Sessile Droplet Research Articles

Concurrent Determination of Heat and Capacity Change of a Sessile Droplet Using a Single Measurement

Microcalorimetry, designed for the independent measurement of enthalpy and heat capacity, has been commercially available for a considerable time. However, heat-related states in samples, especially liquids, can introduce complicated phenomena and challenging measurement and data evaluation processes. Such complexity becomes apparent when observing fluctuations in thermal capacity (Cp) while measuring heat consumption (Q) during water evaporation. This paper presents a continuous heat pulse measurement (CHPM) method for concurrently analyzing Q and Cp in a single test using microcalorimetry. The sample droplet of 400 nL was directly dispensed on the microcalorimeter surface, followed by a light-emitting diode (LED) radiation generating heat to perform CHPM. We repetitively heated the microcalorimeter using heat pulses provided by LED irradiation, with their duration set to 100 ms and 10s repetition, while measuring the temperature response of the microcalorimeter sensor. A MATLAB-based simulation model was established to validate the accuracy of our Cp measurements, which show its value of 0.79% of minimum variance. Water evaporation coupled with simultaneous salt crystallization served as our study model, where the Cp values were calculated from real-time responses to heat pulses provided by LED. The experimental outcomes confirm the suitability of CHPM in extracting key thermal properties and emphasize its versatility as a diagnostic tool, providing a significant method for research and applications in the fields of physics, engineering, and beyond.

Front-Tracking and Gelation in Sessile Droplet Suspensions: What Can They Tell Us about Human Blood?

Recently developed imaging techniques have been used to examine the redistribution of human red blood cells and comparator particles dispersed in carrier fluids within evaporating droplets. We demonstrate that progressive gelation initiates along an annular front, isolating a central pool that briefly remains open to particulate advection before gelation completes across the droplet center. Transition to an elastic solid is evidenced by cracking initiating proximal to front locations. The arrested flow of cellular components, termed a "halted front", has been investigated using a time-lapse analysis "signature". The presence of a deformable biocellular component is seen to be essential for front-halting. We show a dependence of front-halt radius on cell volume-fraction, potentially offering a low-cost means of measuring hematocrit. A simple model yields an estimate of the gel zero-shear yield-stress. This approach to understanding the drying dynamics of blood droplets may lead to a new generation of point-of-care diagnostics.

A novel application of inverse gas chromatography for estimating contact angles in porous media

HypothesisSurface wettability is a critical factor in multi-phase flow within porous media, a processes essential in various applications e.g. in the energy sector. Traditional methods for assessing wettability of porous media by contact angle measurements, such as sessile droplet and micro-CT techniques, are limited by interface pinning, sample size or resolution impacting precision and accuracy. We hypothesized that using smaller and unconstrained probes, specifically gas molecules, to retrieve interactions along a representative sample size via inverse gas chromatography (IGC) could provide a more accurate determination of contact angles. MethodWe propose a procedure to relate IGC results with macro-scale wettability descriptions, such as the Young equation. To test the effectiveness of IGC method, glass bead samples with varying wettability, modified through a silanization process, were prepared. Contact angles for a distilled water-air-sample system were measured using the sessile droplet method and micro-CT for comparative analysis. IGC was employed to determine the surface energy components of these samples, which were then used in the extended Young-Dupré equation to calculate the contact angles. FindingsThe contact angle ranges determined by IGC and micro-CT for untreated glass beads, the most hydrophilic samples, showed great alignment. This consistency is attributed to the chemical amorphous nature of the untreated beads reflected in the assumption that dispersive and specific energetic components of surface sites are uncorrelated, on which the proposed analysis is based. For treated samples, where the silanization process creates correlations between surface energetic components, the alignment between IGC and micro-CT results was less precise. This study successfully demonstrated that IGC, a molecular-scale probe-based technique, can effectively determine the contact angle range, a macroscopic property, for amorphous samples. Future work should incorporate correlations between energetic components of surface detected by IGC to extend this method's applicability to a wider material range.

Study of dried-out pattern formation in urea-protein droplets placed on a glass substrate

In the current work, we have studied the drying of two important bio colloids (protein and urea) using sessile droplets on a glass substrate. Urea denatures protein and alters the behaviour of the protein molecules. The concentration of urea plays a crucial role in determining the functioning of proteins. Therefore, various diseases can be diagnosed if there is any change in concentration of these components in the body fluids (blood and urine).We found that the concentration also alters the final dried-out morphologies in droplets of bio-colloids. The analysis of these patterns will thus assist in understanding the interaction between the molecules. The current investigation provides physical insights into the formation of these different morphologies. The findings can be further extended for the preliminary diagnosis of diseases using patterns formed of bio-fluid droplets.

