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We explore the transient evolution of thermo-fluid-dynamics of evaporating sessile droplets over curved substrates in the liquid and gaseous domains. A computational model using the Arbitrary Lagrangian-Eulerian framework is adopted. The governing equations in both liquid and gaseous domains are solved in a fully coupled manner, considering coupled effects of evaporative cooling and heat advection due to bulk fluid motion. This bulk motion in the liquid domain is caused by natural advection due to thermal actuations such as thermal Marangoni flow and buoyancy-driven convection. For the gaseous domain, the additional effects of solutal convection (due to vapour-concentration variation), Stefan flow and interfacial viscous stresses are also considered. To depict a generalized role of substrate curvature, both concave and convex surfaces with curvatures over a wide range are studied. The surface wettability effects are also explored by varying the true contact angle of the droplets. Computational predictions on evaporation rate and internal flow field are validated against experimental results from literature. The interplay of wetting state and substrate curvature is noted to substantially affect the evaporation process and its thermo-fluidics. The convex curvature significantly augments internal advection while the same is weakened over concave substrates due to altered mass loss rate. Consequently, the duration of multi-vortex Marangoni flows in the development stages of evaporation and the advection in the external gaseous domain is markedly different for different curvatures. Further, on superhydrophobic curved surfaces, the effects of re-distributed evaporative fluxes play a major role. In such cases, the reduced mass flux over a large interfacial area near the periphery expedites the stable state Marangoni and external flow features. [ABSTRACT FROM AUTHOR]

We investigate the effect of ultrasound on the evaporation and crystallization of sessile NaCl solution droplets which were positioned in traveling or standing wave ultrasound field. The experimental results indicated that the ultrasound field can significantly accelerate the evaporation rate of the sessile droplets and refine the crystal grains. By adjusting the distance between the sessile droplets and the ultrasound emitter, it is found that, in traveling wave ultrasound field, the sessile droplet evaporation time and the time for the appearance of NaCl grains exhibited a fluctuating increase as the droplet-emitter distance increased. While in the standing wave ultrasound, the sessile droplet evaporation rate increases with the increasing droplet-emitter distance. Overall, the traveling wave ultrasound field has a stronger effect on grain refinement of the sessile droplets than the standing wave ultrasound field. The grain refinement is attributed to the decrease of critical nucleation radius caused by ultrasound energy and the increase of the nucleation rate caused by the accelerated evaporation rate. In addition, the breakage of grains caused by ultrasonic cavitation would also lead to grain refinement.

[Display omitted] Sessile droplets solubilizing in surfactant solution are frequently encountered in practice, but the factors governing their non-equilibrium dynamics are not well understood. Here, we investigate mechanisms by which solubilizing, sessile oil droplets in aqueous surfactant solution dewet from hydrophobic substrates and spread on hydrophilic substrates. We quantify the dependence of droplet contact line dynamics on drop size and oil, surfactant, and substrate chemistries. We consider halogenated alkane oils as well as aromatic oils and focus on common nonionic nonylphenol ethoxylate surfactants. We correlate these results with measurements of the interfacial tensions. Counter-intuitively, under a range of conditions, we observe complete dewetting of oil from hydrophobic substrates but spreading on hydrophilic substrates. The timescales needed to reach a steady-state contact angle vary widely, with some droplets examined taking over a day. We find that surfactant surface adsorption governs the contact angle on shorter timescales, while partitioning of surfactant from water to oil, and oil solubilization into the water, act on longer timescales to facilitate the complete dewetting. Understanding of the role played by surfactant and oil transport presents opportunities for tailoring sessile droplet behaviors and controlling droplet dynamics under conditions that would previously not have been considered. [ABSTRACT FROM AUTHOR]

The phenomenon of droplets impacting droplets is common in many fields including the chemical, nuclear, and aerospace industries. In this paper, highspeed photography technology is used to obtain the variation law and evolution properties exhibited by droplets colliding with sessile droplets of varying sizes. We further explored how the Weber number (We) and volume ratio (Vp/Vi) influence the behavior of droplets colliding with sessile droplets. The phenomenon of droplets impacting sessile droplets of different volumes is different from that of droplets impacting liquid films. In terms of droplet spreading, compression and the non-splashing liquid crown, the phenomena and laws reported in the present study are applicable for 1 ≤ We ≤ 165 and droplet volume ratios of 1 ≤ Vp/Vi ≤ 6. With a low Weber number, the droplet compresses and deforms downward without coalescence at the initial stage of collision. A high Weber number results in a no-splashing liquid crown. These findings provide important insights into the dynamics of droplet-droplet interactions. [ABSTRACT FROM AUTHOR]

The phenomenon of droplets impacting droplets is common in many fields including the chemical, nuclear, and aerospace industries. In this paper, high-speed photography technology is used to obtain the variation law and evolution properties exhibited by droplets colliding with sessile droplets of varying sizes. We further explored how the Weber number (We) and volume ratio (Vp/Vi) influence the behavior of droplets colliding with sessile droplets. The phenomenon of droplets impacting sessile droplets of different volumes is different from that of droplets impacting liquid films. In terms of droplet spreading, compression and the non-splashing liquid crown, the phenomena and laws reported in the present study are applicable for 1 ≤ We ≤ 165 and droplet volume ratios of 1 ≤ Vp/Vi ≤ 6. With a low Weber number, the droplet compresses and deforms downward without coalescence at the initial stage of collision. A high Weber number results in a no-splashing liquid crown. These findings provide important insights into the dynamics of droplet-droplet interactions.

