Evaporation Of Sessile Droplets Research Articles

Droplet Evaporation on Hot Micro-Structured Superhydrophobic Surfaces: Analysis of Evaporation from Droplet Cap and Base Surfaces

In this study, evaporation of sessile water droplets on hot micro-structured superhydrophobic surfaces is experimentally and theoretically investigated. Water droplets of 4 µL are placed on micro-pillared silicon substrates with the substrate temperature heated up to 120°C. A comprehensive thermal circuit model is developed to analyze the effects of substrate roughness and substrate temperature on the sessile droplet evaporation. For the first time, two components of heat and mass transfer, i.e., one from the droplet cap surface and the other from the droplet base surface, during droplet evaporation are distinguished and systematically studied. As such, the evaporation heat transfer rates from both the droplet cap surface and the interstitial liquid-vapor interface between micropillars at the droplet base are calculated in various conditions. For droplet evaporation on the heated substrates in the range of 40°C – 80°C, the predicted droplet cap temperature matches well with the experimental results. During the constant contact radius mode of droplet evaporation, the decrease of evaporation rate from the droplet base contributes most to the continuously decreasing overall evaporation heat transfer rate, whereas the decrease of evaporation rate from the droplet cap surface is dominant in the constant contact angle mode. The influence of internal fluid flow is considered for droplet evaporation on substrates heated above 100°C, and an effective thermal conductivity is adopted as a correction factor to account for the effect of convection heat transfer inside the droplet. Temperature differences between the droplet base and the substrate base are estimated to be about 2°C, 5°C, 8°C, 13°C and 18°C for droplet evaporation on substrates heated at 40°C, 60°C, 80°C, 100°C, and 120°C, respectively, elucidating the delayed or depressed boiling of water droplets on a heated rough surface due to evaporative cooling.

Direct numerical simulation of evaporating droplets based on a sharp-interface algebraic VOF approach

This study presents a sharp-interface algebraic volume-of-fluid (SA-VOF) approach towards direct numerical simulation of evaporating droplets in a finite-volume framework. An interface identification scheme is introduced to determine a sharp layer of interface cells where liquid-vapor phase change occurs. The rate of vaporization is directly computed from the local gradient of the vapor mass fraction at the interface without any tuning parameter in the evaporation model. In addition, a modified compressive differencing scheme is employed to maintain high resolution of the interface. A solver based on the SA-VOF approach is developed and validated by several case studies including the Stefan problem for evaporation in one dimension, evaporation of sessile droplets in the constant contact angle mode, and evaporation of droplets suspended in a flowing air stream. Comparisons between numerical predictions and either analytical solutions or experimental data show that the SA-VOF approach not only computes the evaporation rate with high accuracy but also ensures highly resolved liquid-vapor interface. The solver demonstrates the capability in revealing minute details of the complex characteristics associated with droplet evaporation.

Morphology Evolution of a Volatile Liquid Lens on Another Immiscible Liquid Surface Induced by Evaporation.

A theoretical model was established to predict the morphology evolution of a volatile liquid lens evaporation on another immiscible liquid substrate surface. The theoretical model considered the dynamic process of contact line motion. On the basis of the boundary conditions established at the contact line, the morphology change of the liquid lens was calculated by numerically solving the Young-Laplace differential equations for the three interfaces. The mass evaporation rate was calculated by the diffusion-controlled evaporation model. Then, an experimental system was established to record the process of a hexane lens evaporation on the surface of an ionic liquid with a depth of 4 mm. The calculated hexane lens radius variation matches well with the experimental measurements, which shows the rationality of the present model. The calculated results show that the evaporation pattern of the liquid lens follows the constant contact-angle evaporation mode for ∼70% of the lifetime. During the later stage of evaporation, the contact angle decreases, accompanied by contraction of the contact line, which is similar to the mixed evaporation mode in the later stage of sessile droplet evaporation on a solid substrate surface. Furthermore, the influences of the initial hexane lens volume and the ionic liquid temperature on the dynamic contact angle were theoretically summarized. This study helps to provide in-depth insights into regulating the lens evaporation process on another immiscible liquid substrate surface to control the particle deposition mode.

Evaporation of Sessile Binary Mixture Droplets: Time Dependence of Droplet Shape and Concentration Profile from One-Dimensional Magnetic Resonance Microscopy.

