One-dimensional numerical simulations based on hybrid Eulerian-Lagrangian approach are performed to investigate the interactions between propagating shock waves and dispersed evaporating water droplets in two-phase gas-droplet flows. Two-way coupling for interphase exchanges of mass, momentum and energy is adopted. Parametric study on shock attenuation, droplet evaporation, motion and heating is conducted, through considering various initial droplet diameters (5-20 μm), number densities (2.5 x 1011 - 2 x 1012 1/m3) and incident shock Mach numbers (1.17-1.9). It is found that the leading shock may be attenuated to sonic wave and even subsonic wave when droplet volume fraction is large and/or incident shock Mach number is low. Attenuation in both strength and propagation speed of the leading shock is mainly caused by momentum transfer to the droplets that interact at the shock front. Total pressure recovery is observed in the evaporation region, whereas pressure loss results from shock compression, droplet drag and pressure gradient force behind the shock front. Recompression of the region between the leading shock and two-phase contact surface is observed when the following compression wave is supersonic. After a critical point, this region gets stable in width and interphase exchanges in mass, momentum, and energy. However, the recompression phenomenon is sensitive to droplet volume fraction and may vanish with high droplet loading. For an incident shock Mach number of 1.6, recompression only occurs when the initial droplet volume fraction is below 3.28 x 10-5.
An evaporating droplet is a dynamic system in which flow is spontaneously generated to minimize the surface energy, dragging particles to the borders and ultimately resulting in the so-called "coffee-stain effect". The situation becomes more complex at the droplet's surface, where surface tension gradients of different nature can compete with each other yielding different scenarios. With careful experiments and with the aid of 3D particle tracking techniques, we are able to show that different types of surfactants turn the droplet's surface either rigid or elastic, which alters the evaporating…
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…
Temperature distributions and the corresponding vortex structures in an evaporating sessile droplet are obtained by performing detailed numerical calculations. A Marangoni convection induced by thermal conduction processes in the drop and the substrate is demonstrated to be able to result not only in a single vortex, but also in two or three vortices, depending on the ratio of substrate to fluid thermal conductivities, on the substrate thickness and the contact angle. The "phase diagrams" containing information on the number, orientation and spatial location of the vortices for quasistationary…
One-dimensional numerical simulations based on hybrid Eulerian-Lagrangian method are performed to study the interactions between propagating shocks and dispersed evaporating water droplets. Two-way coupling for exchanges of mass, momentum, energy and vapour species is adopted for the dilute two-phase gas-droplet flows. Interphase interactions and droplet breakup dynamics are investigated with initial droplet diameters of 30, 50, 70 and 90 μm under an incident shock wave Mach number of 1.3. Novel two-phase flow phenomena are observed when droplet breakup occurs. First, droplets near the two-pha…
This study aims to build a theoretical model to describe the ignition process of spherical spray flame laden with fuel droplets under overall fuel-lean condition. Two characteristic fronts are introduced to reveal where the evaporation starts and ends in the ignition process. The results demonstrate that the flame has been strengthened with extra fuel droplet adding while the minimum ignition energy (MIE) is decreased. The evolution of the two evaporation fronts in the flame kernel and propagating branches has also be revealed coupled with the evaporation zone length.
The flow in an evaporating glycerol-water binary sub-millimeter droplet with Bond number Bo $\ll$ 1 is studied both experimentally and numerically. First, we measure the flow fields near the substrate by micro-PIV for both sessile and pendant droplets during the evaporation process, which surprisingly show opposite radial flow directions -- inward and outward, respectively. This observation clearly reveals that in spite of the small droplet size, gravitational effects play a crucial role in controlling the flow fields in the evaporating droplets. We theoretically analyze that this gravity-driv…
The stationary single vortex Marangoni convection in an axially symmetrical sessile drop of capillary size is considered. The detailed description of the fluid flows is presented for a wide range of contact angles, which takes into account the boundary conditions and the mass balance equation, without explicitly solving the Navier--Stokes equations. The analytical approach developed is compared with the results of numerical simulations and demonstrated to describe reasonably well the single-vortex Marangoni flows. This indicates the substantial role of the boundary conditions in the problem.