We report experimental findings on the formation of salt deposits upon the complete evaporation of a sessile droplet containing sodium chloride. We also offer both quantitative and qualitative information to help comprehend the intricate mechanisms underlying the evaporation problem. We propose a mechanism for solutal instability that aligns with our experimental results and literature findings. During the solute crystallization and eventual deposit formation, we observe two phases: the first phase, where crystal growth is absent, spans from the initial time to 65 % of the evaporation duration. The second phase occurs when the chemical process of crystallization sets in. We provide quantitative data on the crystallization process, utilizing the normalized average distance between crystals as a function of relative humidity and initial salt concentration. [ABSTRACT FROM AUTHOR]

A significant growth of research on digital microfluidics has been achieved over the past several decades, and the field is still attracting increasing attention for fulfilling relevant mechanisms and potential applications. Numerous studies have been devoted to actively manipulating droplets in a variety of fundamental and applicational scenarios. In this work, the deformation of ferromagnetic fluid droplets is studied under an external uniform magnetic field. The droplets are precisely dispersed on the bottom surface of a container assembled with polymer methacrylate (PMMA) plates. Mineral oil is applied instead of air as the surrounding medium for easy stretching and preventing water solvent evaporation in ferrofluid. The design and processing of the container are firstly carried out to observe the shape and characterize the wettability of the droplets in the immiscible mineral oil medium. Furthermore, the droplets' deformation and the working mechanism are given under the action of the horizontal uniform magnetic field. At different magnetic field intensities, the droplet is stretched in the horizontal direction parallel to the applied field. Due to volume conservation, the dimension in the height reduces correspondingly. With the coupling effect of magnetic force, viscous force and interfacial tension, the contact angle first increases with the magnetic field and then basically remains unchanged upon magnetization saturation. Consistent with the experimental results, the numerical method clearly reveals the field coupling mechanism and the nonlinear deformation of the sessile droplet. [ABSTRACT FROM AUTHOR]

We analytically solve the Young–Laplace equation for the shape of a stationary sessile droplet pinned to an inclined substrate, assuming that the droplet’s contact line is circular. In the absence of gravity (or an equivalent external field), a sessile droplet takes the form of a spherical cap. Here, we calculate deviations from this ideal geometry when gravitational effects are non-negligible. Our calculations are based on a perturbation solution in powers of the Bond number Bo, which is a dimensionless parameter measuring the strength of gravity relative to surface tension. The newly derived solution is second-order accurate and builds on our previous work (Timm et al. in Sci Rep 9:19803, 2019), where only the leading-order contributions were calculated. We consider the full range of substrate inclination angle from 0 to π and show that, when the second-order corrections are taken into account, the droplet’s profile is captured more precisely and the volume-conservation error of the solution is reduced considerably, all at a modest computational cost. We also find that our solution accurately approximates the gravity-induced deformation of the droplet for a wide range of droplet volumes and Bond numbers. As an example, we can very well predict the distorted shape of a droplet that is hemispherical at zero gravity up to Bo ≈ 4 , 1.25, and 2.5 when the substrate is tilted from horizontal by 0, π / 2 , and π , respectively. Among other applications, the outcome of our study can serve as the first step toward analyzing the evaporation of sessile droplets deformed by gravity. [ABSTRACT FROM AUTHOR]

We present a sessile droplet manipulation platform that enables the formation and transport of a droplet on a light-absorbing surface via local laser-beam irradiation. The mechanism relies on solutocapillary Marangoni flow arising from a concentration gradient in a binary mixture liquid. Because the mixture is strongly confined in a two-dimensional slit with a spacing of a few micrometers, the wetting film is stably sustained, enabling the rapid formation, deformation, and transport of a sessile droplet. In addition, to sustain the droplet in the absence of laser irradiation, we developed a method to bridge the droplet between the top and bottom walls of the slit. The bridge is stably sustained because of the hydrophilicity of the slit wall. Splitting and merging of the droplet bridges are also demonstrated. [ABSTRACT FROM AUTHOR]

Surfaces with tailored wettability have attracted considerable attention because of their wide range of potential applications. Wettability can be finely designed by controlling the chemistry and/or morphology of a surface. However, the commonly adopted analytical theories of Wenzel and Cassie-Baxter cannot describe a variety of intermediate and metastable states, being a thorough understanding of the combined chemical and morphological effect on surface wettability still lacking. Hence, the design and optimization of these surfaces is generally expensive and time-consuming. In this work, we propose a numerical method based on the phase-field model to predict the wettability of micro-structured surfaces and assist their design. First, we simulated the sessile droplet experiment on flat surfaces to calibrate model parameters. Second, we modelled several surface morphologies, intrinsic contact angles and droplet impact velocities. Finally, we produced and tested 3D printed flat and micro-structured samples to validate the phase-field model, obtaining a reasonable qualitative and quantitative agreement between numerical and experimental results. The validated model proposed here can help design and prototype surfaces with tailored wettability. Furthermore, integrated with atomistic/mesoscopic simulations, it represents the last step of a predictive multi-scale model, where both chemical and morphological features of surfaces can be designed a priori.

In this study, binder evaporation as a significant microscale phenomenon in fluidized bed wet granulation has been investigated in three situations: a single droplet, a sessile droplet, and a liquid bridge. Single droplet evaporation has been analytically modelled by mass transfer analysis from a spherical droplet subjected to the relative velocity of the medium and considering evaporation rate variations versus droplet diameter. Then, the sessile droplet evaporation model has been used from the literature. Finally, the liquid bridge evaporation has been modelled, and the rupture time of the bridge has been computed. The local temperature dependence of air physicochemical properties has been considered in all models. The single and sessile droplet evaporation rates have been successfully validated by the experimental data of the air–water system. The effects of operational conditions and liquid/particle properties on each evaporation event have been evaluated and quantified. The results indicate that both the higher relative velocity between the air and a single droplet and the smaller equilibrium contact angle in a constant volume of sessile droplets increase the evaporation rate. Also, increasing the length of the binder bridge reduces the rupture time. [ABSTRACT FROM AUTHOR]

Substrate roughness can greatly affect the evaporation of sessile droplets, thus determining the efficiency of applications, such as ink-jet printing and coating. Here, we conduct experiments on the evaporation of de-ionized water droplets on glass substrates with roughness in the range 0.1--0.2 µm to investigate its effect on the dynamics of the contact angle and radius, as well as the heat and mass transfer during evaporation. We discover a "stick-jump" phenomenon as part of a five-stage process that is determined by the evolution characteristics of the contact angle and radius and includes the volume expansion, first stick, second stick, jump and final stages. Moreover, we find that the evaporation mode of the droplets is not affected by the increase of substrate roughness, whereas the heat and mass transfer processes intensify with the increase of substrate roughness in the presence of nonuniform evaporation effects. Also, the pinning--depinning mechanism of the "stick-jump" phenomenon during evaporation is carefully analyzed in terms of the Gibbs free energy, thus establishing a relation among Gibbs and excess Gibbs free energies and substrate roughness, which predicts the evaporation dynamics of the droplet. We anticipate that this study unravels key aspects of the droplet evaporation mechanisms on rough substates toward optimizing and advancing relevant technology applications. [ABSTRACT FROM AUTHOR]