Many technological applications like inkjet printing, coating, or cooling processes rely on the evaporation of sessile droplets. Regarding liquid mixtures, the understanding of the underlying physics is still incomplete and process optimization requires trial and error. Our main goal is to establish a novel method in this field, one-dimensional magnetic resonance microscopy, to investigate the evaporation of sessile binary mixture droplets in the microliter range. It allows us not only to determine the droplet volume and shape, including contact angle, but also to measure concentration profiles with a spatial resolution of a few micrometers. These capabilities are demonstrated for a mixture of 1-octanol (OCT) and pentadecafluoro-1-octanol (F-OCT) by combining spatially resolved 1H and 19F nuclear magnetic resonance measurements. We clearly observe three evaporation regimes for the OCT/F-OCT mixture. The first and second regimes are characterized by the predominant evaporation of F-OCT and are separated by a depinning event. The third regime starts when no F-OCT is left and, thus, features the evaporation of a pure OCT droplet. During all stages, concentration gradients perpendicular to the substrate are weak in the studied binary droplet.

Evaporation of a liquid sessile droplet subjected to forced convection

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.

Lifetime Prediction of Sessile Droplet Evaporation with Coupled Fields

The evaporation of sessile droplets has wide applications in various industrial fields. Therefore, it is important to accurately predict the temporal evolution behavior of sessile droplets during evaporation. In this paper, both theoretical analysis and numerical simulation are carried out to explore the evolution of droplet evaporation, with internal thermocapillary convection, interfacial evaporative cooling, and external natural convection coupled together. It is found that internal thermocapillary convection and external natural convection can promote droplet evaporation, while interfacial evaporative cooling can impede it. When a droplet evaporates in a constant contact radius mode, there is a critical initial contact angle, below which the isothermal model can overestimate the evaporation lifetime, and the critical initial contact angle becomes large with increasing substrate superheat. Finally, when the droplet evaporates in the constant contact angle mode, the “2/3 power law” still holds for transient variation of droplet volume, as predicted by the isothermal model. These findings may help obtain insights into the mechanism of droplet evaporation and provide guidance for inkjet printing and surface cooling.

Influence of thermal properties on hydrothermal waves in evaporating sessile droplets

The thermal properties of droplets have a significant effect on the evaporation of sessile droplets. In this study, the influence of nondimensional thermal properties on Marangoni instabilities, especially hydrothermal waves (HTWs), in a sessile droplet evaporating at a constant contact angle mode, is numerically investigated using a nondimensional mathematical model. The model considers the transient deformation of the droplet surface during evaporation in a wide range of Marangoni numbers from 1000 to 40 000, evaporative cooling numbers from 1 to 300, relative heat conductivities from 0.01 to 1000, and Prandtl numbers from 0.01 to 25.0. Included are the different kinds of fluids applied in previous works on Marangoni convection in evaporating sessile droplets. The substrate material varies from a vacuum insulation panel with a heat conductivity of 0.002 W/m·K to silver with 429 W/m·K. The results reveal that a sufficiently large Marangoni number, evaporative cooling number, and relative heat conductivity favor the appearance of HTWs, whereas a large Prandtl number inhibits the appearance of HTWs. The mixture mode of Bénard–Marangoni cells and longitudinal rolls or of longitudinal rolls and HTWs can occur for a small relative heat conductivity. The influence of these thermal properties on the characteristics and dynamic behaviors of HTWs are analyzed and the critical Marangoni numbers for the appearance of HTWs are determined. This work can be helpful for understanding the influence of thermal properties on HTWs in sessile droplets.

Aqueous solutions of AOT as a dispersion medium for stabilization of SiO2 nanoparticles

SiO2 nanoparticles and surfactant sodium bis-(2-ethylhexyl) sulfosuccinate (AOT) are widely used in modern nanochemistry to obtain novel materials in various processes. However, only a few publications are devoted to investigation of the stabilization mechanisms of SiO2 dispersions in aqueous AOT solutions. In this work, the surface electrical properties of SiO2 nanoparticles and the nature of free charges in aqueous solutions were studied over a wide range of AOT concentrations (2.5∙10–6 ÷ 2.5∙10–2 M). The absolute value of ζ-potential of the particles increased from –42 to –58 mV, while the hydrodynamic radius remained constant and equal to ca. 40 nm. Calculations within the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory revealed that stability of hydrosols is caused by the electrostatic component of disjoining pressure. Due to the repulsion of similarly charged nanoparticles and glass substrate, the hydrosols formed coffee rings during evaporation of sessile droplets. The results obtained make it possible to control surface properties of the particles, thus opening the possibility to use SiO2-AOT hydrosols for the formation of various 2D materials and substrates in photonics, catalysis and biosensorics.

