Sessile Drop Evaporation Research Articles

Contact Angle Modulation: In Situ Polymer Deposition during Sessile Drop Evaporation.

The drying kinetics of a sessile drop on a solid surface are a widely studied phenomenon because of their relevance to various fields such as coating, printing, medical diagnostics, sensing, and microfluidic technology. Typically, the drop undergoes drying either at a constant contact radius (R) with a decrease in the three-phase contact angle or at a constant contact angle (θ) with a reduction in the radius with time. These two drying modes are referred to as CCR and CCA, respectively. It is not uncommon where both R and θ may decrease during drying, especially in the penultimate stage of drying. In this work, we report a scenario wherein the θ increases while R decreases during the drying process of an aqueous polymer solution on a high surface energy substrate. This behavior is observed across different polymer systems (such as poly(ethylene oxide) and polyvinyl pyrrolidine), varying molecular weights, and polymer concentrations. As the drop dries, the polymer gets deposited at the three-phase contact line, thus reducing the surface energy of the substrate and leading to an increase in the contact angle. The drop responds by attempting to reach a new equilibrium contact angle through slipping. The temporal increase in contact angle follows a power law scaling behavior. This study demonstrates an in situ modulation of contact angle facilitated by evaporation and polymer deposition, showcasing unconventional drying dynamics.

Heat transport during drop impact onto a heated wall covered with an electrospun nanofiber mat: The influence of wall superheat, impact velocity, and mat thickness

Nanofiber surface coating is a promising method for the enhancement of heat transfer during spray cooling. In the present work, the drop dynamics as well as local and overall heat transfer during single drop impact onto a heated wall covered with a polyacrylonitrile (PAN) nanofiber mat are investigated to obtain insight into the mechanisms governing the heat transport enhancement. The influence of wall superheat, drop impact velocity, and mat thickness on the hydrodynamics and heat transfer from the heated wall to the fluid is studied. The experiments were conducted inside a temperature-controlled test cell with a pure vapor atmosphere maintained with refrigerant FC−72 (perfluorohexane). The temperature field at the solid–fluid interface was observed with a high-speed infrared camera, and the heat flux field was derived by solving a three-dimensional transient heat conduction equation within the substrate. The presence of the nanofiber mat on the heater surface suppresses the drop receding phase due to the pinning of the contact line at the end of the spreading phase. Two different heat transfer scenarios are observed depending on the wall superheat and drop impact velocity: scenario (I), in which the liquid drop completely penetrated through the porous nanofiber mat and made contact with the heater surface; and scenario (II) in which the vapor produced inside the pores of the nanofiber mat prevented the liquid drop from touching the heater surface. In scenario (I), an up 450% heat flow enhancement during the sessile drop evaporation stage has been observed. In scenario (II), a 80% heat flow enhancement at this stage has been registered.

Modeling the effect of shape deformation induced by gravity on the evaporation of pendant and sessile drops

Pendant and sessile drops form a spherical cap only in the absence of gravity. The effect of gravity on drop shape is often neglected on the basis of the assumption that the drop size is smaller than the capillary length [Lc=(σ/gρ)1/2], although the deformation may not be fully negligible even in those cases. This paper focuses on evaluation of the effect that deformation due to gravity has on the evaporation characteristics of pendant and sessile drops. The drop shape is described by the Bashforth–Adams equation, a non-linear second order ordinary differential equation, which is solved numerically using a Runge–Kutta method with variable time steps. Under quasi-steady approximation, the species and energy conservation equations in the gas phase have analytical solutions, even for temperature-dependent gas thermophysical properties, once the solution of a basic Laplace problem is known. The Laplace equation is solved in axial symmetric geometry by using COMSOL Multiphysics®, for a wide range of drop sizes and contact angles, yielding vapor distribution, vapor fluxes, and evaporation rates. Comparison with the results from drops of same size in microgravity (i.e., having a spherical cap shape) shows that the effect is also perceptible for drops with a size smaller than the capillary length and that it can become quite important for those with larger sizes. Complementary results are found for sessile and pendant drops with respect to wall wettability, suggesting that the phenomenon can be analyzed using a unitary approach.