A coupled volume-of-fluid (VOF) and discrete element model (DEM) is developed and used to study the dispersion of particles in an evaporating pinned sessile droplet on a heated substrate. Fully resolved simulations of evaporating droplets are performed to study the effects of substrate temperature and the Marangoni stresses to study the fluid flow and temperature distribution within the droplet. The fluid flow inside the evaporating droplets is used to predict the behavior of particles, studying the effect of relative particle density and the aforementioned effects on the particle dispersion within the droplet. This study shows that the presence of Marangoni stresses significantly affects the flow and temperature distribution inside the droplet, which, in turn, influences the dispersion of particles in the droplet. The fluid velocity induced by the Marangoni stresses is nearly two orders of magnitude larger than the velocity generated by capillary flow as a result of evaporation, promoting a strong convective mixing within the droplet, while working to equilibrate the temperature distribution at the interface. In the absence of Marangoni stresses, the dispersion of particles is governed by the competing effects of adsorption by the downward-moving interface as a result of evaporation, and particle sedimentation under the influence of gravity. However, both these effects become less dominant in the presence of a flow induced by the Marangoni stresses, causing the particles to initially move toward the apex of the droplet along the interface and, subsequently, toward a stagnation point on the interface. [Display omitted] • Two stage VOF–DEM based model for dispersion of particles in evaporating sessile droplets. • Marangoni flow maintains a monotonic interface temperature, resulting in a single vortex flow inside the droplet. • Without Marangoni stresses, the interface capturing competes with the sedimentation of particles. • When the Marangoni stresses are weak, multiple vortices appear inside the droplet resulting in ring-like dispersion. [ABSTRACT FROM AUTHOR]

[Display omitted] • The droplet evaporation under a non-uniform/uniform electric field is studied. • The mechanisms of droplet evaporation under an electric field are revealed. • An LB model is employed to study the internal flow and temperature distribution. • The enhancement ratio of coupling electric field and temperature field is obtained. • The evaporation rate is enhanced by 29.34 times in the non-uniform electric field. Controllable evaporation of sessile droplets is essential in diverse applications, ranging from thermal management to chemical reactions and combustion. Despite considerable advances, further enhancement of droplet evaporation is still challenging. Here, an experimental system that couples uniform/non-uniform electric fields with temperature fields to enhance hydrophilic droplet evaporation is introduced. The electric field can generate Coulomb force by changing the redistribution of charges at the droplet interface, which enables highly flexible and precise control of the sessile droplet. By leveraging the uniform electric field, the droplet is stretched upwards, which increases the heat transfer thermal resistance and the vapor concentration near the droplet interface, leading to the deterioration of droplet evaporation. Whereas the application of a non-uniform electric field will flatten the droplets due to the shear effect of the corona wind on the droplet interface, and the reduction of the heat transfer thermal resistance of the droplets, as well as the vapor concentration near the interface, which promotes the droplet evaporation. The coupling of uniform electric and temperature fields could reverse the inhibition effect of droplet evaporation caused by a purely uniform electric field, and the maximum enhancement ratio reaches 5.11 times. The coupling of a non-uniform electric field and temperature field can enhance droplet evaporation up to 29.34 times. The corresponding numerical simulation study reveals the flow and temperature distribution inside the droplet. This research provides critical insights into the precise manipulation of droplet evaporation by applying an electric field. [ABSTRACT FROM AUTHOR]

Droplet phase change is important for energy storage and saving technology. The initial profile of the droplet is extremely important for its vaporization or solidification on a horizontal surface. To understand the effect of liquid physical properties on droplet profile, a theoretical model was developed in this study, based on the Young-Laplace equation with gravity effect specially considered. After the model was experimentally validated by comparing the geometric shape of water droplets, it was further used for predicting droplet shapes of other materials, and thus analyzing the influence of different physical properties, such as temperature, pressure, surface wettability, etc. Results show that the results of this model agree well with the experimental data. The maximum and average deviations are less than 4.5% and 1.5%, respectively. For all kinds of droplets on the fixed surfaces, when the temperature increases, the droplet contact radius increases and height decreases. The droplets of nitrogen and carbon dioxide are more sensitive to temperature than ethanol and ethylene glycol droplets. For 20 μL droplets on the surface of contact angle 150°, when the temperature changes from 273.15 K to 293.15 K, the droplet contact radiuses increase by 30.6% for carbon dioxide, 1.2% for ethanol and 0.67% for ethylene glycol, and the droplet heights decrease by 42.9%, 2.5%, 1.1%, respectively. Results of this study are meaningful for predicting the phase change process of droplets on the horizontal surface by controlling their initial profiles.

In this article, we experimentally probe the vapor-mediated interaction behavior of evaporating sessile and pendant droplets in an interacting droplet (ID) system. For this purpose, a pendant droplet was introduced in the vapor diffusion domain of a sessile droplet and both were allowed to evaporate simultaneously. The evaporation dynamics were monitored using optical imaging techniques for varied separation (both horizontal and vertical) distances between them. Our observations reveal curtailed mass transfer rate from both the droplets although the evolution of droplet morphology (such as pendant droplet radius, contact radius, and contact angle of sessile droplet) at different stages of evaporation remain similar. The evaporative fluxes from these two droplets interact with one another and thereby reduce the diffusive mobility of vapor molecules in the liquid-vapor interface of both. This condition suppresses the diffusion mechanism and thereby impedes the evaporation rate. We show that the evaporation behavior for two droplets in an interacting droplet system is solely dictated by an effective external vapor concentration depending on the problem geometry. Therefore, to characterize the vapor diffusion domain we hypothesize a vapor front enfolding both the droplets and put forward a theoretical model by applying conservation of mass across it. We also propose a relationship to show the variation of the effective external vapor concentration with the relative separation distance between the droplets. The predictions from theoretical models are found to be in good agreement with our detailed experimental observations. [ABSTRACT FROM AUTHOR]

