Binary Droplet Research Articles

Numerical investigation of impacting heat transfer of binary droplets on superhydrophobic substrates

The droplet impacting on a substrate is widely encountered in daily life and industrial applications. In this paper, the impact dynamics and heat transfer are numerically simulated for both single droplet and binary droplets on a hot superhydrophobic substrate. The dimensionless numerical model is built up through the transient 2D axisymmetric model with a volume of fluid (VOF) model. The effect of the Weber number, Reynolds number, size ratio, contact angle on the spreading dynamics and heat transfer is investigated in details. It is found that the spreading factor and contact time increase with the increasing Weber number. Besides, the maximum spreading factor and contact time of binary droplets are larger than those of a single droplet under the same Reynolds and Weber numbers. The transient heat transfer rate of a single droplet is larger than that of binary droplets impingement due to larger spreading surface area-to-volume. The total input heat of a single droplet is generally larger than that of binary droplets except at large Weber numbers, and the equal-sized binary droplets have the larger total input heat than un-equal-sized binary droplets. For binary droplets impact on a hot superhydrophobic surface, the hot substrate can promote the spreading and retard the receding due to thermo-capillary effect, and thus will enhance heat transfer between the droplet and the hot substrate. These findings may be helpful in gaining insights into the dynamics and heat transfer of binary droplets impact on the hot substrate.

Extended model of bouncing boundary for droplet collisions considering numerous different liquids

Sprays are widely utilised in different technical and industrial applications. The produced droplet size spectrum is one of the most important parameters that determine the spray characteristics and performance. Depending on the operational conditions and the spray structure, the droplet size spectrum obtained after atomisation will be of course modified by collisions between droplets. In numerical calculations, the Euler/Lagrangian approach is a favourable method for obtaining relatively accurate predictions of spraying processes. However, for correctly modelling droplet collisions, reliable boundary line correlations are needed for distinguishing the different droplet collision outcomes, which are bouncing, coalescence, and separations. These boundary lines are summarised in so-called collision maps to demark the various outcome scenarios. The result of a binary droplet collision depends on numerous parameters, namely, the kinetic properties (droplet velocities, droplet diameter ratio, impact angle) and the physical properties of gas and droplets (droplet liquid, density and viscosity, surface tension, type of gas phase, gas phase pressure and temperature). The boundary line for bouncing, primarily used in numerical studies so far, was derived based on experiments with ethanol droplets by Estrade et al. (1999). However, this theoretical derivation, based on an energy balance, unfortunately neglects viscous dissipation effects. Therefore, the deviations of the predicted bouncing region are pretty large for liquids with higher viscosity or other physical properties. Hence, a data-driven model is proposed in this paper, with new assumptions and definitions, considering the dissipated energy during the collision and the shape changes (i.e., deformation) of the collision complex. For that purpose, two new parameters are introduced in the model, namely a shape factor and an energy conversion rate, both depending on the impact parameter B, which describes the lateral displacement of droplets at a collision. Therefore, the new bouncing model is related to the degree of droplet deformation. The dependence on B could be described by linear correlations with two parameters for slope and intercept. These parameters are correlated with the Ohnesorge number, and polynomial fitting functions were derived with the help of numerous available experiments for different liquids. The upper limit of Ohnesorge numbers in the present study was Oh<0.35. Due to the dependence on the Ohnesorge number, the proposed model very well captures the effect of liquid properties on the bouncing boundary, however, not necessarily the influences of environmental conditions and interface modifications. The model was validated by comparison with numerous available experimental results.

Fingering Instability of Binary Droplets on Oil Pool

The interfacial instability of a complex fluid in a multiphase flow system is ubiquitous in both nature and industry. We experimentally investigated the spreading and interfacial instability dynamics of a binary droplet (a water and 2-propanol (IPA) mixture) on an immiscible (sunflower oil) pool. For droplets of 40 wt% IPA solution on sunflower oil, fingering instability occurred at the spreading liquid front. To reveal the interfacial characteristics of the spreading and fingering processes, we analyzed the interplay among the speed, diameter, and number of fingers on the spreading front. Based on our observations, the finger length, wavelength between the fingers, head length, and neck length were quantified. Our experimental results clearly demonstrate that fingering instability can be driven by the capillary effect for a liquid–liquid system as well as the Plateau–Rayleigh instability. We hope that our results will inspire further experimental and numerical investigations to provide deeper insights into the interfacial dynamics of multicomponent droplets in a liquid pool.