Numerical and theoretical analysis of fast evaporating sessile droplets with coupled fields

Sessile evaporating droplets are widely encountered in various scientific and industrial fields, therefore, it is of vital importance for accurate prediction of actual droplet evaporation rates. For slow droplet evaporation, the heat and vapor transport of the droplet are diffusion-controlled, the classic isothermal model can predict the droplet evaporation well. However, for fast droplet evaporation, the convection flow, heat and vapor transfer are strongly coupled together, which brings great difficulty for accurate prediction. In this study, both theoretical analysis and numerical simulation are carried out to study the droplet evaporation with coupled flow, heat and vapor transfer fields. The droplet evaporation is investigated under different evaporative cooling numbers, droplet contact angles and substrate superheats. It is found that droplet evaporation can always be deteriorated by the evaporative cooling effect, while it can be enhanced by thermocapillary convection flow inside the droplet and natural convection outside the droplet. It is surprisingly found that the actual evaporation rates can be higher than those in the isothermal model, especially at low contact angle, high substrate superheat and weak evaporative cooling effect. Besides, a correction factor is proposed to quantify the deviation of actual evaporating rates in our fully coupled model from those in the isothermal model, and provides the dependence of the correction factor on evaporative cooling numbers, contact angles and substrate superheats, which can help predict the actual droplet evaporation rates. These findings may be helpful to get insight into the droplet evaporation and guide for its application.

An immersed boundary-lattice Boltzmann model for simulation of deposited particle patterns in an evaporating sessile droplet with dispersed particles

Use of numerical approach by tracking the particle dynamics and contact line motion to study the complex coffee-ring phenomenon can reveal the underlying transport mechanisms. Here we propose a lattice Boltzmann model coupled with the immersed boundary method to simulate the assembly and deposition of particles suspended inside a drying sessile droplet on a hot substrate. The model deals with sufficiently small size of particles with consideration of the surface contact angle hysteresis. Our simulations show that during the droplet evaporation process, the suspended particles are dragged to the contact line by the evaporation-induced flow, thereby forming the coffee-ring pattern. The formation of ring cluster, in turn, promotes the outward flow due to the capillary force. Furthermore, most of the deposited particles are present around the droplet initial contact line, and the particle ring cluster volume increases almost linearly with particle volumetric fraction. Also, when the contact line is more slippery on the surface, a more uniform deposited particle pattern is formed after the droplet gets dried out. If the substrate temperature is sufficiently high enough, the ring location changes from the droplet's edge to its center to form the “coffee eyes” because of the shorter pinning time of the initial contact line and the Marangoni convection flow inside the droplet. In addition, we discuss the evaporation mode transition from the constant contact radius (CCR) to the mixed mode during the droplet evaporation process.

Pattern Formation upon Evaporation of Sessile Droplets of Polyelectrolyte/Surfactant Mixtures on Silicon Wafers.

The formation of coffee-ring deposits upon evaporation of sessile droplets containing mixtures of poly(diallyldimethylammonium chloride) (PDADMAC) and two different anionic surfactants were studied. This process is driven by the Marangoni stresses resulting from the formation of surface-active polyelectrolyte–surfactant complexes in solution and the salt arising from the release of counterions. The morphologies of the deposits appear to be dependent on the surfactant concentration, independent of their chemical nature, and consist of a peripheral coffee ring composed of PDADMAC and PDADMAC–surfactant complexes, and a secondary region of dendrite-like structures of pure NaCl at the interior of the residue formed at the end of the evaporation. This is compatible with a hydrodynamic flow associated with the Marangoni stress from the apex of the drop to the three-phase contact line for those cases in which the concentration of the complexes dominates the surface tension, whereas it is reversed when most of the PDADMAC and the complexes have been deposited at the rim and the bulk contains mainly salt.

