Sessile Droplet Research Articles

Transients of Marangoni and Stefan advection dynamics during generic sessile droplet evaporation

We probe the transient evolution of Marangoni thermo-hydrodynamics in the liquid domain and the Stefan advection in the gaseous domain during evaporation of sessile droplets with generic contact line dynamics [both constant contact radius (CCR) and constant contact angle (CCA) modes]. A transient arbitrary Lagrangian–Eulerian framework was considered to computationally model the evaporation phenomenon over the droplet lifetime. The governing equations corresponding to the transport processes in both liquid and gaseous domains are simulated in a fully coupled manner, while precisely tracing the liquid–vapor interface and three phase contact line. The effects of the wetting state and contact line dynamics during CCR and CCA modes were explored, and good agreement with experimental observations is noted. The results show that the non-uniformity in an internal temperature field due to evaporation leads to formation of multi-vortex Marangoni patterns in the flow field at initial periods. At the quasi-stable state, the temperature variation becomes monotonic, thereby resulting in a single recirculation vortex in both liquid and gaseous domains. For the CCR mode, the strength of these advection fields is solely governed by a critical contact angle of ∼32°, which is determined to correspond to the critical Marangoni number. Beyond this critical point, viscous action becomes significant, and the fluid motion mitigates progressively with the formation of twin vortices at final stages due to localized heat advection near the contact line. For the CCA mode, the strength of initial vortices augments with progressing time due to amplified evaporative fluxes at smaller contact radius. The internal thermofluidic patterns and evaporative modes in turn modulate the external Stefan flow fields and neighborhood temperature fields. These findings may hold strong implications for efficient functioning of practical droplet based processes involving transport, mixing, and deposition of dissolved particles.

Investigation of Ferrofluid Sessile Droplet Tensile Deformation in a Uniform Magnetic Field

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.

A modeling study on freezing characteristics of sessile and pendant water droplets on cold plate surfaces

The freezing phenomena of sessile and pendant water droplets on horizontal and inverted surfaces are widespread in industrial fields, which always causes great structural destruction and energy waste. Considering the gravity effect on the droplet profile, a theoretical model is developed to calculate the freezing characteristics of sessile and pendant droplets and experimentally verified. The average deviation of the model in the droplet freezing time is 10.53 % and the determination coefficient in the droplet profile is above 98 %. Based on the model, the freezing characteristics of sessile and pendant droplets under different water droplet volumes (characterized by the Bond number, Bo), contact angles and cold plate temperatures are investigated. When Bo ≤ 1, there is almost no difference in the freezing characteristics of sessile and pendant droplets. When Bo > 1, obvious differences are observed with a pendant droplet having a higher height and a longer freezing time. For both sessile and pendant droplets, the freezing height is approximately proportional to the initial height with the sessile droplet yielding a smaller proportion coefficient. Their freezing times can be written as a function of the Bond number, contact angle and cold plate temperature. Under the same condition, the ratio of freezing time by the pendant droplet to that by the sessile one is scaled as Bo1/4 when Bo > 1. The findings in this study help better understand the freezing characteristics of the sessile and pendant droplets and thus optimize anti-icing and anti-frosting technologies.

Joint effect of air flow and substrate wettability on evaporation of a sessile droplet on a solid surface

We study the evaporation of microliter droplets of water on hydrophilic, hydrophobic, and superhydrophobic substrates subjected to airflow around them. While there is a large body of literature on diffusion-limited evaporation, evaporation in the presence of external convection is not fully-explored. We use side-view imaging and a custom-built flow channel to record the evaporating droplets from the side and develop an analytical model for evaporation in the presence of convection. Based on the droplet’s inlet flow velocity and wetted diameter, the maximum Reynolds number is 203. We quantify the time-variation of droplet volume, wetted diameter, and dynamic contact angle as a function of substrate wettability and airflow velocity. We found that the droplet lifetime decreases with the airflow, which is explained by the larger contribution of the convective mass loss rate compared to the diffusive mass flow rate computed by the model. Interestingly, the droplet lifetime is longer on a hydrophobic substrate due to the smallest area of liquid-gas interface among the three substrates for a given airflow. In general, evaporation occurs at constant contact radius (CCR) mode for hydrophilic surface in case of without flow and for all cases of airflow velocity. The CCR followed by constant contact angle (CCA) mode is observed for hydrophobic surface, and CCA followed by mixed mode is reported for superhydrophobic surface. The theoretical model reasonably predicts the measurements of different cases of airflow velocity and substrate wettability.