Techno-economic comparative assessment of the ultrasound, electrostatic and microwave supported coalescence of binary water droplets in crude oil

In this study, comparative assessment of the technical performance, energy usage and economic impact of ultrasound, electrostatics and microwave on the coalescence of binary water droplets in crude oil was conducted. The effect of different oil properties such as crude oil viscosity (10.6–106 mPa s) and interfacial tension (IFT) (20–250 mN/m) on the coalescence time and energy consumption was examined. In addition, operation conditions such as inlet emulsion flow velocity (10–100 mm/s), electric field type, ultrasound frequency and applied voltage amplitude (0–30 kV) were evaluated. The numerical models showed good agreement with experimental findings in the literature. Moreover, the process time of the dewatering process increased with rising inlet flow velocities. The elevation of the coalescence time with velocity can be attributed to the increasing effect of flow disturbance, and the reduction of the emulsion residence time. As regards the IFT, the coalescence time reduced as the IFT was increased. This can be associated with the improved stability of emulsions formed at lowered IFT. As the maximum droplet size is directly proportional to the IFT, lowering the IFT reduces the peak diameter of the droplets that are present in the emulsion. Moreover, the coalescence time followed the order: ultrasound < microwave < electrostatics approaches under varying IFT. The coalescence energy increased from ∼15 J, ∼90 J and ∼25 mJ to ∼61 J, ∼235 J and ∼26 mJ for microwave, electrostatics and ultrasound techniques, respectively, as the viscosity was raised from 10.6 to 106 mPa s. Ultrasound coalescence showed significant energy and economic savings in comparison to microwave and electro-coalescence. Hence, ultrasound coalescence would be a potential method for standalone or integrated demulsification over the two other techniques. However, there are indications that beyond a viscosity of 300 mPa s, the effect of ultrasound becomes weak with significant hindrance to droplet movement and accumulation. This analysis provides fundamental insights on the comparative behavior of the three emulsion separation techniques.

A Generalized Finite Difference Scheme for Multiphase Flow

This paper presents a GPU-based, incompressible, multiphase generalized finite difference solver for simulating multiphase flow. The method includes a dampening scheme that allows for large density ratio cases to be simulated. Two verification studies are performed by simulating the relaxation of a square droplet surrounded by a light fluid and a bubble rising in a denser fluid. The scheme is also used to simulate the collision of binary droplets at moderate Reynolds numbers (250–550). The effects of the surface tension and density ratio are explored in this work by considering cases with Weber numbers of 8 and 180 and density ratios of 2:1 and 1000:1. The robustness of the multiphase scheme is highlighted when resolving thin fluid structures arising in both high and low density ratio cases at We = 180.

Volatility effect on internal flow and contact line behavior during evaporation of binary mixture droplets

Selective evaporation of binary mixture droplets (BMDs), a phenomenon in which the more volatile components preferentially evaporate, affects contact line behavior, the total evaporation time, and internal flows, such as the solutal Marangoni flow. The surface tension gradient on a BMD is related to the local concentration of its constituents. We analyzed the dependence of the internal flow and contact line behavior on the relative volatilities of the components of ethanol–water and ethylene glycol–water BMDs. Particle image velocimetry (PIV) and shadowgraph methods were simultaneously used to measure the internal flow field and contact line behavior for a BMD, respectively. The results showed that the volatility properties of BMDs affect nonmonotonic contact line behavior during evaporation. Furthermore, the selective evaporation of a highly volatile component of BMDs results in vorticities, and internal circulation flow directions depend on the liquid composition. The averaged absolute vorticity was used to distinguish different stages of internal flow transitions of BMDs.