Slow evaporation of a small sessile liquid drop: new solutions based on the electrostatic analogy

Evaporating sessile drop of liquid deposited on horizontal surface is an important object of applications and theoretical investigations. The evaporating flow density dramatically depends on contact angle of the droplet. Previously, the dependence of the flux density on the polar angle was established for arbitrary contact angles. The expression has the form of an integral and is rather complicated for use in modelling algorithms. In this paper, we propose new exact solutions for the set of some specific contact angles (135-180 degrees). The analogy of the drop evaporation problem with a similar problem from the field of electrostatics of equipotential surfaces, which has been solved in general terms before us, was used. The results of British mathematician H.M. Macdonald and Soviet scientist G.A. Grinberg were used in the derivation. Thus, relatively simple expressions for the evaporation flux density were found.

Disorder-to-order transition of long fibers contained in evaporating sessile drops

We demonstrate self-organization of hydrophilic fibers, contained in a sessile droplet in a disordered initial configurations, to transform into an order deposit. Findings suggest new avenues to decorate solid surfaces with filamental structures.

Evaporation of Small Sessile Drop Deposited on a Horizontal Solid Surface: New Exact Solutions and Approximations

Evaporating a liquid sessile drop deposited on a horizontal surface is an important object of applications (printing technologies, electronics, sensorics, medical diagnostics, hydrophobic coatings, etc.) and theoretical investigations (microfluidics, self-assembly of nanoparticles, crystallization of solutes, etc.). The arsenal of formulas for calculating the slow evaporation of an axisymmetric drop of capillary dimensions deposited on a flat solid surface is reviewed. Characteristics such as vapor density, evaporation flux density, and total evaporation rate are considered. Exact solutions obtained in the framework of the Maxwellian model, in which the evaporation process of the drop is limited by vapor diffusion from the drop surface to the surrounding air, are presented. The summary covers both well-known results obtained during the last decades and new results published by us in the last few years, but practically unknown to the wider scientific community. The newest formulas, not yet published in refereed publications, concerning exact solutions for a number of specific contact angles are also presented. In addition, new approximate solutions are presented (total evaporation rate and mass loss per unit surface area per unit time in the whole range of contact angles θ∈[0, π), drop lifetime in constant contact radius evaporation regime and constant contact angle mode), which can be used in modeling without requiring significant computational resources.

Water Drop Evaporation on Slippery Liquid-Infused Porous Surfaces (SLIPS): Effect of Lubricant Thickness, Viscosity, Ridge Height, and Pattern Geometry.

Sessile drop evaporation and condensation on slippery liquid-infused porous surfaces (SLIPS) is crucial for many applications. However, its modeling is complex since the infused lubricant forms a wetting ridge around the drop close to the contact line, which partially blocks the free surface area and decreases the drop evaporation rate. Although a good model was available after 2015, the effects of initial lubricant heights (hoil)i above the pattern, and the corresponding initial ridge heights (hr)i, lubricant viscosity, and solid pattern type were not well studied. This work fills this gap where water drop evaporations from SLIPS, which are obtained by infusing silicone oils (20 and 350 cSt) onto hydrophobized Si wafer micropatterns having both cylindrical and square prism pillars, are investigated under constant relative humidity and temperature conditions. With the increase of (hoil)i, the corresponding (hr)i increased almost linearly on lower parts of the drops for all SLIPS samples, resulting in slower drop evaporation rates. A novel diffusion-limited evaporation equation from SLIPS is derived depending on the available free liquid-air interfacial area, ALV, which represents the unblocked part of the total drop surface. The calculation of the diffusion constant, D, of water vapor in air from (dALV/dt) values obtained by drop evaporation was successful up to a threshold value of (hoil)i = 8 μm within ±7%, and large deviations (13-27%) were obtained when (hoil)i > 8 μm, possibly due to the formation of thin silicone oil cloaking layers on drop surfaces, which partially blocked evaporation. The increase of infused silicone oil viscosity caused only a slight increase (12-17%) in drop lifetimes. The effects of the geometry and size of the pillars on the drop evaporation rates were minimal. These findings may help optimize the lubricant oil layer thickness and viscosity used for SLIPS to achieve low operational costs in the future.

