitous to multitude of applications such as microfluidics, surface patterning, and ink-jet printing. However, the rich physics governing the universality in the underlying dynamics remains grossly elusive. Here, we bring out hitherto unexplored universal features of the evaporation dynamics of a sessile droplet entrapped in a 3D confined fluidic environment. We show, through extensive set of experiments and theoretical formulations, that the evaporation timescale for such a droplet can be represented by a unique function of the initial conditions. Moreover, using same theoretical considerations, we are able to trace and universally merge the volume evolution history of the droplets along with evaporation lifetimes, irrespective of the extent of confinement. We also showcase the internal flow transitions caused by spatio-temporal variation of evaporation flux due to confinement. These findings may be of profound importance in designing functionalized droplet eva...

Universal evaporation dynamics of a confined sessile droplet

Particle-laden droplet-based systems ranging from micro- to nanoscale have become increasingly popular in applications such as inkjet printing, pharmaceutics, nanoelectronics, and surface patterning. All such applications involve multidroplet arrays in which vapor-mediated interactions can significantly affect the evaporation dynamics and morphological topology of precipitates. A fundamental study was conducted on nanocolloidal paired droplets (droplets kept adjacent to each other as in an array) to understand the physics related to the evaporation dynamics, internal flow pattern, particle transport, and nanoparticle self-assembly, primarily using optical diagnostic techniques [such as micro-particle image velocimetry (μPIV)]. Paired droplets exhibit contact angle asymmetry, inhomogeneous contact line slip, and unique single-toroid microscale flow, which are unobserved in single droplets. Furthermore, nanoparticles self-assemble (at the nanoscale) to form a unique variable-thickness (microscale) tilted do...

Insights into Vapor-Mediated Interactions in a Nanocolloidal Droplet System: Evaporation Dynamics and Affects on Self-Assembly Topologies on Macro- to Microscales.

Evaporation of sessile droplets has been a topic of extensive research. However, the effect of confinement on the underlying dynamics has not been well explored. Here, we report the evaporation dynamics of a sessile droplet in a confined fluidic environment. Our findings reveal that an increase in the channel length delays the completion of the evaporation process and leads to unique spatio-temporal evaporation flux and internal flow. The evaporation modes (constant contact angle and constant contact radius) during the droplet lifetime however exhibit global similarity when normalized by appropriate length and timescales. These results are explained in light of an increase in vapor concentration inside the channel due to greater accumulation of water vapor on account of increased channel length. We have formulated a theoretical framework which introduces two key parameters namely an enhanced concentration of the vapor field in the vicinity of the confined droplet and a corresponding accumulation lengthscale over which the accumulated vapor relaxes to the ambient concentration. Using these two parameters and modified diffusion based evaporation we are able to show that confined droplets exhibit a universal behavior in terms of the temporal evolution of each evaporation mode irrespective of the channel length. These results may turn out to be of profound importance in a wide variety of applications, ranging from surface patterning to microfluidic technology.

Confinement-induced alterations in the evaporation dynamics of sessile droplets

We provide a comprehensive physical description of the vaporization, self-assembly, agglomeration, and buckling kinetics of sessile nanofluid droplets pinned on a hydrophobic substrate. We have deciphered five distinct regimes of the droplet life cycle. Regimes I-III consists of evaporation-induced preferential agglomeration that leads to the formation of a unique dome-shaped inhomogeneous shell with a stratified varying-density liquid core. Regime IV involves capillary-pressure-initiated shell buckling and stress-induced shell rupture. Regime V marks rupture-induced cavity inception and growth. We demonstrate through scaling arguments that the growth of the cavity (which controls the final morphology or structure) can be described by a universal function.

Lalit Bansal

Papers

Suppression of coffee ring: (Particle) size matters

Universal evaporation dynamics of a confined sessile droplet

Insights into Vapor-Mediated Interactions in a Nanocolloidal Droplet System: Evaporation Dynamics and Affects on Self-Assembly Topologies on Macro- to Microscales.

Confinement-induced alterations in the evaporation dynamics of sessile droplets

Universal buckling kinetics in drying nanoparticle-laden droplets on a hydrophobic substrate.