Characterizing combustion and atomization of PODEn and ethanol/PODEn binary droplets

Polyoxymethylene dimethyl ethers (PODEn) constitute a promising e-fuel family from CO2 feedstock, while their droplet combustion characteristics are still insufficiently understood. This work reports an experimental investigation on the combustion and atomization characteristics of PODEn (n = 1–4) and ethanol/PODEn binary droplets, with special attentions on the influence of content ratio, highly volatile component, and boiling point difference between components (ΔTbp). History of square of normalized droplet diameter was recorded during the combustion process, from which two stages including stable combustion and atomization can be derived. Three different behaviors, i.e., puffing, ejection, and micro-explosion, were observed in the atomization stage of the investigated binary droplets with ΔTbp generally greater than 50 K, while only puffing and ejection were observed as ΔTbp becomes lower. For PODE1/PODE4 binary droplets, the atomization index which defines the relative reduction of droplet lifetime caused by atomization is found to peak at 70 % PODE1, while for ethanol/PODE4 binary droplets, the atomization index rises quickly at small ethanol content and thus peaks early at 50 % ethanol. This is mainly because that the evaporation propensities of ethanol and PODE4 are both promoted in the ethanol/PODE4 binary droplets as their activity coefficients become greater than one, while those of PODE1 and PODE3 are both suppressed in the PODE1/PODE4 binary droplets. For both PODEn and ethanol/PODEn binary droplets at the fixed content ratio of 50 %/50 %, the atomization delay time and micro-explosion intensity both increase with ΔTbp first and keep almost invariable as the weakly volatile component varies from PODE3 to PODE4, while the atomization index becomes proportional to ΔTbp. On the other hand, the ethanol/PODEn binary droplets generally have higher micro-explosion intensities and consequently higher atomization indices, indicating their stronger atomization propensities than the PODEn binary droplets.

Analytical and experimental study on binary droplet evaporation: Inhibitory effect of adding mineral oil adjuvant to water

This work fundamentally explains the inhibitory effect of adjuvant on water droplet evaporation in pesticide application. An analytical droplet evaporation model coupled with the instantaneous distribution of temperature and species concentrations in the vapor film boundary layer accompanying with the droplet diameter decrease is developed to describe not only the droplet evaporation but also the surrounding boundary layer evolution process. Thermal and concentration boundary layer thicknesses as well as the property variations at the liquid-vapor interface are updated at each time step during the calculation. An adjuvant factor is defined to assess the inhibitory effect of the adjuvant on water droplet evaporation. The results show that adding a tiny amount of mineral oil adjuvant can inhibit water droplet evaporation. The analysis of droplet evaporation evolution demonstrates that the inhibitory effect is mainly controlled by mass diffusion where the concentration gradient surrounding the liquid-vapor interface dominates the overall phase change. A regression formula is introduced to express the dependence of droplet lifetime on temperature and humidity. The proposed model is proved to be suitable for the mixing condition with a tiny amount of adjuvant, which can be used to describe the mechanism of evaporation inhibition of pesticide adjuvant in plant protection.

Sequentially Selective Coalescence of Binary Self-Propelled Droplets upon Collective Motion

Subsequent synthesis and detection using droplets as microreactors have shown promise in the development of novel materials and drugs because microreactors enable small-scale synthesis and detection of covalent/non-covalent intermolecular interactions. Self-organization exhibited by autonomous droplets under non-equilibrium conditions is beneficial for manipulating the sequentiality and selectivity of droplet coalescence because expensive equipment or elaborate techniques are not required with the autonomy of droplets. However, to our knowledge, selective coalescence caused by the collective motion of self-propelled droplets has not been demonstrated in inanimate systems. Here, we report sequentially selective coalescence based on the dynamic collective pattern of self-propelled droplets composed of ethyl salicylate (ES) or butyl salicylate (BS). When ES and BS droplets were placed on an aqueous sodium dodecyl sulfate (SDS) solution, the collective motion of droplets resulted in three stages of selective coalescence on the time development. Initially, coalescence was observed only between different types of self-propelled droplets. Subsequently, the formed droplets selectively coalesced with ES droplets. Finally, mature droplets merged with BS droplets. The sequentially selective coalescence was discussed from the dynamic pattern formation of swarming droplets and the collapse of the SDS monolayer at the o/w interface caused by the difference in Laplace pressure and the interfacial instability at the contact point between droplets. Thus, this study formulates a strategy of sequentially selective coalescence of droplets via the collective motion of non-identical self-propelled droplets, promoting a new type of powerful and efficient automation technology based on an autonomous inanimate manner of spatiotemporal pattern formation under non-equilibrium conditions for the droplet manipulation.