Sessile drop evaporation in a gap – crossover between diffusion-limited and phase transition-limited regime

We consider the time evolution of a sessile drop of volatile partially wetting liquid on a rigid solid substrate. The drop evaporates under strong confinement, namely, it sits on one of the two parallel plates that form a narrow gap. First, we develop an efficient mesoscopic long-wave description in gradient dynamics form. It couples the diffusive dynamics of the vertically averaged vapour density in the narrow gap to an evolution equation for the profile of the volatile drop. The underlying free energy functional incorporates wetting, interface and bulk energies of the liquid and gas entropy. The model allows us to investigate the transition between diffusion-limited and phase transition-limited evaporation for shallow droplets. Its gradient dynamics character allows for a long-wave as well as a full-curvature formulation. Second, we compare results obtained with the mesoscopic long-wave model to corresponding direct numerical simulations solving the Stokes equation for the drop coupled to the diffusion equation for the vapour as well as to selected experiments. In passing, we discuss the influence of contact line pinning.

Characterization of the Temperature Profile near Contact Lines of an Evaporating Sessile Drop

Evaporation of a sessile drop is ubiquitous in nature and has many industrial applications. Despite extensive studies over recent decades, a critical issue, i.e., how temperature varies near contact lines, remains elusive. In this work, we report to date the first direct experimental measurement showing the microscopic temperature distribution near contact lines of an evaporating pinned sessile drop. Using a fluorescence-based thermometry, we find that the temperature at the free interface near contact lines varies drastically along the radial direction, engendering a concentric fringe pattern that evolves over the evaporation lifespan. The formation of such fringe patterns is attributed to a combined mechanism of locally enhanced evaporative cooling at the drop edge and the development of interfacial convective vortices due to Bénard-Marangoni instability. We also study the evaporation dynamics at different initial contact angles and find that the characteristics of this fringe pattern vary as the initial contact angle decreases. Our experimental investigation and theoretical analysis in this work reveal insights to the understanding of droplet evaporation dynamics in various heat transfer systems.

Vapor concentration and temperature field measurement of an evaporating sessile drop by tomographic laser absorption spectroscopy

Drop evaporation is a ubiquitous phenomenon that has been studied for over a century. However, the surrounding gas-phase field including the temperature and vapor concentration distribution is not sufficiently studied experimentally. In this paper, a sensor based on tunable laser absorption spectroscopy is designed to study the vapor-phase temperature and concentration distribution of evaporating sessile drops, and data processing method involving data pre-processing and tomographic reconstruction is proposed to realize high-precision, spatially resolved measurement, which was realized by scanning the mechanical galvanometer in the horizontal direction. With free-knot splines smoothing and “denucleated” onion-peeling algorithm, temperature and H2O concentration distributions surrounding the evaporated drop at three different substrate plate temperatures are observed. The concentration and temperature in close vicinity to the gas–liquid interface are reconstructed accurately despite the high-gradient changes. A spatial resolution of under 100 μm with a temporal resolution of 10 s has been realized. Quantitative depiction of the temperature and concentration fields shows evidence of convection and indicates that while the concentration level sharply peaks at the interface, temperature in the close vicinity to the drop shows flattening or even dipping trends. The in situ laser measurement results are validated against contact measurement, theoretical prediction with saturated vapor pressure, and model simulation of COMSOL. Uncertainties have been evaluated based on both repeated measurements and model prediction of input uncertainty propagation. Temperature and concentration measurement uncertainties are estimated to be <1.5% and <3.5%, respectively, even though all experiments were performed in open air with non-negligible buoyancy-induced convection.

Effect of temperature and surfactants on evaporation and contact line dynamics of sessile drops

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.

Analytical solutions for modelling the evaporation of sessile drops

An analytical model for drop evaporation in gaseous environments that accounts for the effect of Stefan flow and temperature dependence of the thermo-physical properties is extended to the case of sessile drops. The exact solution to the conservation equations in toroidal coordinates based on the Mehler-Fock transform is reformulated in terms of simple functions by using the method of images for specific values of the contact angle. The method is then extended in approximate form to general values of the contact angles. The accuracy of this approximation is quantified for hydrophobic and hydrophilic cases, thus showing the applicability of the model to a wide range of wettability conditions.

