Sessile Droplet Research Articles

An improved Coupled Level Set and Volume of Fluid (i-CLSVoF) framework for sessile droplet evaporation

Surface-tension-dominant droplet evaporation is ubiquitous and of importance to many applications. We present an improved Coupled Level Set and Volume of Fluid (i-CLSVoF) framework without explicit interface reconstruction for modelling micro-sized droplets with and without evaporation. In the i-CLSVoF framework, an improved surface tension force model with additional filtering steps to filter un-physical spurious velocities is developed and implemented. A simple, yet efficient, velocity-potential based approach is proposed to reconstruct a divergence-free velocity field for the advection of the free surface during droplet evaporation. This approach fixes the numerical issues resulting from the evaporation-induced velocity jump at the interface. The smeared mass source term approach incorporated in this work guarantees greater numerical stability than the non-smeared approach. Three different evaporation models (constant mass flux, thermally driven evaporation and droplet evaporation at room temperature) are implemented in the i-CLSVoF. Corresponding numerical benchmark cases (dam break, droplet relaxation and droplet evaporation subjected to different evaporation models) are conducted to validate the surface tension and the evaporation models. Good agreement between the numerical and corresponding analytical solutions is found. The model developed in this work shows convincing performance in modelling surface-tension-dominant flow with and without evaporation.

High frame-rate imaging of the shape oscillations and spreading dynamics of picolitre droplets impacting on a surface

The post-impact dynamics and spreading rates of picolitre liquid droplets on surfaces are critical to many practical and industrial applications, as well as respiratory disease transmission mechanisms. Here we use a high framerate imaging method to explore the shape oscillations and spreading of individual ∼10–180 pl volume droplets (corresponding to ∼30–70 μm in initial droplet diameter) impacting on a surface under ambient conditions with 10 μs temporal resolution. The method allows the surface tension to be accurately extracted from the measured frequency of post-impact shape oscillations for sessile droplets in this size range with surface tensions greater than 40 mN m−1 and viscosities up to at least 3.2 mPa s. The Tanner's law model for predicting sessile droplet spreading rates provides an accurate account of the “steady-state” spreading rate for all droplets with surface tensions in the range 22–73 mN m−1 studied here. However, Tanner's law does not account for the delay in the onset of spreading observed for droplets in this size range, caused by competition between shape oscillations and spreading governing the morphology at short time periods, particularly for surface tensions >22 mN m−1.

On the dynamics of head-on collision of sessile droplets on the traveling substrate

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.

Particle deposition dynamics in evaporating droplets using lattice Boltzmann and magnetic particle simulation

Herein, a simulation model is proposed that combines the lattice Boltzmann method (LBM) and a magnetic particle model to observe particle ring patterns in evaporating sessile droplets, controlling them using a magnetic field. Brownian dynamics and van der Waals force models are applied to the nanoparticles. The interactions between the magnetic particles are simulated using the magnetic particle model, which is validated using previous experimental particle distribution results. The particle deposition patterns are compared according to the substrate wetting conditions. The distribution exhibited a clear coffee-ring pattern as the pinning time of the contact line increased. In the case of a non-pinned droplet, the thermal Marangoni flow was maintained, and the adhesion of the particles was delayed by the vortex. A thick, uniform ring pattern was formed when a magnetic field was applied to the particles. The particle bundles formed by the magnetic field were resistant to flow. To verify this result, the average particle velocity was measured. Consequently, particle transfer was classified into three stages. In Stage I, capillary force dominates, Marangoni flow develops in Stage II, and particle adhesion occurs in Stage III. With an increase in the magnetic strength, the velocity change exhibited a decrease across all stages.

Assembly of nanoparticles at symmetric coffee stain locations

The precise picture of the nanoparticle array deposits on the substrate surface is crucial since many uses for nanostructures are dependent on how the assembled array's collective behavior responds to various physicochemical properties. The well-known seed-mediated approach was used to synthesize gold nanorods stabilized by CTAB molecules. Due to the Helium Ion Microscope’s (HIM) remarkable ability to reveal the real nature of the deposited entities, gold nanorod arrays at symmetrical parts of the coffee-stain ring have been studied using this technique. The object of this study is to evaluate three different positions within the coffee-stain ring at the convective symmetric locations. In the context of the self-assembled mechanism, the formation of various liquid crystalline phases induced by the evaporating symmetric convective flow inside the sessile droplet have been examined and compared at the symmetric positions within the ring.