Diverse wetting behavior of a binary mixture of antagonist liquids: Nanodroplet with finite precursor film and leak-out phenomenon

The binary mixtures containing the partial and total wetting liquids corresponding to a specified substrate are commonly seen. However, studies of their wetting behavior, particularly the leak-out phenomenon, are very scarce. The wetting state of a nanodroplet of the binary mixture on a smooth substrate is investigated by Many-body dissipative particle dynamics. The influences of the molecular size of the partial wetting liquid and the affinity between the two liquids on the leak-out phenomenon are examined. Dependent on the mixture composition (ϕp), three wetting regimes of the nanodroplet can be identified: (I) total wetting, (II) partial wetting with precursor film, and (III) partial wetting. The binary droplet always spreads spontaneously in regime (I), while its contact angle (CA) changes with the composition monotonously in regime (III). However, in regime (II), the CA remains constant regardless of the composition. The droplet morphology exhibits the fried-egg shape, a spherical cap surrounded by a precursor film. The compositions in both egg yolk and egg white regions remain unaltered for varying ϕp in the plateau regime (II). Although the affinity between the two liquids is strong, some of the total wetting liquid always escape from the spherical cap to precursor film in regime (II), the so-called leak-out phenomenon. The outcome can be beneficial to the application of nanotechnologies such as lithography and microfluidics.

Light-manipulated binary droplet transport on a high-energy surface.

Flexible and precise manipulation of droplet transport is of significance for scientific and engineering applications, but real-time and on-demand droplet manipulation remains a challenge. Herein, we report a strategy using light for the outstanding manipulation of binary droplet motion on a high-energy surface and reveal the underlying mechanism. Upon irradiation to a substrate by a focused light beam, the substrate can provide a localized heating source via photothermal conversion, and a binary droplet can be flexibly transported on a high-energy surface with free contact-line pinning, exhibiting light-propelled droplet transport. We theoretically showed that the surface tension gradient across the droplet interface resulting from the localized photothermal effect is responsible for actuating droplet transport. Remarkably, the high reconfigurability and flexibility of light allowed for binary droplet transport with dynamically tunable velocity and direction as well as arbitrary trajectory assisted by 2D channels on a high-energy surface. Complex droplet transportation, controllable droplet coalescence, and anti-gravity motion were realized. The promising applicability of this light-fueled droplet platform was also demonstrated by directional transport of biosample droplets containing DNA molecules and cells, as well as successional microreactions.

Phase Field Modeling of Air Entrapment in Binary Droplet Impact with Solidification Microstructure Formation

A novel numerical model was developed to investigate air entrapment in binary droplet impact with solidification microstructure formation under practical plasma spraying conditions. The evolving liquid–gas interface was tracked by the explicit finite difference solution to the Cahn–Hilliard equation, coupled with the Navier–Stokes equations. Another diffuse interface model was invoked to trace solid–liquid and grain–grain boundaries. The model was discretized using an explicit finite difference method on a half-staggered grid. The velocity pressure coupling was decoupled with the projection method. The in-house code was written in Fortran and was run with the aid of the shared memory parallelism, OpenMP. The time duration over which gas compressibility matters was estimated. Typical cases with air entrapment were studied with the model. The effect of droplet porosity on air entrapment was probed into as well: the larger the porosity of a droplet, the bigger the trapped air bubble. The grain growth near the air bubble is skewed. Moreover, a case without air entrapment was also shown herein to stress that air bubbles could be suppressed or even eliminated in plasma spraying by adjusting the landing positions of successive droplets.