The deposition of particles on a surface by an evaporating sessile droplet is important for phenomena as diverse as printing, thin-film deposition and self-assembly. The shape of the final deposit depends on the flows within the droplet during evaporation. These flows are typically determined at the onset of the process by the intrinsic physical, chemical and geometrical properties of the droplet and its environment. Here, we demonstrate deterministic emergence and real-time control of Marangoni flows within the evaporating droplet by an external point-source of vapor. By varying the source lo…
A finite element model was developed to compute the fluid flow inside a sessile evaporating droplet on hydrophilic substrate in ambient conditions. The evaporation is assumed as quasi-steady and the flow is considered as axisymmetric with a pinned contact line. The Navier-Stokes equations in cylindrical coordinates were solved inside the droplet. Galerkin weight residual approach and velocity pressure formulation was used to discretise the governing equations. Six node triangular mesh and quadratic shape functions were used to obtain higher accuracy solutions. Radial velocity profiles in axial…
The Greek aperitif Ouzo is not only famous for its specific anise-flavored taste, but also for its ability to turn from a transparent miscible liquid to a milky-white colored 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 [H. Tan et al., Proc. Natl. Acad. Sci. USA 113(31) (2016) 8642]. Due to the enhanced evaporation n…
Hypothesis: Evaporation of surfactant droplets on leaves is complicated due to the complex physical and chemical properties of the leaf surfaces. However, for certain leaf surfaces for which the evaporation process appears to follow the standard constant-contact-radius or constant-contact-angle modes, it should be possible to mimic the droplet evaporation with both a well-chosen synthetic surface and a relatively simple mathematical model. Experiments: Surfactant droplet evaporation experiments were performed on two commercial crop species, wheat and capsicum, along with two synthetic surfaces…
We study the evolution of the mass of evaporating single microdroplets of sodium do-decyl sulphate (SDS) / diethylene glycol (DEG) mixture. First, we recognise and deconvolute the influence of residual water evaporation [Kolwas et al. Soft Matter 2019;15:1825], which accelerates the composite droplet evaporation, a simple exponential decay of the evaporating droplet surface change rate. This enables us to study the influence of SDS concentration on the composite droplet evaporation. Next, we establish a simple relationship between the average SDS concentration and the droplet evaporation rate …
We investigate numerically quasi-steady internal flows in an axially symmetrical evaporating sessile droplet depending on the ratio of substrate to fluid thermal conductivities, fluid volatility, contact angle and droplet size. Temperature distributions and vortex structures are obtained for droplets of 1-hexanol, 1-butanol and ethanol. To this purpose, the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the droplet and substrate and diffusion of vapor in air have been jointly taken into account. The equations have been solved by finite element method using A…
Atomization of emulsion droplets is ubiquitous across a variety of application domains ranging from NextGen combustors to fabrication of biomedical implants. An understanding of the atomization mechanism in emulsions can result in a paradigm shift in customized designs of efficient systems, be it in energy or biotechnology sectors. In this paper, we specifically study the breakup mechanism of an evaporating contact-free (acoustic levitation) emulsion droplet (water-oil) under external heating. Three distinct regimes are observed during the lifespan of the evaporating droplet. Initially, the dr…
Eulerian-Lagrangian simulations are conducted for two-dimensional Rotating Detonative Combustion (RDC) fueled by bi-disperse n-heptane sprays without any fuel pre-vaporization. Parametric studies are performed to study the influences of droplet diameter and droplet distribution on detonation wave are studied. The extinction process of the detonation wave is also been analyzed. It is found that small n-heptane droplets (e.g., 2 um) are completely vaporized in the fuel refilling area. Increasing the droplet diameter causes the droplet to fail to evaporate completely within the fuel refilling are…
An analysis of the projectile motion in stagnant air is presented for an evaporating respiratory micro-droplet which has been ejected from the mouth as an isolated droplet. It is assumed that the air resistance is a nonlinear function of the droplet's velocity and that the rate of decrease of the droplet's external surface area depends only on the relative humidity and the ambient temperature. The droplet's initial content is considered to be 98 wt% water, 1 wt% salt and 1 wt% protein. The change of the average density of the droplet due to water evaporation is determined, up to the instant wh…
A new mathematical analysis of exhaled respiratory droplet dynamics and settling distances in the vicinity of vortical environments is presented. Recent experimental and theoretical studies suggest that vortical flow structures may enhance the settling distances of exhaled respiratory droplets beyond the two-meter distancing rule recommended by health authorities lately. We propose a mathematical framework to study the underlying physical mechanism responsible for the entrapment and subsequently delayed settling times of evaporating droplets and solid particles. A dipolar vortex is considered …