A second-order-accurate approximation for the shape of a sessile droplet deformed by gravity

A second-order-accurate approximation for the shape of a sessile droplet deformed by gravity

Coalescence of immiscible sessile droplets on a partial wetting surface

Droplet coalescence is a common phenomenon and plays an important role in multidisciplinary applications. Previous studies mainly consider the coalescence of miscible liquids, even though the coalescence of immiscible droplets on a solid surface is a common process. In this study, we explore the coalescence of two immiscible droplets on a partial wetting surface experimentally and theoretically. We find that the coalescence process can be divided into three stages based on the time scales and force interactions involved, namely (I) the growth of a liquid bridge, (II) the oscillation of the coalescing sessile droplet and (III) the formation of a partially engulfed compound sessile droplet and the subsequent retraction. In stage I, the immiscible interface is found not to affect the scaling of the temporal evolution of the liquid bridge, which follows the same 2/3 power law as that of miscible droplets. In stage II, by developing a new capillary time scale considering both surface and interfacial tensions, we show that the interfacial tension between the two immiscible liquids functions as a non-negligible resistance to the oscillation which decreases the oscillation periods. In stage III, a modified Ohnesorge number is developed to characterize the visco-capillary and inertia-capillary time scales involved during the displacement of water by oil; a new model based on energy balance is proposed to analyse the maximum retraction velocity, highlighting that the viscous resistance is concentrated in a region close to the contact line.

Dust mitigation by a water droplet in between movable and modified wetting states surfaces

A novel approach for mitigating environmental dust from hydrophobic surfaces using a water droplet is presented. A sessile droplet is sandwiched between two parallel plates, one of which is moveable and hydrophilic while the other is stationary and hydrophobic. Investigations are conducted into how plate spacing affects the dust mitigation rate and the droplet's level motion. The high-speed camera analyzes the droplet motion for various plate spacing, dusty regions, and droplet sizes. In a controlled laboratory setting, the movement of fluid and dust particles inside a droplet is simulated. The results showed that when a droplet is still, it effectively reduces dust. The droplet meniscus expands by decreasing the gap between the droplet and the surface, increasing the dust removal rate. While the Magdeburg force and surface tension influence the droplet's adhesion to a hydrophobic surface, surface tension remains the primary factor affecting droplet pinning on a hydrophilic plate, more so than pinning on a dusty hydrophobic surface. When compressing, a current is created in the droplet fluid, greatly accelerating the rate at which dust is removed from the hydrophobic surface. We also move a dangling droplet over a dirty surface to evaluate its cleaning effectiveness and find that a 60 µL droplet has a 97% cleaning effectiveness and can remove dust from up to 450 mm2 of surface area. Our study provides insight into the unique method of removing dust from active surfaces and sheds light on droplet pinning forces generated by the Magdeburg effect in nano-cavities during vertical and horizontal movement.

Liquid-Liquid Phase Separation Induced by Vapor Transfer in Evaporative Binary Sessile Droplets.

Drying of binary sessile droplets consisting of ethanol and octamethyltrisiloxane on a high-energy surface is investigated. During the process of evaporation, the droplets undergo liquid-liquid phase separation, resulting in the appearance of microdroplets at the liquid-air interface, which subsequently violently burst. This phase separation is attributed to water vapor transfer into the droplet, which modifies the solubility and leads to the formation of a ternary mixture. The newly formed ternary mixture may undergo nucleation and growth or spinodal decomposition, depending on the droplet composition path. By control of the relative humidity of air, phase separation can be mitigated or even eliminated. The droplets also display high mobility and complex wetting behavior due to phase separation, with two contracting and two spreading stages. The mass loss experiments reveal that the droplets undergo three distinct drying stages with an enhanced evaporation rate observed during the phase separation stage. A modified diffusion-limited model was employed to predict the evaporation rate, accounting for the physiochemical changes during evaporation and proved to be consistent with experimental observations. The findings of this work enhance our understanding of a coupled fundamental process involving the evaporation of multicomponent mixtures, wetting, and phase separation.

Droplet boiling on micro-pillar array surface – Nucleate boiling regime

Despite spray cooling in the form of droplet boiling on a textured surface being a very promising phase-change heat dissipating method, the understanding of droplet/bubble two-phase dynamics in the nucleate boiling is extraordinarily limited. In this study, we report sessile droplet boiling on micro-pillar array surface in the nucleate boiling regime using a three-dimensional lattice Boltzmann model comprehensively. Effects of micro-pillar size on bubble behaviors inside droplet are discussed in detail, covering bubble nucleation, growth, coalescence, and rupture. For the micro-pillars with large side length or small spacing, nucleation sites are activated around micro-pillar top surface. The preferential activation location of nucleation sites is determined by temperature, confined space and fluid flow. In bubble growth stage, the variation of bubble radius with time follows the square root law, being consistent with previous experiments. Bubbles merge into a large central bubble beneath droplet for the short micro-pillars while into a vapor layer for the long micro-pillars. Emergence of large central bubble prolongs droplet lifetime but deteriorates heat transfer. In addition, increasing micro-pillar side length or decreasing micro-pillar height can delay activation of nucleation sites.