Line tension of sessile droplets: Thermodynamic considerations.

We deduce a thermodynamically consistent diffuse interface model to study the line tension phenomenon of sessile droplets. By extending the standard Cahn-Hilliard model via modifying the free energy functional due to the spatial reflection asymmetry at the substrate, we provide an alternative interpretation for the wall energy. In particular, we find the connection of the line tension effect with the droplet-matrix-substrate triple interactions. This finding reveals that the apparent contact angle deviating from Young's law is contributed by the wall energy reduction as well as the line energy minimization. Besides, the intrinsic negative line tension resulting from the curvature effect is observed in our simulations and shows good accordance with recent experiments [Tan etal. Phys. Rev. Lett. 130, 064003 (2023)0031-900710.1103/PhysRevLett.130.064003]. Moreover, our model sheds light upon the understanding of the wetting edge formation which results from the vying effect of wall energy and line tension.

Effect of high directional convex structure on droplet morphology and contact angle

The morphology of a surface has certain influences on its wettability as reflected by the shape of a sessile droplet thereon. The topological structure of superhydrophobic silicone rubber (MVQ) prepared by template method has the characteristics of simple shape and regular arrangement, but such a structure will lead to unstable contact angle (CA) of superhydrophobic surface. Through this study, it is found that the CA value of the original flat MVQ surface is the same in any direction. However, from 0° to 90°, it is observed that the CA on the MVQ surface, the contact radius between water droplets and MVQ and the projected area of water droplets are different. In different directions, the maximum error of CA is 13.75°, the maximum error of contact radius between water droplets-MVQ is 209.5 μm, and the maximum error of projected area of water droplets is 0.284 mm2. In addition, it is found that the contact radius between water droplets and the surface of silicone rubber decreases with the increase of the projected area of water droplets in the direction of larger CA. In order to explain the error of CA and droplet shape due to directionality, this phenomenon is explained by micro-morphology and three-dimensional morphology combined with contact line density theory. This discovery is beneficial to design super-hydrophobic surface with high directionality and realize the application of micro-channel control technology.

The impact of a two-dimensional vibration excitation on the critical incident flow velocity of a sessile droplet

The movement of a sessile droplet can be initiated by different mechanisms. In addition to an incident flow, a vibration or differences in the surface properties can initiate the movement of a droplet. In many cases, the mechanisms occur in combination and their interaction is not well understood. We report on the investigation of superposition of an incident flow and a two-dimensional vibration excitation acting simultaneously. The focus is on the analysis of the critical air flow velocity required for the detachment of a droplet. More precisely, it is investigated how a simultaneous two-dimensional vibration affects the critical incident flow velocity. In particular, the influence of a phase shift of both excitation sources with respect to each other is investigated. For this purpose a rectangular Plexiglas flow channel equipped with two electromagnetic shaker is used. One oscillation source acts vertical to flow direction, while the second shaker operates simultaneously in horizontal direction. Two scenarios are considered for the orientation of the horizontal vibration excitation. Case 1: the horizontal vibration excitation is in the direction of the incident flow. Case 2: the horizontal vibration is transverse to the incident flow. The excitation frequency and acceleration are varied within the series of experiments. Water droplets of different volumes (7.8 – 23.4 μl) are studied. The substrate is polymethylmethacrylate (PMMA), which has a hydrophilic character, at static contact angles of about 74°for a water droplet. The data obtained reveal that the critical velocity for detachment of a sessile droplet can be significantly reduced by superimposing an oscillatory excitation only for certain frequencies. A significant decrease in the critical velocity is observed for an excitation in the range of the first and second eigenfrequencies. The phase offset of the two vibration sources will also affect the critical droplet detachment velocity if the horizontal excitation source is parallel to the incident flow. However, if the excitation is in the horizontal plane perpendicular to the incident flow, a phase shift between the two vibration sources has no effect.