The pioneering work of Deegan et al. [Nature 389, (1997)] showed how a drying sessile droplet suspension of particles presents a maximum evaporating flux at its contact line which drags liquid and particles creating the well known coffee stain ring. In this Fluid Dynamics Video, measurements using micro Particle Image Velocimetry and Particle Tracking clearly show an avalanche of particles being dragged in the last moments, for vanishing contact angles and droplet height. This explains the different characteristic packing of the particles in the layers of the ring: the outer one resembles a cr…
Building on the recent theoretical work of Wray, Duffy and Wilson [J. Fluid Mech. 884, A45 (2020)] concerning the competitive diffusion-limited evaporation of multiple thin sessile droplets in proximity to each other, we obtain theoretical predictions for the spatially non-uniform densities of the contact-line deposits (often referred to as "coffee stains" or "ring stains") left on the substrate after such droplets containing suspended solid particles have completely evaporated. Neighbouring droplets interact via their vapour fields, which results in a spatially non-uniform "shielding" effect.…
Phase segregation triggered by selective evaporation can emerge in multicomponent systems, leading to complex physiochemical 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 behavior (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 experimentally reveal the over…
The evaporation of dispersed, liquid droplets in jet-sprays occurs in several industrial applications and in natural phenomena. Despite the relevance of the problem, a satisfactory comprehension of the mechanisms involved has not still be achieved because of the wide range of turbulent scales and the huge number of droplets involved. In this context, we address a DNS of a turbulent jet spray at relatively high Reynolds number, i.e. Re=10,000. We focus on the effect of the jet Re on the evaporation process and the preferential segregation of droplets, comparing the outcomes also with a DNS at l…
Evaporating liquid droplets are omnipresent in nature and technology, such as in inkjet printing, coating, deposition of materials, medical diagnostics, agriculture, food industry, cosmetics, or spills of liquids. While the evaporation of pure liquids, liquids with dispersed particles, or even liquid mixtures has intensively been studied over the last two decades, the evaporation of ternary mixtures of liquids with different volatilities and mutual solubilities has not yet been explored. Here we show that the evaporation of such ternary mixtures can trigger a phase transition and the nucleatio…
We investigate evaporation of a sessile droplet on a non-wetted surface in the framework of diffusion-limited and quasi-steady evaporation. We extend previous models and numerically solve Laplace equation for the diffusion of liquid vapor in ambient. We propose a unified, simple and accurate expression of the evaporation mass flux valid for 90^o < theta < 180^o, where theta is the equilibrium contact angle. In addition, using the derived expression of the evaporation mass flux, we propose a simple and accurate expression of the evaporation mass rate for a non-wetted surface, which does not exh…
A model is developed for describing the transport of charged colloidal particles in an evaporating sessile droplet on the electrified metal substrate in the presence of a solvent flow. The model takes into account the electric charge of colloidal particles and small ions produced by electrolytic dissociation of the active groups on the colloidal particles and solvent molecules. We employ a system of self-consistent Poisson and Nernst--Planck equations for electric potential and average concentrations of colloidal particles and ions with the appropriate boundary conditions. The fluid dynamics, …
Ring-shaped deposits can be often found after a droplet evaporates on a substrate. If the fluid in the droplet is a pure liquid and its contact line remains pinned during the process, the mechanism behind such ring-shaped deposition is the well-known coffee-stain effect. However, adding small amounts of salt to such a droplet can change the internal flow dramatically and consequently change the deposition mechanism. Due to an increase of surface tension in the contact line region, a Marangoni flow arises which is directed from the apex of the droplet towards the contact line. As a result, part…
The effect of evaporation on droplet sedimentation times is crucial for estimating the risk of infection from virus-containing airborne droplets. For droplet radii in the range 100 nm < R < 60 μm, evaporation can be described in the stagnant-flow approximation and is diffusion limited. Analytical equations are presented for the droplet evaporation rate, the time-dependent droplet size and the sedimentation time, including the significant effect of evaporation cooling. Evaporation makes the time for large droplets to sediment much longer and thus significantly increases the viral air load. Usin…
The evaporation of droplets occurs in a large variety of natural and technological processes such as medical diagnostics, agriculture, food industry, printing, and catalytic reactions. We study the different droplet morphologies adopted by an evaporating droplet on a surface with an elliptical patch with a different contact angle. We perform experiments to observe these morphologies and use numerical calculations to predict the effects of the patched surfaces. We observe that tuning the geometry of the patches offers control over the shape of the droplet. In the experiments, the drops of vario…