Electrokinetic Thin-Film Model for Electrowetting: The Role of Bulk Charges.

The electrowetting behavior of a charge-carrying sessile droplet is relevant to applications such as point-of-care diagnostics. Often biomedical assays involve droplets that contain charged molecules such as dissolved ions, proteins, and DNA. In this work, we develop a reduced-order electrokinetic model for electrowetting of such a charge-carrying droplet under a parallel-plate electrode configuration. An inertial-lubrication model based on the weighted residual integral boundary layer (WRIBL) technique is used to obtain evolution equations that describe the spatiotemporal evolution of the fluid-air interface and the depth-integrated flow rate. The solutions to the evolution equations are obtained numerically by using the spectral collocation method. We investigate the role of domain and surface charges, characterized by the Debye length, on droplet wetting. Under low relaxation timescales, both droplet deformation and wetting alteration under an AC field are shown to be equivalent to that under a root-mean-square (RMS) DC field. We show that an electrolytic sessile droplet can exhibit a larger deformation in comparison to the two asymptotic limits of a perfect conductor and a perfect dielectric droplet, corresponding, respectively, to very low and high Debye lengths. The effects of several other parameters such as the inherent equilibrium wettability, permittivity ratio, and electric field strength are also investigated.

Understanding the formation of particle bands and fingering patterns during evaporation of a sessile droplet containing colloids

Sessile droplets containing dispersed colloids evaporate on substrates leaving distinct deposition patterns. Applications using the droplets technique require a critical understanding of the complex particle dynamics that affect the deposition pattern. The fingering-like pattern formed when surfactant-laden droplets containing dispersed colloids evaporate is not yet well understood. The lateral imbalanced capillary meniscus forces (CMFs) between particles moving along the Marangoni vortex (MV) cluster particles into bands that deposit to form the fingering-like pattern. This work investigates the effect of particle shape, particle, and surfactant concentration on the phenomenon. Further, the importance of the contact angle and contact line (CL) dynamics of the droplet is also discussed. The results demonstrate that manipulating these parameters can control the band formation and the resulting deposition pattern. The findings of this work would be pivotal for a critical understanding of particle self-assembly and pattern morphologies of evaporating surfactant-laden droplets.

Resulting deposition patterns in various sessile droplets undergoing evaporation

Resulting deposition patterns in various sessile droplets undergoing evaporation

The effect of the spatial variation of the evaporative flux on the deposition from a thin sessile droplet

A mathematical model for the effect of the spatial variation of the local evaporative flux on the evaporation of and deposition from a thin pinned particle-laden sessile droplet is formulated and solved. We then analyse the behaviour for a one-parameter family of local evaporative fluxes with the free parameter $n \, (>-1)$ that exhibits qualitatively different behaviours mimicking those that can be obtained by, for example, surrounding the droplet with a bath of fluid or using a mask with one or more holes in it to achieve a desired pattern of evaporation enhancement and/or suppression. We show that when $-1< n<1$ (including the special cases $n=-1/2$ of diffusion-limited evaporation into an unbounded atmosphere and $n=0$ of spatially uniform evaporation), all of the particles are eventually advected to the contact line, and so the final deposit is a ring deposit at the contact line, whereas when $n>1$ all of the particles are eventually advected to the centre of the droplet, and so the final deposit is at the centre of the droplet. In particular, the present work demonstrates that a singular (or even a non-zero) evaporative flux at the contact line is not an essential requirement for the formation of a ring deposit. In addition, we calculate the paths of the particles when diffusion is slower than both axial and radial advection, and show that in this regime all of the particles are captured by the descending free surface before eventually being deposited onto the substrate.