Drying behaviour of nanofluid sessile droplets on self-affine vis-à-vis corrugated nanorough surfaces.

In recent years, evaporative self-assembly of sessile droplets has gained considerable attention owing to its wide applicability in many areas. While the phenomenon is well studied for smooth and isotropically rough (self-affine) surfaces, investigations comparing the outcomes on self-affine vis-à-vis corrugated surfaces remains to be done. In this experimental work, we compare the wetting and evaporation dynamics of nano-colloidal microlitre droplets on self-affine and corrugated nanorough surfaces having identical roughnesses and interface properties. The coupled influence of particle size, concentration, and surface structuring has been explored. Differences in wettability and evaporation dynamics are observed, which are explained via the interaction between wetting fluid and anisotropic surface roughness. Our findings exhibit different temporal behaviour of contact radius and angle in the evaporation process of the droplets. Further, the corrugated surface exhibits anisotropic wettability with a monotonic change in droplet shape as evaporation proceeds, finally giving rise to irregular dried patterns. The scaled rim width and crack spacing of the particulate deposits are examined. Our results can inspire fabrication of surfaces that can facilitate direction-dependent droplet motion for specific applications.

Experimental and numerical investigations on flash evaporation of a sessile droplet under reduced pressure

Flash evaporation of droplets under reduced pressures is versatile in industrial applications for its low energy consumption. More vigorous flash explosions may occur by the subsecond expansion of internal bubbles, leading to inefficient heat transfer and facility damage. In this work, we propose using the aerosol with an inherent low thermal conductivity as the substrate to study the flash evaporation of sessile droplets, which reduces the number of nucleate sites and suppresses the flash explosion, in contrast to the pendant one. We experimentally reveal the effect of ambient pressure, initial droplet temperature, and size on droplet temperature evolution and evaporation rate. A revised diffusion coefficient is proposed based on the experimental droplet lifetime with the aid of D2-law, which is utilized in axisymmetric simulations for acquiring the flow field, temperature, and vapor concentration distribution. The analogy between experimental and numerical results has demonstrated the validity of this revision. The interplay of two convection flows aroused by the Marangoni effect and thermal convection is displayed at the early stage of flash evaporation, and the latter is predominant for the rest of evaporation.

Single Phase Transition Leads to the Nanoparticle Deposition in an Evaporating Sessile Droplet

Single Phase Transition Leads to the Nanoparticle Deposition in an Evaporating Sessile Droplet

Experimental Investigation of the Water Droplet Evaporation on Inclined Surfaces by Taguchi and ANOVA Optimization Analysis

Abstract We experimentally investigated the evaporation characteristics of a sessile water droplet on a glass substrate with different surface roughness levels. The influence of five parameters is evaluated for the evaporation process: substrate temperature (30 °C, 45 °C, and 60 °C), surface roughness (P0, P600, and P60), droplet volume (3, 5, and 8 µL), water droplets initial temperature (30 °C, 40 °C, and 60 °C), and inclination angle (0 deg, 45 deg, and 75 deg) of the glass substrate. The Taguchi orthogonal array design of L27 is utilized to establish minimal candidate trial points for experimental works, and more trials have been conducted to quantify the effects accurately. Then, analysis of variance (ANOVA) has been used to evaluate the evaporation times for the sessile droplets. The results indicate that evaporation times decrease with rising substrate temperatures, increasing substrate inclination angle, and increasing initial water droplet temperatures. In contrast, evaporation times rise with increasing surface roughness and droplet volumes. After evaluation of the ANOVA analysis, surface roughness levels and droplet volumes are considered the most influential parameters after substrate temperatures, which is the most effective parameter on the evaporation times. On the other hand, initial water droplet temperatures and substrate inclination angle are less effective considering droplet evaporation times. A linear regression fit was derived via ANOVA analysis for the evaporation time, and the best mean deviation was found to be 10% from the experiments. The experimental outcomes were compared to previous research, and correlations were derived. The proposed correlation has given good results considering experimental and literature data.

Reduced-Order Model for Surfactant-Laden Electrified Sessile Droplets.