The process of fuel droplet evaporating is one of the most important factors that directly affect the efficiency of the combustion process. Therefore, the current study reviews previous studies that focused on the process of evaporation of a drop of fuel. The review is divided into points. The first part is concerned with modeling of the evaporation process under different initial condition and temperature of the droplet. The second part present the experimental studies concerned with measuring the evaporation time of the droplet, as well as the shape of the droplet during the evaporation process. Most of the studies related to this subject can be divided into three categories: The first category is the studies that are concerned with the process of heating the droplet and studying the evaporation time for different types of fuels or by adding nanomaterials to the fuel and studying their effect on the evaporation process. The second category is the studies concerned with the mechanics of droplet evaporation and the study of droplet shape. The third category is the studies that focus on studying the effect of initial conditions, such as temperature and pressure, as well as the concentration of gasses surrounding the drop and their types. There are other studies concerned with projecting the electric field onto the drop during the evaporation process and studying its effect. [ABSTRACT FROM AUTHOR]

Experiments on measuring the rate of evaporation of liquid sessile droplets into air show that the rate of evaporation increases in the presence of forced convection flows. However, data on the effect of convection on evaporation are often contradictory and should be clarified. The paper presents a numerical analysis of evaporation from the surface of a water droplet subjected to forced convection in the gas phase. The drop is located on a smooth horizontal isothermal substrate; the mode with constant contact angle is considered. The shape of the drop has axial symmetry, the same for the velocities and pressure. Forced convection compatible with the symmetry conditions are represented by flows directed downward along the axis of the system and diverging along the sides near the drop and the substrate. The mathematical model is constructed for evaporation controlled by diffusion in the gas phase and takes into account surface tension, gravity, and viscosity in both media, buoyancy and Marangoni convection. The results indicate the existence of the mutual influence of liquid and gaseous media. Thus, a drop vibrates under the influence of movements in the atmosphere, which generates a density wave in the gas: the drop «sounds». The magnitude of the velocity in a liquid is 50 times less than the characteristic velocity in air. It is found that the evaporation rate does not change in the presence of forced convection flows, which contradicts most of the experimental works. The reason for the discrepancies is supposed to be the appearance of nonequilibrium conditions at the boundary of the condensed phase: under these conditions, the evaporation regime ceases to be diffusional.

Researches on droplet evaporation has a vast range of applications in different fields. The mechanisms of droplets evaporation have been a topic of investigation for decades. The droplet after spreading on the substrate exhibits constant evaporation rate for a constant base diameter and decreasing contact angle; followed by another evaporation mode with constant contact angle and decreasing base diameter; and finally, evaporation with decreasing of both contact angle and base diameter. In the present study, the evaporation rate and mechanisms influenced by surfactant and temperature effects are analysed. The evaporation was demonstrated to be related to the dynamics of the sessile droplet spreading ability and the depinning event. It remains complex to predict the evaporation of the sessile droplet due to the continuous change in surfactant local concentration. Moreover, the temperature change modifies the surface tension and the induced inner flows. These two questions find answers in the triple line dynamic which controls the evaporation rate. The forces controlling the depinning with surfactant was quantified. A clear constant force was found following depinning. Such dynamic equilibrium demonstrates also the effect of the friction, surface roughness and moreover the limit of surfactant concentration in the triple line direct vicinity. The evaporation rate shows two particularities: one is the classical decrease of the evaporation rate after depinning; the second in case of surfactant, there is an enhancement appearing at later droplet lifetime, which could be a consequence of film evaporation contributing to the evaporation near the triple line. The local evaporation does not change significantly despite the change in the contact angle with respect to surfactant concentration. The substrate temperature enhances evaporation rate. The coupled temperature and surfactant effect show a local evaporation rate decreasing with surfactant concentration increase at ambient temperature (around 20 °C) and enhancement with surfactant concentration at higher temperature.

A significant growth of research on digital microfluidics has been achieved over the past several decades, and the field is still attracting increasing attention for fulfilling relevant mechanisms and potential applications. Numerous studies have been devoted to actively manipulating droplets in a variety of fundamental and applicational scenarios. In this work, the deformation of ferromagnetic fluid droplets is studied under an external uniform magnetic field. The droplets are precisely dispersed on the bottom surface of a container assembled with polymer methacrylate (PMMA) plates. Mineral oil is applied instead of air as the surrounding medium for easy stretching and preventing water solvent evaporation in ferrofluid. The design and processing of the container are firstly carried out to observe the shape and characterize the wettability of the droplets in the immiscible mineral oil medium. Furthermore, the droplets’ deformation and the working mechanism are given under the action of the horizontal uniform magnetic field. At different magnetic field intensities, the droplet is stretched in the horizontal direction parallel to the applied field. Due to volume conservation, the dimension in the height reduces correspondingly. With the coupling effect of magnetic force, viscous force and interfacial tension, the contact angle first increases with the magnetic field and then basically remains unchanged upon magnetization saturation. Consistent with the experimental results, the numerical method clearly reveals the field coupling mechanism and the nonlinear deformation of the sessile droplet.

We present a sessile droplet manipulation platform that enables the formation and transport of a droplet on a light-absorbing surface via local laser-beam irradiation. The mechanism relies on solutocapillary Marangoni flow arising from a concentration gradient in a binary mixture liquid. Because the mixture is strongly confined in a two-dimensional slit with a spacing of a few micrometers, the wetting film is stably sustained, enabling the rapid formation, deformation, and transport of a sessile droplet. In addition, to sustain the droplet in the absence of laser irradiation, we developed a method to bridge the droplet between the top and bottom walls of the slit. The bridge is stably sustained because of the hydrophilicity of the slit wall. Splitting and merging of the droplet bridges are also demonstrated.

We investigate the effect of ultrasound on the evaporation and crystallization of sessile NaCl solution droplets which were positioned in traveling or standing wave ultrasound field. The experimental results indicated that the ultrasound field can significantly accelerate the evaporation rate of the sessile droplets and refine the crystal grains. By adjusting the distance between the sessile droplets and the ultrasound emitter, it is found that, in traveling wave ultrasound field, the sessile droplet evaporation time and the time for the appearance of NaCl grains exhibited a fluctuating increase as the droplet-emitter distance increased. While in the standing wave ultrasound, the sessile droplet evaporation rate increases with the increasing droplet-emitter distance. Overall, the traveling wave ultrasound field has a stronger effect on grain refinement of the sessile droplets than the standing wave ultrasound field. The grain refinement is attributed to the decrease of critical nucleation radius caused by ultrasound energy and the increase of the nucleation rate caused by the accelerated evaporation rate. In addition, the breakage of grains caused by ultrasonic cavitation would also lead to grain refinement. [ABSTRACT FROM AUTHOR]