Numerical model for sessile drop evaporation on heated substrate under microgravity

• One-sided numerical model is developed for sessile drop evaporation on heated substrate under microgravity. • Flow motion is analyzed by 3D resolved computations of evaporating sessile drop. • Transition from primary to secondary instability occurs at critical aspect ratio. • First time fine effects of secondary instabilities on evaporation rate are captured. Although sessile drops have simple geometries, the physics involved in their evaporation process is complex owing to their numerous intricate interactions and their fluid nature. An accurate quantitative model of the evaporation process will enable increased understanding and control over the process. In this study, a numerical model is developed for sessile drop evaporation on a heated substrate under microgravity based on the results of rocket and parabolic experiments to understand the ’internal dynamics of a sessile drop. The model is quantitatively validated through experiments. Subsequently, a correlation between substrate temperature and evaporation rate is suggested for an ethanol sessile drop. The flow motion is analyzed by conducting three-dimensional resolved computations of an evaporating sessile drop. This provides insights into the Marangoni effect in the dynamics of the evaporation process and the occurrence of secondary instabilities. For the first time, the fine effects of secondary instabilities on the evaporation rate are captured. Our numerical model is valid in the absence of convection in the vapor phase, producing an interface of an evaporating drop in a fully saturated vapor, which typically exists under microgravity conditions.

Sessile drop evaporation approach to detect starch adulteration in milk

Milk adulteration is a major challenge faced by the dairy sector. Starch is a common milk adulterant with negative impact on consumer health. The major shortfalls in the present methods for detection and quantification of starch in milk are the higher limit of detection (LOD) and the need for additional chemical reagents. Hence, developing a chemical-free method with lower LOD for starch in milk is urgently required, especially in low- and middle-income countries. We propose a sessile drop evaporation-based approach to detect starch adulteration in milk. The influence of starch adulteration on the evaporative deposition patterns is studied using light microscopy as a function of dilution level (10–50%, v/v), starch type (potato and tapioca starches) and starch concentration (0.005–0.2%, w/v). The dried deposit patterns formed after drying drops of pristine and adulterated milk at 60 °C are dictated by the competing effects of outward capillary flow and inward Marangoni flows. Confocal Raman spectroscopy indicated the presence of fatty acids and other lipophilic constituents at the center, a combination of proteins and lipophilic constituents at the edge, and starch in regions close to the coffee stain, i.e., at the edge of the dried deposits. Higher level of water addition and lower level of starch adulteration resulted in the formation of coffee ring deposits with larger width. Surface profilometry indicated a decrease in the height of coffee-ring with increase in the concentration of both water and starch. The width and maximum height of edge deposits thus measured are proposed as the parameters to quantify starch concentration in milk. The proposed approach is effective in detecting starch concentration as low as 0.005% (w/v), as well as identifying the starch type, thereby facilitating facile, rapid, chemical-free, and in situ detection of starch adulteration in milk.

Flow and heat measurement within self-rewetting mixtures of 1-pentanol and water drops

Recently interest has arisen in the use of so-called self-rewetting mixtures for micro-scale heat transfer systems. Such fluids, in which the surface tension can increase with increasing temperature, are expected to offer superior evaporative cooling performance by extending the region of operation before dry-out of the heated surface sets in. Whilst improved performance has been shown in some practical situations using these fluids, it is not entirely clear as to the mechanism of such improvements. We have studied the flow within evaporating sessile drops of 1-pentanol-water mixtures using micro-PIV and have observed three stages in the evaporation process. During the first stage there appears to be a single toroidal vortex with flow inwards along the base of the drop. The vortex only occupies the central region of the drop and appears to pulsate, reducing in size during evaporation. This is followed by a second transition stage to a third stage in which the flow is directed radially outward, as observed by us for pure water droplet evaporation and in the latter stages of ethanol-water drop evaporation.