A comprehensive understanding of the physics of electrowetting of a surfactant-laden droplet is important for applications in rapid healthcare diagnostics. A majority of biological samples examined during point-of-care (POC) diagnostics are biofluids with dissolved surfactants, such as the respiratory droplets containing protein (mucin) and surfactant molecules like dipalmitoylphosphatidylcholine. The presence of these surfactant molecules is anticipated to have a significant impact on the performance of electrowetting-based POC diagnostic devices. A reduced-order model is developed using the weighted residual integral boundary layer theory for the electrowetting of a surfactant-laden sessile droplet in a parallel plate electrode configuration. Thin film evolution equations are obtained for the fluid-fluid interface, the surfactant concentration, the depth-integrated flow rate, and the interfacial charge density. We show that the presence of surfactants opposes and decreases the strength of the electrohydrodynamic flow due to Marangoni stress-driven convection. The droplet then responds to an AC field with a suppressed amplitude of oscillation and the same mean deformation as that under DC forcing. Thus, low-frequency AC forcing with a suitable surfactant can plausibly be employed as a viable alternative to more energy-intensive high-frequency AC forcing.

Application of acoustic levitation for studying convective heat and mass transfer during droplet evaporation

The observation of acoustically levitated droplets offers great potential for studying their evaporation characteristics under well-defined ambient conditions. In contrast to alternatives such as sessile droplets or droplets suspended by a tiny fiber, the key advantage of acoustic levitation is the contact-free nature of the experimental method. However, acoustic streaming effects or droplet deformation by acoustic forces may affect the heat and mass transfer considerably. Consequently, the droplet evaporation process is usually dominated by these intrusive effects of the acoustic field. The main objective of this study is to present an experimental setup, which minimizes the disturbing effects of the levitation technique in order to enable a solid investigation of convective heat and mass transfer during droplet evaporation. To achieve this goal, a high resonance frequency of 100kHz is chosen and the investigation is limited to substantially smaller droplets compared to other studies in the literature. Moreover, an air flow is injected through a hole pattern in the reflector in order to control the relative velocity between the droplet and the gas phase. Particle Shadow Velocimetry is used to characterize the gas flow field in a stepwise approach, initially without any levitated droplet. Subsequently, the vortex structures around non-evaporating droplets are discussed. Eventually, evaporating water droplets are studied. The applied optical diagnostics offer the distinct advantage that the droplet size can be measured simultaneously with the surrounding gas flow field. Hence, the evaporation rate can be evaluated for different combinations of droplet size and relative velocity to the gas phase. For the entire range of resulting Reynolds numbers, the experimentally obtained evaporation rates were found to agree very well with results of a numerical evaporation model when a well-established correlation is used to account for convective heat and mass transfer.

Real-time three-dimensional micro-imaging of liquid front in spreading sessile droplet under transient spreading states.

Dynamic wetting behaviors of sessile droplets on substrates play crucial roles for various industrial chemical processes. In the case of complete wetting, it has been proposed that a precursor film which is nanometer-order thickness and micrometer-order length further expands outside the macroscopic contact line of the sessile droplet. While the time evolution of the precursor film is believed to strikingly affect the macroscopic wetting behavior (e.g., spreading velocity), it had been hard to visualize the three-dimensional shape of the precursor film at the early stage of wetting. Further, although the spreading velocity rapidly decreases upon time at the early stage of the wetting (transient state) and then converged to be a constant at later time (steady state), conventional fluid mechanics theories generally describe only the wetting behavior at the steady state. Therefore, experimental observation of time evolution of the precursor film shape in the transient state is essential to proceed the theories to the next step. Here, a monochromatic laser interference microscope was developed to visualize three-dimensional shape of the wetting front of sessile droplets in real time. By detecting an interference of the laser reflected at the liquid and substrate surfaces, the precursor film was successfully visualized with a time resolution of 20ms and a thickness resolution of about 3.5nm at worst. For 10 cSt silicone oil on Si substrate, a 60-nm-thick and 70-μm-long precursor film was observed for 2-10min after dropping and its spreading velocity which decreased with time was quantitatively analyzed.