Understanding the evaporation process of binary sessile droplets is essential for optimizing various technical processes, such as inkjet printing or heat transfer. Liquid mixtures whose evaporation and wetting properties may differ significantly from those of pure liquids are particularly interesting. Concentration gradients may occur in these binary droplets. The challenge is to measure concentration gradients without affecting the evaporation process. Here, spectroscopic methods with spatial resolution can discriminate between the components of a liquid mixture. We show that confocal Raman microscopy and spatially resolved NMR spectroscopy can be used as complementary methods to measure concentration gradients in evaporating 1-butanol/1-hexanol droplets on a hydrophobic surface. Deuterating one of the liquids allows analysis of the local composition through the comparison of the intensities of the C-H and C-D stretching bands in Raman spectra. Thus, a concentration gradient in the evaporating droplet was established. Spatially resolved NMR spectroscopy revealed the composition at different positions of a droplet evaporating in the NMR tube, an environment in which air exchange is less pronounced. While not being perfectly comparable, both methods--confocal Raman and spatially resolved NMR experiments--show the presence of a vertical concentration gradient as 1-butanol/1-hexanol droplets evaporate. [ABSTRACT FROM AUTHOR]

We report the complex evaporation kinetics of saline sessile droplets on surfaces with elevated temperatures. Our previous studies show that on non-heated substrates, saline sessile droplets evaporate faster compared to the water counterparts. In the present study, we discover that on heated surfaces, the saline droplets evaporate slower than the water counterpart, thereby posing a counter-intuitive phenomenon. The reduction in the evaporation rates is directly dependent on the salt concentration and the surface wettability. Natural convection around the droplet and thermal modulation of surface tension is found to be inadequate to explain the mechanisms. Flow visualizations using particle image velocimetry (PIV) reveal that the morphed advection within the saline droplets is a probable reason behind the arrested evaporation. Infrared thermography is employed to map the thermal state of the droplets. A thermo-solutal Marangoni based scaling analysis is put forward and the major governing non-dimensional numbers have been accounted for in the analysis. It is observed that the Marangoni flow and internal advection borne of thermal and solutal gradients are competitive, thereby leading to the overall decay of internal circulation velocity compared to the equivalent pure water case, which reduces the evaporation rates. The theoretically proposed advection velocities conform to the experimental results. This study sheds rich insight on a novel species transport behaviour in saline droplets. [ABSTRACT FROM AUTHOR]

Active electric-driven droplet manipulation in digital microfluidics constitutes a promising domain owing to the unique and programmable wettability inherent in sessile ionic droplets. The coupling between the electric field and flow field enables precise control over wetting characteristics and droplet morphology. This study delves into the deformation phenomena of ionic sessile ferrofluid droplets in ambient air induced by uniform electric fields. Under the assumption of a pinned mode throughout the process, the deformation is characterized by variations in droplet height and contact angle in response to the applied electric field intensity. A numerical model is formulated to simulate the deformation dynamics of ferrofluid droplets, employing the phase field method for tracking droplet deformation. The fidelity of the numerical outcomes is assessed through the validation process, involving a comparison of droplet geometric deformations with corresponding experimental results. The impact of the electric field on the deformation of dielectric droplets is modulated by parameters such as electric field strength and droplet size. Through meticulously designed experiments, the substantial influence of both field strength and droplet size is empirically verified, elucidating the behavior of ionic sessile droplets. Considering the interplay of electric force, viscous force, and interfacial tension, the heightened field intensity is observed to effectively reduce the contact angle, augment droplet height, and intensify internal droplet flow. Under varying electric field conditions, droplets assume diverse shapes, presenting a versatile approach for microfluidic operations. The outcomes of this research hold significant guiding implications for microfluidic manipulation, droplet handling, and sensing applications., (© 2024 Wiley‐VCH GmbH.)

Digital microfluidics based on sessile droplets has emerged as a promising technology for various applications including biochemical assays, clinical diagnostics, and drug screening. Digital microfluidic platforms provide an isolated microenvironment to prevent cross-contamination and require reduced sample volume. Despite these advantages, the droplet-based technology has the inherent limitation of the quiescent flow conditions at low Reynolds number, which causes mixing samples confined within the droplets to be challenging. Recently, solutal Marangoni flows induced by volatile liquids have been utilized for sessile droplet mixing to address the above-mentioned limitation. The volatile liquid vaporized near a sessile droplet induces a surface tension gradient throughout the droplet interface, leading to vortical flows inside a droplet. This Marangoni flow-based droplet mixing method does not require an external energy source and is easy to operate. However, this passive method requires a comparably long time of a few tens of seconds for complete mixing since it depends on the natural evaporation of the volatile liquid. Here, we propose an improved ultrasound-induced heating method based on a nature-inspired ultrasound-absorbing layer and apply it to enhance solutal Marangoni effect. The heater consists of an interdigital transducer deposited on a piezoelectric substrate and a silver nanowire-polydimethylsiloxane composite as an ultrasound-absorbing layer. When the transducer is electrically actuated, surface acoustic waves are produced and immediately absorbed in the composite layer by viscoelastic wave attenuation. The conversion from acoustic to thermal energy occurs, leading to rapid heating. The heating-mediated enhanced vaporization of a volatile liquid accelerates the solutal Marangoni flows and thus enables mixing high-viscosity droplets, which is unachievable by the passive solutal Marangoni effect. We theoretically and experimentally investigated the enhanced Marangoni flow and confirmed that rapid droplet mixing can be achieved within a few seconds. The proposed heater-embedded sessile droplet mixing platform can be fabricated in small size and easily integrated with other digital microfluidic platforms. Therefore, we expect that the proposed sample mixing method can be utilized for various applications in digital microfluidics and contribute to the advancements in the medical and biochemical fields.