Evaporation-driven particle self-assembly can be used to generate three-dimensional microstructures. We present a new method to create these colloidal microstructures, in which we can control the amount of particles and their packing fraction. To this end, we evaporate colloidal dispersion droplets on a special type of superhydrophobic micro-structured surface, on which the droplet re- mains in Cassie-Baxter state during the entire evaporative process. The remainders of the droplet consist of a massive spherical cluster of the microspheres, with diameters ranging from a few tens up to several …
Evaporating salty droplets are ubiquitous in nature, in our home and in the laboratory. Interestingly, the transport processes in such apparently simple systems differ strongly from evaporating "freshwater" droplets since convection is partly inverted due to Marangoni stresses. Such an effect has crucial consequences to the salt crystallization process and to the deposits left behind. In this work we show unprecedented measurements that, not only confirm clearly the patterns of the flow inversion, but also elucidate their impact on the distribution of non-volatile solutes. Contrary to what has…
The dispersion of respiratory saliva droplets by indoor wake structures may enhance the transmission of various infectious diseases, as the wake spreads virus-laden droplets across the room. Thus, this study analyses the interaction between vortical wake structures and exhaled multi-component saliva droplets. A self-propelling analytically-described dipolar vortex is chosen as a model wake flow, passing through a cloud of micron-sized evaporating saliva droplets. The droplets' spatial location, velocity, diameter, and temperature are traced and coupled to their local flow field. For the first …
We investigate deposit patterns and associated morphology formed after the evaporation of an aqueous droplet containing mono- and bi-dispersed colloidal particles. In particular, the combined effect of substrate heating and particle diameter is investigated. We employ high-speed visualization, optical microscopy and scanning electron microscopy to characterize the evaporating droplets, particle motion, and deposit morphology, respectively. In the context of mono-dispersed colloidal particles, an inner deposit and a typical ring form for smaller and larger particles, respectively, on a nonheate…
A theoretical framework is established to model the evaporation from continuously fed droplets, promising tools in the thermal management of high heat flux electronics. Using the framework, a comprehensive model is developed for a hemispherical water droplet resting on a heated flat substrate incorporating all of the relevant transport mechanisms: buoyant and thermocapillary convection inside the droplet and diffusive and convective transport of vapor in the gas domain. At the interface, mass, momentum, and thermal coupling of the phases are also made accounting for all pertinent physical aspe…
This paper presents an experimental study on thermal transport to single water droplets evaporating on heated bi-phobic surfaces consisting of a superhydrophobic matrix with a circular hydrophobic pattern with strong contact line pinning. A single water droplet of 8 ul volume is placed on a preheated surface and allowed to evaporate in an open laboratory environment. We investigate the influence of substrate orientation (horizontal and vertical) on evaporation dynamics. Using optical and infrared imaging, we report droplet fluid dynamics and heat transfer characteristics of the evaporating dro…
In this work, we unravel the role of surface properties of colloidal particles on the formation of supraparticles (clusters of colloidal particles) in a colloidal Ouzo droplet. Self-lubricating colloidal Ouzo droplets are an efficient and simple approach to form supraparticles, overcoming the challenge of the coffee stain effect in situ. Supraparticles are an efficient route to high-performance materials in various fields, from catalysis to carriers for therapeutics. Yet, the role of the surface of colloidal particles in the formation of supraparticles using Ouzo droplets remains unknown. Ther…
We experimentally investigate the profile and morphology of the ring-like deposits obtained after evaporation of a sessile water droplet containing polystyrene colloidal particles on a hydrophilic glass substrate. In particular, the coupled effect of particle size and concentration are studied. The deposits were qualitatively visualized under an optical microscope and profile of the ring was measured by an optical profilometer. The profile of the ring resembles a partial torus-like shape for all cases of particles size and concentration. The cracks on the surface of the ring were found to occu…
The shape of deposits obtained from drying drops containing colloidal particles matters for technologies such as inkjet printing, microelectronics and bioassay manufacturing. In this work, the formation of deposits during the drying of nanoliter drops containing colloidal particles is investigated experimentally with microscopy and profilometry, and theoretically with an inhouse finite-element code. The system studied involves aqueous drops containing titania nanoparticles evaporating on a glass substrate. Deposit shapes from spotted drops at different pH values are measured using a laser prof…
A colloidal dispersion droplet evaporating from a surface, such as a drying coffee drop, leaves a distinct ring-shaped stain. Although this mechanism is frequently used for particle self-assembly, the conditions for crystallization have remained unclear. Our experiments with monodisperse colloidal particles reveal a structural transition in the stain, from ordered crystals to disordered packings. We show that this sharp transition originates from a temporal singularity of the flow velocity inside the evaporating droplet at the end of its life. When the deposition speed is low, particles have t…
