Transient Prediction of Nanoparticle-Laden Droplet Drying Patterns through Dynamic Mode Decomposition.

Nanoparticle-laden sessile droplet drying has a wide impact on applications. However, the complexity affected by the droplet evaporation dynamics and particle self-assembly behavior leads to challenges in the accurate prediction of the drying patterns. We initiate a data-driven machine learning algorithm by using a single data collection point via a top-view camera to predict the transient drying patterns of aluminum oxide (Al2O3) nanoparticle-laden sessile droplets with three cases according to particle sizes of 5 and 40 nm and Al2O3 concentrations of 0.1 and 0.2 wt %. Dynamic mode decomposition is used as the data-driven learning model to recognize each nanoparticle-laden droplet as an individual system and then apply the transfer learning procedure. Along 270 s of droplet drying experiments, the training period of the first 100 s is selected, and then the rest of the 170 s is predicted with less than a 10% error between the predicted and the actual droplet images. The developed data-driven approach has also achieved the acceptable prediction for the droplet diameter with less than 0.13% error and a coffee-ring thickness over a range of 2.0 to 6.7 µm. Moreover, the proposed machine learning algorithm can recognize the volume of the droplet liquid and the transition of the drying regime from one to another according to the predicted contact line and the droplet height.

Dendritic nanoparticle self-assembly from drying a sessile nanofluid droplet.

The pattern formation left by a drying nanofluid droplet is related to the evaporation induced particle self-assembly. The experimental results demonstrate the formation of dendritic particle deposition after the liquid phase of unpinned sessile nanofluid droplets is fully evaporated. The dried-in particle assemblies exhibit the dendritic patterns connecting the sprawling branches with a central core structure. The branched structures are formed by particles merging in the receding front. A three-dimensional lattice-gas kinetic Monte Carlo model is developed to simulate the particle self-assembling behaviour in a drying particle-laden droplet with the dewetting three-phase line. The parameter study is carried out to demonstrate the trend of the dendritic pattern formation. The various patterns are simulated by varying the chemical potentials and the interaction energies among particles, liquids, and substrates. The dendritic particle depositions are measured in three dimensions after the nanofluid droplet is completely dried. Qualitative agreement is observed between the experimental and the numerical results. Thicker branches and larger central cores are observed with an increase of particle concentrations.

Disk-Ring Deposition in Drying a Sessile Nanofluid Droplet with Enhanced Marangoni Effect and Particle Surface Adsorption.

The present study is to explore the central particle deposition from drying a sessile nanofluid droplet experimentally and theoretically. Normally, a pinned colloidal droplet dries into a coffee-ring pattern as a result of moving the particles to a three-phase line by the radial direction capillary flow. However, the strong evaporation can generate the nonuniform temperature at the evaporating droplet interface and the droplet periphery temperature is higher than that close to the droplet centerline. The induced Marangoni flow would reversibly transport the particles at the periphery toward the centerline. We have thus designed the experiments to increase the droplet evaporation rate in vacuum conditions and accordingly to enhance the Marangoni effect. We have observed distinguishable disk deposition inside the outer coffee ring. A three-dimensional diffusion-limited cluster-cluster aggregation Monte Carlo model has been developed to simulate the deposition process. With modeling the Marangoni effect, particle adsorption at the liquid-air interface and particle aggregation behaviors, the formation of the disk pattern inside a coffee ring has been simulated. The qualitative agreement has been found in the comparison of local deposition distribution between the related experiment and simulation.

Surface temperature transition of a controllable evaporating droplet.

Surface temperature is a critical factor affecting the droplet evaporation; however, it is a continuous matter under discussion. We design controllable experiments for sessile ethanol droplet evaporation to investigate the surface temperature distribution evolution. It is found that the evaporation process of a droplet with a constant contact radius can involve five phases: non-wave phase, onset of thermal waves, decrease of thermal waves, transition phase, and final non-wave phase. Under fixed evaporation conditions and a fixed substrate temperature, the phase sequence is solely dependent on the instantaneous contact angle, but independent of the droplet initial volume. Three typical radial temperature distributions are observed at the evaporating droplet surface: a monotonic decrease from the edge to the apex; a nonmonotonic distribution with the highest temperature observed between the edge and the apex; or a monotonic increase from the edge to the apex. The three temperature distributions and the two transitions between them are responsible for the five phases in the evaporation process. However, the early phases may not exist in the sessile droplet with a relatively small initial contact angle. Both the evaporation pressure and the substrate temperature can affect the occurrence of the five phases in the evaporation process. It is noteworthy that the splitting and merging of thermal waves occur simultaneously during evaporation. During the decrease of the thermal waves phase, the number of waves decreases linearly with the contact angle tangent. The decreasing slope is influenced by the evaporation pressure and the substrate temperature.