Sessile droplets' evaporation is a complex process that involves fluid flow coupled with heat and mass transfer. In this study, mathematical modelling of sessile droplet evaporation on hydrophobic substrates is developed and simulations are carried out on COMSOL. The model results are validated with the data available in the literature. Postvalidation, the simulation of droplet evaporation is carried out on the various substrate hydrophobicities and various environmental conditions. For these conditions, contours are plotted for temperature, velocity, and mass concentration for the droplet and moist air domain. The result shows that Marangoni convection plays a very important role in droplet evaporation. A high rate of evaporation is observed at the droplet interface at low relative humidity and a large degree of subheating. The effect of air velocity on the evaporation rate is studied, however, its effect is very marginal as compared to relative humidity and degree of subheating. The heat flux at the three‐phase contact line is large for a smaller Prandtl number fluid. Overall, the evaporation rate increases with increasing the Prandtl number because it has a large value of Marangoni convection. [ABSTRACT FROM AUTHOR]

Magnetic field-mediated wetting of ferrofluid droplets has emerged to be of fundamental importance because of its plethora of applications ranging from chemical and biomolecular analysis to soft robotics and medical imaging. However, while extensive studies continue to be reported on the underlying experimental facets, a fundamental theoretical depiction of the observed contact angle variation with the applied magnetic field remains grossly elusive, as attributable to a complex dependence of the induced magnetization on the droplet's intrinsic magnetic properties. Circumventing these constraints, here we put forward a first-principle analytical model that delineates the variation in the contact angle as a function of an applied magnetic field on a sessile ferrofluid droplet, by appealing to energy minimization principles. One key feature of our analysis is the consideration of the local magnetization as a function of the magnetic field itself, resulting in a new contribution to the interfacial energy by virtue of normal traction at the droplet's contact with its non-magnetic surroundings. This theory is supported by experiments identified in prior research to elucidate the fundamental physics of relevance. Our results highlight the substantial influence of the saturation magnetization and the initial susceptibility of the ferrofluid on the resulting contact angle alterations, as well as possible non-trivial routes of highly selective and precise enhancement or attenuation in the extent of wetting. These findings are likely to be of fundamental importance towards establishing the design foundations of portable magnetic resonance imaging devices, micromixers, and microreactors, magnetically-manipulated automatic control of soft fluidic matters, among others. [Display omitted] • Energy minimization relates the contact angle with the applied magnetic field on a sessile ferrofluid drop. • Local magnetization as a function of the magnetic field itself results in a new contribution to the interfacial energy. • Effects of the saturation magnetization and the initial susceptibility on the contact angle alterations are unraveled. • Lower relative magnetization and higher base-state susceptibility improve the wetting dramatically. [ABSTRACT FROM AUTHOR]

[Display omitted] 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. Surfactant droplet evaporation experiments were performed on two commercial crop species, wheat and capsicum, along with two synthetic surfaces, up to a 90° incline. The time-dependence of the droplets' contact angles, height, volume and contact radius was measured throughout the evaporation experiments. Mathematical models were developed to simulate the experiments. With one clear exception, for all combinations of surfaces, surfactant concentrations and angles, the experiments appear to follow the standard evaporation modes and are well described by the mathematical models (modified Popov and Young–Laplace-Popov). The exception is wheat with a high surfactant concentration, for which droplet evaporation appears nonstandard and deviates from the diffusion limited models, perhaps due to additional mechanisms such as the adsorption of surfactant, stomatal density or an elongated shape in the direction of the grooves in the wheat surface. [ABSTRACT FROM AUTHOR]

• CAs of liquid on solid measured with sessile droplet (SD) and captive bubble (CB) methods. • Deviation from the supplementary rule is observed for rough surfaces. • Sum of dynamic CAs by SD and CB methods deviates from 180 ° as roughness increases. • An analytical model is developed to substantiate the characteristic trend. • Experimental observations corroborate the model predictions. Hypothesis : Quantitative characterization of surface wettability through contact angle (CA) measurement using the sessile droplet (SD) or captive bubble (CB) methods is often limited by the intrinsic wetting properties of the substrate. Situations may arise when an extreme surface wettability may preclude using one of the two methods for predicting the behaviors of droplets or bubbles on the surface. This warrants a relationship between the dynamic CAs measured via the SD and CB methods. While the two dynamic CAs (e.g., the advancing CA of SD and receding CA of CB) add up to 180° on a smooth surface, the simple geometric supplementary principle may not apply for rough surfaces. Experiments : We perform a systematic wettability characterization of solid substrates with varying degrees of roughness using the sessile-droplet and captive-bubble methods, and interpret the experimental observations using a theoretical model. Findings : The dynamic contact angles measured by the sessile-droplet and captive-bubble methods deviate from the supplementary principle as the surface roughness is increased. We present a theoretical explanation for this disparity and predict the values of the contact angles using prevalent thermodynamic models of wetting and contact-angle hysteresis on rough substrates. The theoretical prediction is in good agreement with the experimental observations. [ABSTRACT FROM AUTHOR]

The evaporation of a drop deposited on a heated substrate is a complex process, which combines several phenomena such as the Marangoni effect, mass and thermal transfers, etc. We developed, in this paper, a mathematical model and a numerical simulation code used to carry out an in-depth study about the evaporation of a drop deposited on a heated substrate surrounded by air. This numerical study was supported by experimental work. The numerical findings obtained showed the existence of a condensation phenomenon for certain configurations. At the beginning of the experiment, the evaporation started at the triple point. However, a local region of the interface remained relatively cold. In this region, the concentration gradient (Cv, Csat) directed from the liquid-gas interface to the air resulted in condensation of water steam. Although this phenomenon is temporary and visible only at the start of evaporation process, its study makes it possible to better understand and optimize the evaporation kinetics. [ABSTRACT FROM AUTHOR]

The present article experimentally and theoretically probes the evaporation kinetics of sessile saline droplets. Observations reveal that presence of solvated ions leads to modulated evaporation kinetics, which is further a function of surface wettability. On hydrophilic surfaces, increasing salt concentration leads to enhanced evaporation rates, whereas on superhydrophobic surfaces, it first enhances and reduces with concentration. Also, the nature and extents of the evaporation regimes (constant contact angle or constant contact radius) are dependent on the salt concentration. The reduced evaporation on superhydrophobic surfaces has been explained based on observed (via microscopy) crystal nucleation behaviour within the droplet. Purely diffusion driven evaporation models are noted to be unable to predict the modulated evaporation rates. Further, the changes in the surface tension and static contact angles due to solvated salts also cannot explain the improved evaporation behaviour. Internal advection is observed (using PIV) to be generated within the droplet and is dependent on the salt concentration. The advection dynamics has been used to explain and quantify the improved evaporation behaviour by appealing to the concept of interfacial shear modified Stefan flows around the evaporating droplet. The analysis leads to accurate predictions of the evaporation rates. Further, another scaling analysis has been proposed to show that the thermal and solutal Marangoni advection within the system leads to the advection behaviour. The analysis also shows that the dominant mode is the solutal advection and the theory predicts the internal circulation velocities with good accuracy. The findings may be of importance to microfluidic thermal and species transport systems. • Saline sessile droplets are observed to vaporize faster than sessile water droplets. • The evaporation rate increases with concentration, but decreases on superhydrophobic surfaces. • Internal hydrodynamics is noted to lead to the improved evaporation. • The thermal and the solutal Marangoni effects are found to be the driving mechanism of the advection. • The advection modifies the external Stefan flow, which morphs the vaporization rates. [ABSTRACT FROM AUTHOR]