Conditions of enhanced evaporation for nanofluids droplet and inhibition of coffee-ring effect under buoyancy and Marangoni convection

Evaporation of nanofluid droplets whose size is larger than capillary length is common in industrial processes, but there is currently a lack of research on the evaporation kinetics and more complex deposition patterns under the combined effects of buoyancy and Marangoni convection of large evaporating droplet. Experimental investigations on evaporation of Al2O3H2O nanofluid sessile droplet with initial contact line diameter of 4 mm on heating PTFE coating substrate are reported. The variation in contact angle, contact radius, and droplet volume over time under different conditions were obtained through experiments. The average evaporation rate is calculated. Internal flow characteristics are inferred through the surface temperature distribution detected by the top view infrared camera. The constant contact radius mode takes place at the beginning of evaporation. Then mixed evaporation mode and stick slip mode may occur for different substrate temperature, nanoparticle mass concentration and nanoparticle size. Increasing nanoparticle size causes a decrease in average evaporation rate. Whether the use of nanofluids can improve evaporation rate and heat transfer or not depends on multiple factors. Convection cells exist, and three kinds of deposition patterns are formed due to the underlying coupled transport phenomena. Under the combined effect of buoyancy and Marangoni convection in this article, the most common coffee-ring pattern does not appear. The deposition patterns are directly affected by the pinning stability, which decrease at higher temperature.

Simply controlling the surface structure of graphene oxide films using multiple drop-casting

Aqueous graphene oxide inks are promising to fabricate a large-area thin film which can be utilized in various applications such as sensors and energy storage and conversion. In this work, we experimentally demonstrate a facile way to controllably fabricate wrinkled structures on the surface of graphene oxide films by using a drop-casting method. Simple drop-casting of the graphene oxide ink enabled to fabricate randomly distributed wrinkles uniformly over the entire film deposited after water was totally evaporated. Deposition mechanism after a single drop-casting was clearly demonstrated, which involves graphene oxide flake transport, aggregation/deposition at the pinned contact edge of a sessile droplet during water solvent evaporation and also buckled deformation(wrinkle formation) of the deposited graphene oxide thin film due to compressive stress by the receding water droplet contact line. Multiple drop-casting on the initially formed wrinkled structures of the graphene oxide film allowed the wrinkles to grow in their width and height linearly by increasing the number of drop-casting, which resulted in the increase of the size polydispersity and area density of wrinkles. The wrinkle growth mechanism during multiple drop-casting was explained in the perspective of collision and accumulation of graphene oxide flakes dispersed within additional dropped droplet on the initially formed wrinkles during water evaporation and droplet contact line recession, which was supported by high-resolution imaging of the films using scanning electron microscopy (SEM) and atomic force microscopy (AFM). This work suggests that the behavior of the graphene oxide flakes dispersed within a sessile droplet can affect surface structures of deposited thin films, and it can be foundational to extend the simple multiple drop-casting strategy to controlled fabrication of various 2D nanomaterial thin films with wrinkled structures by appropriately controlling ink solution and evaporation conditions, which can be used in a variety of functional applications.

Understanding the self-pinning driven jamming behavior of colloids in drying droplets

The jamming of the colloids in a dried droplet is influenced by various parameters, where substrate wettability is notably crucial. Evaporating a sessile droplet on a wettable surface advances the pinning of the contact line which leads to the enhancement in the velocity of colloidal particles during the drying of the droplet (Marin et al., 2011). Now, the question arises: will the jamming of the colloidal particles in the case of evaporation of a droplet on the superhydrophobic surface (SH) and air-suspended spray colloidal droplet exhibit the increase in velocity of colloidal particles during drying of the droplet? The drying arrangement of the colloidal particles has been probed using electron microscopy and small-angle X-ray scattering. The fast Fourier transform of the electron microscopy images has been established utilizing ImageJ software. The supraparticles resulting from the evaporation of the droplet on the SH surface as well as by spray drying demonstrated a localized ordered arrangement on the outer surface whereas the arrangement becomes random in the inner region. The transition from ordered to the random arrangement of colloidal particles from the outer region to the inner region is due to the increase in the velocity of the colloidal particles during evaporation. The increase in the velocity can be attributed to the self-pinning of the colloids at the water-air interface resulting in elastic shell formation due to the locking of the colloidal particles in Van der Waals minima. Due to the presence of the menisci between the colloids, the formed shell behaves as nanomembrane, and the evaporation of the solvent through these nanopores accelerates and results in an increase in the velocity of the colloidal particles. Further, increasing polydispersity in the size of colloids led to random disordered jamming even on the top surface of the dried supraparticles.