Wetting Transition at a Threshold Surfactant Concentration of Evaporating Sessile Droplets on a Patterned Surface.

Wetting transitions induced by varying the components in a solution of a drying droplet can lead to its evolving shape on a textured surface. It can provide new insights on liquid pattern control through manipulating droplet solutions. We show the pronounced transitions of wetting for surfactant solution droplets drying on a micropyramid-patterned surface. At low initial surfactant concentrations, the droplet maintains an octagonal shape until the end of drying. At intermediate initial surfactant concentrations, the early octagon spreads to a square, which later evolves to a stretched rectangle. At high initial surfactant concentrations, the droplet mainly exhibits the "octagon-to-square" transition, and the square shape is maintained until the end. The octagon-to-square transition occurs at similar temporal volume-averaged surfactant concentrations for the various initial surfactant concentrations. It results from the dependence of the surface energy change of spread over the micropyramid structure on the temporal volume-averaged surfactant concentration. At high initial surfactant concentrations, the accumulation of the surfactant near the contact line driven by outward flows could raise the local viscosity and enhance the pinning effect, leading to the great suppression of the "square-to-rectangle" transition.

Controlling Octagon-to-Square Wetting Interface Transition of Evaporating Sessile Droplet through Surfactant on Microtextured Surface.

Producing and maintaining specific liquid patterns during evaporation holds great potential for techniques of printing and coating. Here we report the control over the evolution of surfactant solution droplets on the micropyramid substrates during evaporation. The polygonal droplet shape is achieved during the drying rather than solely at the beginning. As the initial surfactant concentration is 0.04 mM, the droplet maintains its initial octagonal shape throughout the lifetime. Interestingly, the initial octagonal shape transforms into a square during the evaporation as the initial surfactant concentration reaches 0.8 mM. These findings can shed light on wetting pattern control for complex solutions required in various applications.

Wettability Effect on Evaporation Dynamics and Crystalline Patterns of Sessile Saline Droplets.

The evaporative dynamics and crystalline patterns from sessile saline droplets on various substrates are experimentally investigated. On the silicon wafer and poly(methyl methacrylate) (PMMA) plate, the saline droplets exhibit unique evaporative dynamics such that the contact angle keeps increasing for a lasting period. Such an enlargement in contact angle is attenuated at a higher salt concentration. Interestingly, the onset of precipitation is almost overlapped with the end of contact angle enlargement when the contact angle reaches its apex. The lower wettability and the smaller pinning effect of silicon wafer and PMMA result in the morphology of crystalline cubes at the droplet center. On the soda lemon glass, the high wettability and lifetime pinning stage of the droplet lead to spherical profiles of precipitation. The crystalline deposit depends on the salt concentration on soda lemon glass such that it is comprised of exterior cracked layers of salt and interior separated small cubes for low salt concentrations, whereas large crystalline chunks stay near the droplet rim for high salt concentrations.

Octagonal Wetting Interface Evolution of Evaporating Saline Droplets on a Micropyramid Patterned Surface.

Textured surfaces have been extensively employed to investigate the dynamics, wetting phenomena, and shape of liquid droplets. Droplet shape can be controlled via the manipulation of topographic or chemical heterogeneity of a solid surface by anchoring the three-phase line at specific sites. In this study, we demonstrate that droplet shape on a topographically patterned surface can be modified by varying the concentration of salt potassium chloride (KCl) in the droplet solution. It is found that at the beginning of evaporation the octagonal shape of the solid-liquid interface is changed to a rectangle with corners cut upon increasing the salt concentration. Such a variation in the solid-liquid interface versus the salt concentration is explained by the analysis of free energy difference. It indicates that the increases in solid-liquid and liquid-vapor surface tensions by raising the salt concentration result in a favored extension of the three-phase line intersecting the micropyramid bottom sides than the counterpart intersecting the micropyramid diagonal edges. The saline droplets experience a pinning stage at first and a depinning one afterward. The onset of depinning is delayed, and at which the instantaneous contact angle is larger upon raising the salt concentration. The three-phase line which intersects the micropyramid diagonal edges recedes ahead of the one along the micropyramid bottom sides, making the octagonal wetting interface evolve toward a circle. A close view at the droplet edge indicates that the three-phase line repeats "slow slip-rapid slip" across row by row of micropyramids during the depinning stage.