Boiling evaporation characteristics of sessile droplets and its transition evaporation mode

Providing an enormous heat transfer, droplet boiling evaporation is widely used in the liquid cooling for nucleate reactors and high-power electronic devices and other fields. This paper reported a combined theoretical and experimental study on the evaporation characteristics of the droplets attached to a high temperature wall (>100°C). Different from the non-boiling evaporation, the effect of droplet temperature on evaporation time, contact angle and evaporation process are investigated. Nucleate boiling regime in the evaporation of a single droplet, especially the transition from static evaporation to nucleate boiling is investigated. Our results report that the evaporation of sessile droplets in boiling regime is very intense, and can be classified into five stages according to the change in internal bubble morphology, namely the wall bubble germination, wall bubble growth, global bubble germination, global bubble growth, and central large bubble formation. Droplet evaporation does not follow the constant contact diameter pattern in the non-boiling regime, but consists of growth period, steady period, and decline period. Basically consistent with the experimental results, the feasibility of numerical simulation to study the droplet evaporation in the boiling regime is verified.

Contact-line deposits from multiple evaporating droplets

Evaporating sessile droplets interact with neighboring droplets via their vapor fields, resulting in nonaxisymmetric evaporative fluxes from their surfaces. One of the consequences of this asymmetry is that, unlike the uniform deposits left at the contact lines of isolated droplets, the deposits left at the contact lines of droplets with neighbors are, in general, nonuniform. In this work we develop a theoretical model for the contact-line deposits from multiple evaporating droplets, and find its predictions for a pair of identical droplets to be in excellent agreement with recent experimental results.

Evaporation of a sessile droplet on flat surfaces: An axisymmetric lattice Boltzmann model with consideration of contact angle hysteresis

Droplet evaporation is a widely encountered heat and mass transfer phenomenon. Due to its 3D in nature, it is challenging to simulate the complex 3D droplet evaporation process. Here, we propose an axisymmetric lattice Boltzmann (LB) model to simulate the dynamics of contact line motion during sessile droplet evaporation on a flat heated surface, taking contact angle hysteresis into consideration. We demonstrate that this LB model can numerically simulate the evaporation processes of sessile droplet evaporation processes undergoing constant contact angle (CCA), constant contact radius (CCR), and mixed modes sequentially. The classical D2-law for droplet surface mass transfer is confirmed numerically by using the case of a floating droplet evaporation, thereby proving that the axisymmetric LB model is capable of 3D simulation. Our simulated results on temporal variations of contact radius, contact angle are found in good agreement with two different sets of literature experimental data. Specifically, we compute the local mass transfer rate on the droplet surface from the simulated velocity field to show that the evaporation rate near the triple-phase contact region is much higher than that at the droplet apex region, with the peak heat flux occurring near the location of the dynamic contact line. The contact angle fluctuates with stick-slip motion are found during the CCA stage of the evaporation process at higher substrate temperatures. Additionally, we analyse the non-quasi-equilibrium evaporation mode and contact line slip velocity on substrates surface at higher temperatures.

Pattern Formation upon Evaporation of Sessile Droplets of Polyelectrolyte/Surfactant Mixtures on Silicon Wafers

Pattern Formation upon Evaporation of Sessile Droplets of Polyelectrolyte/Surfactant Mixtures on Silicon Wafers

Numerical model using a Volume-Of-Fluid method for the study of evaporating sessile droplets in both unpinned and pinned modes

We propose a numerical study of the evaporation of sessile droplets using a Volume-Of-Fluid (VOF) method in the free-software Basilisk. We consider pure liquid droplets forming a spherical-cap onto a smooth or rough substrate and we investigate two different modes of evaporation: the unpinned mode where the contact angle is constant and the pinned mode where the wetting area is constant. The numerical method used to implement the contact angle and for the reconstruction of the interface is fully described, especially for the pinned mode for which we present a new VOF implementation. In the unpinned mode, the parametric studies predict that the volume decreases in time according two phases, which matches the signature behavior of evaporating unpinned droplets, irrespective of the geometrical parameters. In the pinned mode, the volume follows a linear decrease for the whole evaporation time and the contact angle analysis indicates a linear decrease in time which was expected according to the theory and validated with some experiments we performed.