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The manipulation of sessile droplets on hydrophobic surfaces with high controllability, accuracy, and flexibility is vital for various applications of engineering sciences and technology. In this research, the combined effects of a uniform electric field, dielectric infused surface (DIS), and surfactants were investigated for the manipulation and control of sessile droplets on hydrophobic substrates. DIS reduced surface adhesion and enabled the action of electrohydrodynamic and electrophoretic forces. Experimental analysis revealed three different modes of droplet behavior on DIS under varying electro-physical conditions: elongation without motion, elongation with motion, or dispersion. These modes were observed for surfactant concentrations below the critical micelle concentration (C CMC), while elongation leading to restricted spreading of droplet occurred above C CMC. The modes were mapped in the parametric space of electric capillary number (Ca e) vs. non-dimensional surfactant concentration (C * = C s / C CMC), with Ca e representing the ratio of interfacial electric to capillary stresses and C s representing the surfactant concentration. A simple theoretical analysis based on interfacial electric and capillary stress balance distinguished between the stable and unstable configurations. This research contributes to advancing the understanding of droplet manipulation and control, which are critical in emerging microfluidic or biological applications. [Display omitted] • Different dynamic regimes such as droplet elongation with or without motion, and droplet dispersion are observed. • Regimes are delineated with respect to surfactant concentration and applied electric field. • Critical electric field strength delineating different regimes are identified. • Sessile droplet disperses as its major axis spread 1.5 times its initial configuration. [ABSTRACT FROM AUTHOR]

In this work, the dynamics of the head-on collision of two sessile water droplets, namely the moving droplet and pinning droplet, on a traveling substrate was experimentally investigated. Unlike the traditional scenario of sessile droplets collision, the traveling substrate propelled the moving droplet attached to it to move at a certain speed. The results revealed that there are only two distinct regimes of collision consequences: coalescence without separation and separation with separation. A series of time-resolved photographic images mapping all the collision regimes in the parameter space of Capillary number and size ratio were used to identify the controlling factors for different collision results. The breakup of the receding meniscus in separation regime was discussed in detail as it is caused by the change of the droplet morphology. The findings indicated that the length of the receding meniscus played a significant role in the droplet impact dynamics, and when it exceeded about 8.2 mm, the receding meniscus broke up. Furthermore, it was demonstrated that the sum of the volume of initial pinning droplet's receding meniscus and the volume of the moving droplet before collision is equal to the volume of the receding meniscus at its maximum length after collision. The critical Capillary number/size ratio for the transition between these two regimes was derived based on the volume principle before and after the collision. The model-predicated results show good agreement with the experiments. The findings could contribute to a better understanding of the droplet collision dynamics and the optimization of the anti-icing, self-cleaning and inkjet printing devices. [Display omitted] [ABSTRACT FROM AUTHOR]

Numerous formulation processes of materials involve a drying step, during which evaporation of a solvent from a multicomponent liquid mixture, often confined in a thin film or in a droplet, leads to concentration and assembly of nonvolatile compounds. While the basic phenomena ruling evaporation dynamics are known, precise modeling of practical situations is hindered by the lack of tools for local and time-resolved mapping of concentration fields in such confined systems. In this article, the use of fluorescence lifetime imaging microscopy and of fluorescent molecular rotors is introduced as a versatile, in situ, and quantitative method to map viscosity and concentration fields in confined, evaporating liquids. More precisely, the cases of drying of a suspended liquid film and of a sessile droplet of mixtures of fructose and water are investigated. Measured viscosity and concentration fields allow characterization of drying dynamics, in agreement with simple modeling of the evaporation process.

The effect of the thermal properties of the system on the lifetime of an evaporating sessile droplet of water is analysed using a fully coupled model which involves determining the temperature of the droplet, the substrate and the atmosphere. The evolutions, and hence the lifetimes, of droplets of water evaporating in both of the extreme modes are calculated. In particular, it is shown how the lifetimes of droplets of water can be strongly influenced by thermal effects. Droplets with larger initial contact angles or on less conductive substrates generally have longer lifetimes than those with smaller initial contact angles or on more conductive substrates, and the physical mechanism by which the thermal properties of the system influence the evaporation can be understood in terms of the thermal anchoring between the droplet and the lower surface of the substrate.

Evaluating and predicting evaporation kinetics of a sessile droplet present challenging exercises because of its strong dependence on the substrate hydrophobicity (contact angle) and the evaporation mode at the three-phase contact line. For sessile water droplets containing surfactants, the existence of surfactant would not only change droplet's geometry during the evaporation course, but could also affect the liquid cohesive energy density; thereby interactively affecting the evaporation kinetics. Here we present a new analytical model for the Hildebrand solubility parameter, which represents the cohesive energy density, as a function of time, thus a function of surfactant concentration inside a drying droplet. This distinct expression for the solubility parameter is independent of the droplet's geometry, therefore can be used to assess the variation of cohesive energy density during the evaporation course independently of both surface hydrophobicity and the evaporation mode. Our model resolve conflicting effects of water-soluble surfactants like sodium dodecyl sulfate (SDS) reported in the literature. It is shown that SDS can alter the evaporation rate differently (significantly or insignificantly) depending on the closeness of the studied system to the theoretical droplet lifetime extremum at the contact angle of 90°. The presence of SDS, up to the critical micellar concentration, does not significantly ease the vaporization of water through the air-liquid interface; nor SDS lead to faster evaporation rate by preferentially oscillating and vibrating of the adsorbed SDS molecules at the free water surface. Our theoretical analysis also provides a new approach to calculating the Hildebrand solubility parameter to estimate the cohesive energy density of different solvents. [ABSTRACT FROM AUTHOR]