Droplet evaporation on superhydrophobic surfaces

Over the last decades, a fabulous variety of synthetic superhydrophobic surfaces have been created, offering unique anti-wetting properties. A significant focus for these surfaces has been on their stay-dry and self-cleaning properties. However, unless in a saturated environment, water droplets lose mass through evaporation and this itself is a field of significant interest, which is illustrated by a flood of recent studies on surface contamination and potential surface transmission of infection by evaporating sessile droplets during the Covid-19 pandemic. Superhydrophobic surfaces alter a droplet's contact with a substrate and the surrounding environment, thus changing pinning and heat transfer properties. The droplet shape also alters the space into which vapor can diffuse. Despite the many excellent reviews on superhydrophobic surfaces, there does not appear to have been a focus on the overlap with evaporating sessile droplets. Here, we address this gap by outlining the diffusion-limited sessile droplet evaporation theory, applications on patterned superhydrophobic surfaces, effect of evaporative cooling on drop evaporation rates, and practical applications of drop evaporation on superhydrophobic surfaces, such as nanoparticle assembly, biomedical assay, analytical chemistry, and crystallization applications. Finally, we provide our personal views of possible future directions in these overlapping areas.

Characterization of the solvent specific evaporation from a carbon nanotube buckypaper doped by goethite nanowires

Non-functionalized carbon nanotube based self-supporting buckypaper doped by goethite nanowire was prepared (characterized by TEM, XRD, FTIR, DLS, electrophoresis, SEM) and studied to determine the wetting and evaporation properties of the composite. The wetting and vaporization of water, methanol, ethanol, 2-propanol, acetone, 1,4-dioxane were monitored at 50 °C parallel by weight and electrical resistance measurements and also by thermography in case of water and ethanol. Based on the weight measurements, the different stages of the evaporation (evaporation of sessile droplet, vaporization of the condensed and adsorbed solvents from the porous system) could be distinguished, which could be characterized by their evaporation rate and the amount of liquid remaining in the porous system at the end of the given stages. The evaporation profiles determined from the electrical resistance measurements are characteristic for the evaporating solvents, similar to the mass measurement results. The details of the wetting process can be analyzed by thermography based on the area and temperature of the wetted region. The relationship between the physical properties of the solvents and the parameters characteristic for the evaporation obtained from the weight and electrical resistance measurements was statistically analyzed using Pearson correlation coefficients method. There is a very high correlation for example between surface tension and tt (PCC = 0.971) or ts (PCC = 0.992), and also between the boiling point and Area(R) (PCC = 0.929). These results allow us to predict the possibility of this setup in a potential future analytical application.

Vapor distribution changes evaporative flux profiles of a sessile droplet

HypothesisWe propose that during the evaporation of sessile droplets, the evaporative flux profile is primarily influenced by droplet geometry and composition under diffusion-limited conditions. Most studies have focused solely on the evaporation feature from the liquid to the gas phase, neglecting the extent to which the evaporated vapors affect the evaporation process. We hypothesize that if the molecular weight of the evaporated vapors is significantly high or low compared to the ambient gas, it could alter the evaporative flux. ExperimentsWe employed a direct optical measurement technique, specifically Mach-Zehnder interferometry. This demonstrated that the distribution of evaporated vapor molecules can substantially modify the evaporative flux profile. FindingsOur study discovered that substantial density gradients between vapor and air could either suppress or enhance the evaporative flux, depending on the droplet's orientation. This research offers fresh insights into evaporative fluxes by taking into account the relative vapor concentration and gravitational effects.

Freezing Characteristics of a Water Droplet on a Multiscale Superhydrophobic Surface.

Superhydrophobic surfaces have the potential to retard ice formation owing to their super water-repellant nature arising from high static contact angle and low contact angle hysteresis. Most of the previous studies have focused on patterned surfaces with mono-scaled prismatic structures. In contrast, the freezing behavior on multiscaled rough superhydrophobic surfaces that are of practical significance is relatively little studied. This article presents, for the first time, the freezing dynamics of a water droplet interacting with multiscale fractal superhydrophobic surfaces which validates well with experimental measurements. It is shown that the dual effects of increased contact angle and poor interfacial conduction due to trapped air cavities within the roughness features of the superhydrophobic surface lead to increasing freezing time with increasing surface hydrophobicity, determined as a function of the fractal surface parameters. A comparison of the freezing dynamics of sessile droplets of identical contact angle on a smooth versus a rough superhydrophobic surface shows that interfacial asperity thermal resistance contributes to over 14% increase in the freeze time. It is further shown that by tailoring the multiscale characteristics, the freeze time may be increased by up to 7-fold compared to freezing on a smooth surface. The application of the numerical model to studying ice formation on several practical superhydrophobic surfaces of a range of metallic materials and fabrication methods is also discussed, which offers guidelines for the design of anti-icing surfaces in practice.