Multi-axis alignment of Rod-like cellulose nanocrystals in drying droplets

HypothesisRadial capillary flow in evaporating droplets carry suspended nanoparticles to its periphery where they are deposited and form a coffee-ring. Rod-like nanoparticles seeking to minimize their capillary energy will align with their long-axis parallel to the contact line. Particles exhibiting electrostatic repulsion, such as cellulose nanocrystals (CNCs), establish a competition between capillary flow-induced impingement against a growing coffee-ring and entropic minimization leading to enhanced particle mobility. Therefore, balancing these effects by manipulating the local particle concentration in drying droplets should result in deposition with a controlled orientation of CNCs. ExperimentsThe dynamic local order in aqueous suspensions of CNCs in evaporating sessile droplets was investigated through time-resolved polarized light microscopy. The spatial distribution of alignment in deposited CNCs was explored as a function of nanoparticle concentration, droplet volume, initial degree of anisotropy, and substrate hydrophobicity. Computational analysis of the rotational Péclet number during evaporation was also investigated to evaluate any effects of shear-induced alignment. FindingsMultiple modes of orientation were identified suggesting local control over CNC orientation and subsequent properties can be attained via droplet-based patterning methods. Specifically, high local particle concentrations led to tangential alignment and lower local particle concentrations resulted in new evidence for radial alignment near the center of dried droplets.

Consistent evaporation formulation for the phase-field lattice Boltzmann method.

A consistent evaporation model is developed for the conservative Allen-Cahn-based phase-field lattice Boltzmann method that uses an appropriate source term to recover the advection-diffusion equation for the specific humidity. To evaluate the accuracy of the proposed scheme, simulations are conducted of a steady-state one-dimensional Stefan flow for a flat interface and a three-dimensional evaporating sessile droplet on a flat substrate for a curved interface. It is confirmed that the results for the evaporative mass flux of the Stefan flow agree well with those obtained from the analytical solution within a specific humidity range of 0.8 or less at the liquid-gas interface. For the sessile droplet case, the results for the dependence of the contact angle on the evaporative mass flux and its profile show good agreement with those obtained from the model of Hu and Larson [J. Phys. Chem. B 106, 1334 (2002)JPCBFK1520-610610.1021/jp0118322].

Experimental study on the interfacial heat transfer of sessile droplet evaporation using temperature-sensitive paint

The present work is aimed at analyzing changes in the interfacial temperature distribution and interfacial heat flux distribution during sessile droplet evaporation. In particular, two kinds of nonintrusive measurement techniques, temperature-sensitive paint (TSP) and infrared imaging were used simultaneously. TSP was used to capture the interfacial temperature distribution, and then a one-dimensional unsteady transient model was established to obtain the heat flux distribution. An infrared camera was applied to observe the thermal patterns during droplet evaporation from the top view. Three kinds of liquids, pentane, HFE-7100 and hexane, were used during our experiments, and the experimental results show that the contact line profile captured by TSP was consistent with that captured by an infrared camera. Three stages could be observed during droplet evaporation: initial droplet heating, convection cell evaporation and thin film evaporation. Convection cells could be observed in the infrared images during the second stage, and an obvious temperature gradient at the contact surface could also be seen from the images captured by TSP. In addition, the heat flux at the contact line was higher than that at the centre. Finally, the heat dissipation due to droplet evaporation could also be obtained by double integration of interfacial heat flux data with contact area and evaporation time, which further demonstrated the soundness of the present experimental and calculated methods.

Estimation the dielectric properties of solvation shells and nano-cavities by solvatochromic shift of organic dye

We investigated the preferential solvation effect of pyridinium-N-phenolate betaine (organic dye) taken as a molecular probe in two binary solvents (water-BuOH and water-BuNH2) in concentration range 0-100%. The Onsager-Liptay model was used to connect the spectral solvatochromic shift in solvation shell of the dye with the dielectric permittivity of the environment around its chromophore. That makes it possible to estimate the effective dielectric constant in the microscopic region of the probe, based on the values of the experimentally measured solvatochromic shifts. It was shown that the solvation shell of the dye is significantly depleted with the second component of binary solvent in water solution. It is true both for the water-BuOH and water-BuNH2 solvents. The absolute spectral shift in case of water-BuNH2 solvent is greater than in the second case. However, the relative depletion is stronger in case of water-BuOH. The innovative potential of the method is in the development the nanoprobe devices to measure the dielectric constant of small objects and nano-regions, to control instantaneous solvent concentration into evaporating sessile droplet of binary solvent in different zones of the droplet.