• A PNIPAm film with dramatically switchable wettability from superhydrophilic (5.4 ± 2.4) ° to hydrophobic (139.4 ± 2.3) ° was fabricated. • The PNIPAm film was first successfully prepared on diverse substrates especially nonplanar surfaces. • Controllable contact line motion along on-demand directions was realized by applying temperature gradient on the film. Thermoresponsive films used to actuate microscale liquid droplets play an important role in lab-on-chip field. However, the limitation of applicable substrates and the rigid requirements for building block copolymers are obstacles. In this study, a thermosensitive poly(N -isopropylacrylamide) (PNIPAm) film was prepared by photo-grafting on modified polydimethylsiloxane (PDMS) layer. Polytetrafluoroethylene microparticles were sprayed and embedded in PDMS to obtain the modified layer with low surface energy and micro-roughness, which enhanced the wettability of PNIPAm switching between superhydrophilic and hydrophobic. As PDMS layer can be easily attained by either spin-coating or dip-coating, the thermoresponsive film (TRF) can be applied on diverse substrates without limitation. With applied temperature gradient on the TRF, the contact lines of sessile droplets moved spontaneously along on-demand directions by temperature control. Forces acting on droplets were calculated to analyze the factors that affect the contact line motion as well as the available temperature range. Such novel film will provide potential applications in microfluidic devices especially in portable paper-like lab-on-chip accompanied by the advantages of simple preparation, high adaptability to nonplanar surfaces, easy access to temperature control and low energy consumption. [ABSTRACT FROM AUTHOR]

Highlights • Spoke-like patterns with several rolls uniformly distributed in azimuthal direction were observed in droplets. • Each roll straightly extends to the center of droplet and its axis is parallel to radial axis. • Patterns are longitudinal rolls driven by inclined temperature gradient. Abstract Marangoni instabilities in an easily volatile sessile droplet of n-hexane evaporating at constant contact angle mode were investigated through a series of experiments. Once the droplet is deposited onto the substrate, a kind of spoke-like pattern with several rolls uniformly distributed in azimuthal direction is generated soon in the droplet. Different from the Bénard-Marangoni cell and the hydrothermal wave, each roll straightly extends to the center of the droplet and the axis of the roll is parallel to the radial axis of the droplet. They do not propagate neither in radial direction nor in azimuthal direction. With the receding of the wetting radius, the neighbor two rolls merge into one roll and a few of new rolls quickly generate in random positions, and the roll number gradually decreases until the vanishment of droplet. During evaporation, they sustain a quasi-steady state. We believe that these rolls belong to the longitudinal rolls driven by the inclined temperature gradient in droplet. The influences of the substrate temperature, the ambient temperature and the contact angle on the behavior of the longitudinal rolls are analyzed. [ABSTRACT FROM AUTHOR]

Highlights • Quasi-steady state flower-like patterns of Bénard-Marangoni (BM) instabilities were observed in a droplet evaporating at CCA mode. • BM cell is intrinsically circular-arc except for the straight connecting boundaries between cells. • BM cell number decreases following a square function of the evaporating time. Abstract Marangoni instabilities in a sessile droplet evaporating at constant contact angle mode on a heated substrate were investigated through a series of experiments. The quasi-steady state flower-like patterns of Bénard-Marangoni instabilities were observed, which uniformly distributed along the azimuthal direction of droplet. With the receding of triple line, the cell number of the Bénard-Marangoni convection decreases one by one following a square function of the evaporating time while the flower-like pattern maintains the quasi-steady state continuously. Different from the classical polygonal cells in flat liquid layer, the shape of cells in droplet is circular-arc. The critical Marangoni numbers for the incipience as well as those for the disappearance of the Bénard-Marangoni patterns were determined experimentally. Besides numerical simulations were conducted and the detailed characteristics of the Bénard-Marangoni instability patterns inside the droplet are explained thoroughly. [ABSTRACT FROM AUTHOR]

In order to understand the effect of Marangoni convection on the evaporation rate and the flow pattern, we performed a series of three-dimensional numerical simulations on evaporation process of sessile water droplet by introducing a kinetic model. Substrate temperature and the ratio of vapor pressure varied from 299 K to 308 K and from 0.92 to 0.99, respectively. The variation range of contact angle θ was between 9.15° and 120°. Results show that the axisymmetric ring-shape temperature distribution on droplet free surface transforms into a serrated temperature distribution because of the enhancing Marangoni convection with the increase of substrate temperature. In addition, with the decrease of vapor pressure, the total evaporation rate on free surface will be increased and the Marangoni effect will be enhanced. The flow pattern is axisymmetric at 90o ≤ θ ≤ 120o when the substrate temperature is fixed. However, it shifts to a multi-cellular pattern with the decrease of contact angle as a result of the competition between Marangoni flow and the evaporation. Additionally, the total evaporation rate increases with the increase of contact angle when contact angle is above 60o, but when the contact angle is below 60o, the trend is reverted. The temperature distribution becomes distinct at a small contact angle. [ABSTRACT FROM AUTHOR]

Highlights • Bénard-Marangoni convection cells as well as hydrothermal waves were observed in an evaporating sessile droplet. • Marangoni instabilities occur even when substrate temperature is lower than room temperature. • The critical conditions for the incipience of Marangoni instabilities were determined. Abstract Marangoni instabilities of a sessile droplet of 0.65 cSt silicone oil evaporating at constant contact line mode are experimentally investigated in a wide range of the substrate temperatures (T w) from those lower than room temperature (T a) to those higher than it. For T w > T a , the Bénard-Marangoni convection cells are observed and the cell patterns vary from the quasi-steady state to irregular oscillatory state with the droplet evaporation. For T w < T a , the irregular oscillatory Bénard-Marangoni cells are observed when T w is higher than 10.6 °C. The cell size is larger while there are less cell numbers compared to that of T w > T a. When T w is higher than 14.3 °C three kinds of convection mode, i.e. the travelling hydrothermal waves, the coexistence of hydrothermal waves and irregular oscillatory Bénard-Marangoni convection, and the irregular oscillatory Bénard-Marangoni convection, occur successively with droplet evaporating. The critical contact angles for the incipience of these Marangoni instabilities are determined. [ABSTRACT FROM AUTHOR]