Multiple Marangoni flows in a binary mixture sessile droplet

A multicomponent droplet evaporation problem has widely been investigated due to diverse industrial applications, including ink-jet printing, surface coating and patterning, medical diagnosis, spraying cooling, and fuel combustion. During evaporation, the Marangoni flow caused by selective evaporation should be observed, and it plays an important role in determining the drying process and the final dried deposit pattern. However, most of the works focused on measuring the internal flow field although the Marangoni flow mainly occurred near the liquid–gas interface. In this study, using particle image velocimetry, we tried to measure the interfacial Marangoni flows where the measurement focal plane was set in the vicinity of the apex of the binary mixture droplet. We observed distinctive multiple Marangoni flows in time, such as (i) directional circulating flow, (ii) complicated mixing flow, and (iii) spontaneous bursting flow. Finally, we found that the Reynolds number is different for each case. Based on the flow field measurement result and dimensionless number analysis, we considered a stress balance model that qualitatively described the local surface tension gradient and Marangoni stress.

Influences of Liquid Viscosity and Relative Velocity on the Head-On Collisions of Immiscible Drops

Many researchers have devoted themselves to the collision processes of binary droplets of the same liquid. However, the liquids used in their study were limited, and the phase diagram of the collision outcome was depicted in terms of the Weber and the non-dimensional impact parameter. In this research, the variety of liquid was broadened, and the phase diagram characterized by the Weber number and the Ohnesorge number for head-on collisions of immiscible drops was provided. First, a ternary flow model of binary collision of immiscible drops in quiescent ambient air was proposed. Second, the three-phase fluid interface was tracked and updated by iterating the VOF (Volume of Fluid) functions. The flow field was also updated with the PISO (Pressure-Implicit with Splitting of Operators) algorithm. Finally, the effects of the impact velocity and the viscosities of the liquids on the deformation degree of droplets were analyzed.

Relationship between Onset of Sliding Behavior and Size of Droplet on Inclined Solid Substrate.

Whether a droplet slides or not on inclined solid surface is mainly influenced by a balance between the adhesion force at contact area and the gravitational force exerted on the droplet. Especially as the adhesion force is a key parameter for the determination of the sliding behavior of droplets. The adhesion force is mainly estimated by experimental observation for the sliding motion of the droplet. However, at present it is unknown whether the adhesion force is a constant value regardless of the droplet size or not. In the present study, focused on the onset for sliding of water-ethanol binary mixture droplets on inclined solid surface, experimental investigation on the sliding droplets is performed by considering the droplet volumes ranging from 7 to 600 μL in order to understand the effect of the size of the droplet on the adhesive property. The results are discussed using the existing analytical models. From the results, it is found that the adhesion force increases in the case of large droplet volume, while the force reaches constant value in the case of small droplet volume. This difference is related to the degree of the droplet shape deformation, which leads to a change in the contact angle. Finally, a simple empirical model for the adhesion force including the size effect is proposed.

Quantum phases of self-bound droplets of Bose-Bose mixtures

We systematically investigate the ground-state properties of self-bound droplets of quasi-two-dimensional binary Bose gases by using the Gaussian state theory. We find that quantum droplets consists two macroscopic squeezed phases and a macroscopic coherent phase. We map out the phase diagram and determine all phase boundaries via both numerical and nearly analytical methods. In particular, we find three easily accessible signatures for the quantum phases and the stablization mechanism of the self-bound droplets by precisely measuring their radial size. Our studies indicate that binary droplets represent an ideal platform for in-depth investigations of the quantum nature of the droplet state.

Evaporation of a Sessile Colloidal Water-Glycerol Droplet: Marangoni Ring Formation.