Tunable encapsulation of sessile droplets with solid and liquid shells

Droplet encapsulations using liquid or solid shells are of significant interest in microreactors, drug delivery, crystallization, and cell growth applications. Despite progress in droplet-related technologies, tuning micron-scale shell thickness over a large range of droplet sizes is still a major challenge. In this work, we report capillary force assisted cloaking using hydrophobic colloidal particles and liquid-infused surfaces. The technique produces uniform solid and liquid shell encapsulations over a broad range (5–200 μm shell thickness for droplet volume spanning over four orders of magnitude). Tunable liquid encapsulation is shown to reduce the evaporation rate of droplets by up to 200 times with a wide tunability in lifetime (1.5 h to 12 days). Further, we propose using the technique for single crystals and cell/spheroid culture platforms. Stimuli-responsive solid shells show hermetic encapsulation with tunable strength and dissolution time. Moreover, scalability, and versatility of the technique is demonstrated for on-chip applications.

Drying of sessile droplets of binary colloidal aqueous mixtures of carbon nanotubes and platelets of Laponite®

Drying of sessile droplets of binary colloidal aqueous mixtures of carbon nanotubes (CNT) and platelets of Laponite® (Lap) has been studied. The concentration of CNT was fixed at CCNT= 0.01% wt., and the relative concentration of Lap and CNT, was varied within x = CLap/CCNT= 0–2. Formation of the three different zones related to formation of the almost transparent round "enlightenment" in the center, outer “gray” ring, and thin “coffer” ring at the external boundary was detected. Observed effects were explained accounting for the effects of Lap on the facilitation of dispersion of CNT in aqueous systems.

Melting Process of Frozen Sessile Droplets on Superhydrophobic Surfaces.

Superhydrophobic surfaces can exhibit icephobicity in many ways due to their large contact angles and small rolling angles. The melting process of frozen droplets on superhydrophobic surfaces is still unclear, hindering the understanding of surface icephobicity. In this experimental study of the melting process of frozen sessile droplets on superhydrophobic surfaces, we find two types of melting morphologies with opposite vortex directions on a single-scale nanostructured (SN) superhydrophobic substrate and a hierarchical-scale micronanostructured (HMN) superhydrophobic substrate. Melting pattern visualizations and flow field measurements showed Marangoni convection and natural convection occurring in the melting sessile droplets. For the HMN superhydrophobic substrate, the internal flow was found to be dominated by Marangoni convection due to the temperature gradient along the surface of the droplet. For the SN superhydrophobic substrate, Marangoni convection was inhibited by the superhydrophobic particles at the surface of the droplet, which were shed from the fragile superhydrophobic substrate during the freezing-melting process, as confirmed by surface characterizations of the substrate and flow measurements of a water pool. These results will help researchers better understand the melting process of frozen droplets and in designing novel icephobic surfaces for numerous applications.

Investigation of electrohydrodynamic effects on sessile droplet evaporation using the lattice Boltzmann method

Droplet evaporation on hot substrates within an electric field plays an essential role during the electrospray cooling process. However, there is only a vague understanding of electrohydrodynamic (EHD) effects on droplet evaporation. In this paper, the coupled set of governing equations, including the Poisson equations, the energy equations, and the Navier-Stokes equations, is implemented within the lattice Boltzmann (LB) framework to examine the evaporation of leaky dielectric droplets. The contact angle hysteresis (CAH) as well as the influences of fluid-solid conjugate heat transfer are taken into consideration in this model. The method’s accuracy is validated quantitatively by using three basic cases. The results suggest that the sessile droplet could be elongated or flattened under EHD effects. When the droplet is elongated, the acceleration of the rate of evaporation is controlled by the interrelationship between thermal conduction and electric-induced convection in the droplet, i.e., the average Peclet number (Pe) value. As Pe is less than 1.0, the interior of the droplets is controlled by thermal conduction, and the applied electric field would prolong the droplet evaporation time. As Pe is greater than 2.0, the electric convection promotes evaporation compared to neutral droplets. In the case that the droplets are compressed inside the electric field, the evaporation time progressively decreases as the intensity of the electric field increases. These insights help us understand how EHD affects sessile droplet evaporation and illustrate the huge potential of electric fields for thermo-fluid manipulation.

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.