Nonaxisymmetry and flow transition in evaporating water drops

Understanding the internal flow in evaporating sessile drops is of paramount importance in a myriad of applications such as ink-jet printing, surface patterning, and medical diagnostics. Marangoni flow driven by a gradient in surface tension is an essential internal flow mechanism, whose characteristics in evaporating water drops remain elusive in the literature. Here, by employing infrared thermography and particle image velocimetry, we show that the manifestation of Marangoni flow as a convective cell at the liquid–vapor interface results in a nonaxisymmetric internal flow field. Eventually, during evaporation, the flow transitions to a buoyancy-dominated regime, where an axisymmetric toroidal flow is observed. This transition marks a reversal in the flow along with an order of magnitude decrease in velocity. We corroborate this experimentally observed transition using previously reported analytical and scaling frameworks. Finally, we present hitherto unreported features correlating the three aspects of evaporating water drops, viz., contact line dynamics, thermal field, and internal flow field, which are generally investigated independently.

Effect of Temperature and Surfactants on Evaporation and Contact Line Dynamics of Sessile Drops

Effect of Temperature and Surfactants on Evaporation and Contact Line Dynamics of Sessile Drops

Experimental investigation of hydrodynamics and heat transport during horizontal coalescence of two drops impinging a hot wall

This paper presents an experimental study on hydrodynamics and heat transport during the horizontal coalescence of two drops impinging a hot wall. The study addresses the influence of distance between impact locations, the time interval between drop impact, and wall superheat on the transport processes. The experiments were conducted under a pure vapor atmosphere with the refrigerant FC-72 at a saturation temperature of 54°C, corresponding to a system pressure of 0.94 bar. The drops were generated with a constant diameter and a constant impact velocity. The temperature field at the surface of the heater was measured by an infrared camera with a high spatial and temporal resolution. The local heat flux distribution was derived from the temperature field by solving the transient three-dimensional heat conduction equation within the substrate. The total heat flow was evaluated by integrating the local heat fluxes over the footprint of the drop. The impact parameters (drop size and impact velocity), the time interval between drop impact, and the distance between impact locations were evaluated through post-processing of the black-and-white images captured employing a high-speed camera. The results for simultaneous drop impingement reveal that the heat transported from the wall to the fluid is not affected by the presence of neighboring drop as long as the drops do not contact each other. In the case of horizontal coalescence of drops, the heat flow is reduced both during the spreading and receding phases and during the sessile drop evaporation phase. This can be explained by the reduction of solid–liquid interface and of three-phase contact line length after the coalescence. An increase in wall superheat leads to reducing the footprint of the drop and increasing of heat flow. Asymmetric behavior of the drop hydrodynamics and heat flux is observed during the non-simultaneous drop impingement.

The effect of surface structures on evaporation and free convection in evaporating sessile drops

The effect of various surface structures of the AlMg6 aluminum-magnesium alloy on the evaporation rate and convection in a sessile droplet was experimentally studied. Structures on the surface were created using laser exposure. The evaporation of water droplets on heated structured surfaces was compared with a smooth wall. The wall temperature Tw = 68 °C. The data obtained for the evaporation rate without taking into account the diameter of the droplet base for a structured hydrophilic surface is 11-13% higher than for a smooth surface. The difference between structured hydrophilic and hydrophobic surfaces was 4-6%. The strongest effect of convection enhancement was observed for a structured hydrophobic surface.

Tunable coffee-ring formation of halloysite nanotubes by evaporating sessile drops.

Halloysite nanotubes (HNTs) are one-dimensional clay nanomaterials with a length of 200-1000 nm and a diameter of ∼50 nm. Understanding the self-assembly behavior of such unique nanoparticles is important to develop their applications in functional devices. In this study, the "coffee-ring" patterns of HNTs are investigated which are formed by evaporation of the sessile droplets of HNT aqueous dispersion on different substrates. The coffee-ring pattern with various dimensions was characterized using a polarizing microscope (POM), a scanning electron microscope (SEM), and a 3D optical profilometer. The diameter, height, and area of the coffee-ring patterns depend on the concentration of HNT dispersion, the droplet volume, and surface wettability. POM and SEM results suggested that the nanotubes were highly ordered in the edge and the middle of the coffee-ring. The coffee-ring effect of HNTs could be suppressed by increasing the evaporation temperature of substrates or adding polymer additives. In addition, multiple-ring patterns consistent with protein rings surrounding HNT rings were formed, which can be utilized to detect the presence of proteins in biological samples. This work illustrated the relationship between the formation of coffee-ring patterns and the experimental conditions, which provided an additional research chance and allowed application development for HNTs using the liquid droplet self-assembly.