The transport and aggregation of particles in suspensions is an important process in many physicochemical and industrial processes. In this work, we study the transport of particles in an evaporating binary droplet. Surprisingly, the accumulation of particles occurs not only at the contact line (due to the coffee-stain effect) or at the solid substrate (due to sedimentation) but also at a particular radial position near the liquid–air interface, forming a “ring”, which we term as the Marangoni ring. The formation of this ring is primarily attributed to the solutal Marangoni flow triggered by the evaporation dynamics of the water–glycerol droplet. Experiments and simulations show fair agreement in the volume evolution and the general structure of the solutal Marangoni flow, that is, the Marangoni vortex. Experiments show that the location of the Marangoni ring is strongly correlated with the Marangoni vortex. However, finite element numerical simulations fail to describe the particle distribution seen in the experiments. Interestingly, the particles not only accumulate to form the Marangoni ring but also assemble as colloidal crystals close to the liquid–air interface, yielding iridescence. The formation of the colloidal crystals in the experiments is strong evidence that non-hydrodynamic interactions, which are not represented in the simulations, also play a significant role in our system.

Simulation of two-phase flows at large density ratios and high Reynolds numbers using a discrete unified gas kinetic scheme

In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a three-dimensional code based on the discrete unified gas kinetic scheme (DUGKS) is developed, incorporating two major improvements. First, the particle distribution functions at cell interfaces are reconstructed using a weighted essentially non-oscillatory scheme. Second, the conservative lower-order Allen–Cahn equation is chosen instead of the higher-order Cahn–Hilliard equation to evolve the free-energy-based phase field governing the dynamics of two-phase interfaces. Five benchmark problems are simulated to demonstrate the capability of the approach in treating two-phase flows at large density ratios and high Reynolds numbers, including three two-dimensional problems (a stationary droplet, Rayleigh–Taylor instability, and a droplet splashing on a thin liquid film) and two three-dimensional problems (binary droplets collision and Rayleigh–Taylor instability). All results agree well with the previous numerical and experimental results. In these simulations, the density ratio and the Reynolds number can reach a large value of O(1000). Our improved approach sets the stage for the DUGKS scheme to handle realistic two-phase flow problems.

Non-monotonic effect of ethanol concentration on the spreading of an ethanol-water binary droplet impact on a supercooled surface

We investigate the effect of ethanol concentration on the spreading dynamics of an ethanol-water binary droplet impact on a supercooled surface. The maximum spreading factor, comprised of the maximum internal spreading factor and dimensionless fingering length, decreases and then increases with the ethanol concentration. It is attributed to the change in ethanol concentration which varies liquid viscosity and surface tension directly, and surface cooling which lowers the droplet temperature and thus varies liquid properties that further affect droplet spreading. The maximum internal spreading factor which is also non-monotonic with the ethanol concentration dominates the maximum spreading. The heat transfer analysis on droplet spreading shows that the temperature reduction of the droplet from impact to maximum spreading is non-monotonic dependent on the ethanol concentration, while shows different trends with surface cooling at various ethanol concentration. Deviations of the predicated maximum spreading factor, considering the droplet temperature reduction, obtained by reported correlations from the experimental ones in this study could be mainly due to the difficulty in accurately predicting the temperature-dependent spreading boundary layer thickness of the droplet. The maximum spreading time decreases and then increases with the ethanol concentration, while it keeps decreasing with the surface supercooling. A new correlation of the maximum spreading time is proposed by incorporating the coefficient of surface supercooling and capillary-inertial time of the droplet which involves density and surface tension.

Particulate-Droplet Coalescence and Self-Transport on Superhydrophobic Surfaces.

Particulate transport from surfaces governs a variety of phenomena including fungal spore dispersal, bioaerosol transmission, and self-cleaning. Here, we report a previously unidentified mechanism governing passive particulate removal from superhydrophobic surfaces, where a particle coalescing with a water droplet (∼10 to ∼100 μm) spontaneously launches. Compared to previously discovered coalescence-induced binary droplet jumping, the reported mechanism represents a more general capillary-inertial dominated transport mode coupled with particle/droplet properties and is typically mediated by rotation in addition to translation. Through wetting and momentum analyses, we show that transport physics depends on particle/droplet density, size, and wettability. The observed mechanism presents a simple and passive pathway to achieve self-cleaning on both artificial as well as biological materials as confirmed here with experiments conducted on butterfly wings, cicada wings, and clover leaves. Our findings provide insights into particle-droplet interaction and spontaneous particulate transport, which may facilitate the development of functional surfaces for medical, optical, thermal, and energy applications.