Deposit of Red Blood Cells at low concentrations in evaporating droplets is dominated by a central edge growth

Evaporation of blood droplets and diluted blood samples is a topic of intensive research, as it is considered a potential low-cost diagnostic tool. So far, samples with a volume fraction down to a few percent of red blood cells have been studied, and these were reportedly dominated by a “coffee-ring” deposit. In this study, samples with lower volume fractions were used to investigate the growth of the evaporative deposit from sessile droplets in more detail. We observed that blood samples and salt solutions with less than 1% volume fraction of red blood cells are dominated by a central deposit. We characterized the growth process of this central deposit by evaporating elongated drops and determined that it is consistent with the Kardar-Parisi-Zhang process in the presence of quenched disorder. Our results showed a sensitivity of the deposit size to fibrinogen concentration and the shape of red blood cells, suggesting that this parameter could be developed into a new and cost-effective clinical marker for inflammation and red blood cell deformation.

Pattern recognition of drying lysozyme–glucose droplets using machine learning classifiers

Out-of-equilibrium processes, such as sessile droplet drying, often result in distinctive macroscopic residual patterns in systems containing molecules, proteins, and colloids. Protein–glucose mixtures are particularly effective models for studying the behavior of complex fluids containing biomolecules. This study investigates the drying patterns of lysozyme droplets with varying initial glucose concentrations. Without glucose, the crack patterns are chaotic and dispersed throughout the droplet. Interestingly, cracks predominantly form around the droplet edges at intermediate glucose concentrations, while the deposits become uniform and crack-free at high glucose concentrations. To understand and classify the unique patterns related to the initial compositional changes, we developed an automated pattern recognition pipeline. We used two methods for analyzing images captured throughout the drying process. The first method involved extracting statistical textural parameters from the images as quantitative features for machine learning classifiers. The second method utilized a neural network-based classifier to directly classify the images, achieving an accuracy of 97%. The results demonstrate the effectiveness of using images from the entire drying process, not just the final images, for pattern classification. This approach may be useful in gaining a fundamental understanding of unique crack pattern that emerge when glucose is added to a protein solution.

Gravitational effects on optical lens fabrication: First insides on Earth- and microgravity experiments

Abstract Understanding the effects of gravity on manufacturing processes is a pioneering extension of the process parameter space used to date. Until now, the improvement of manufacturing technologies has mainly focused on process parameters such as temperature, pressure, and material composition, as access to variable gravity environments is limited. The Einstein-Elevator opens up new possibilities for the variation of these process parameters and the development of in-space manufacturing technologies. Together with the research of innovative production processes for optical components within the PhoenixD Cluster of Excellence, this creates an entirely new field of research. The research presented here focuses on investigating gravity's effects on dispensed optical lens production. Using a jet dispenser, sessile droplets are produced during a flight phase in the Einstein-Elevator and cured directly by UV polymerization. As part of this study, optical lenses were produced and compared under microgravity and Earth's gravitational conditions. Geometric properties such as height and contact angle of the lenses produced were analyzed. It was found that lenses fabricated under microgravity have a larger contact angle than those fabricated under Earth gravity. Similarly, the height increases with decreasing gravity. These results are consistent with the theoretical assumptions described, although generalized theories to describe the morphology of a sessile droplet are not yet available. The case study findings on the influence of gravity as a process parameter on drop morphology represent a fundamental improvement for additive manufacturing technologies, especially for in-space manufacturing.

Ambient-gas forced convection dictated evaporation kinetics of generic sessile droplets

We probe the temporal evolution of internal thermo-hydrodynamic features of evaporating sessile droplets under external forced convection. A transient numerical model based on Arbitrary Lagrangian-Eulerian (ALE) framework is adopted. The governing equations corresponding to the transport phenomena (mass, momentum and energy) are solved in a fully coupled manner in both the droplet (liquid) and ambient (gaseous) domains while accurately tracing the droplet interface evolution. The role of initial wetting state, external convection velocity and convective heating/cooling effects due to the air-flow are explored in details, and good agreements are noted with previous reports from literature. Results show that although the evaporation rate is augmented significantly in forced convection conditions, the same does not increase in proportion at higher Reynolds numbers. This is primarily due to the enhanced cooling effects that reduce saturated vapor concentration at droplet surface, and thereby supress the diffusion mechanism. Also, depending upon the contact angle, the evaporative cooling effects are compensated partially or completely due to convective heating. This altered thermal profile substantially influences internal hydrodynamic features (Marangoni flow and heat advection) during the transient and stable regimes of droplet evaporation. At higher degrees of convective heating, the droplet interface temperature becomes higher than its base temperature. This condition results in a completely opposite internal Marangoni vortex at stable state compared to that induced due to evaporative cooling effects. We also provide a regime map to show the role of the gas-phase Stefan number on the droplet-phase hydrodynamic regimes.

Predicting sessile droplet evaporation kinetics via cascaded deep networks and tree-based machine learning approach

The intricate nature of sessile droplet evaporation phenomenon makes detailed experimental studies time consuming and requires sophisticated apparatus; while complete numerical simulations are computationally expensive and also time-intensive. In this article, for the first time, we explore the applicability of machine learning (ML) approaches to predict the evaporation kinetics of generalized sessile droplets under various conditions. An in-house dataset, obtained using an experimentally well validated numerical model, is used to develop the ML models: deep artificial neural network (ANN) and decision tree algorithms such as Random Forest (RF) and extreme gradient boosting (XGB). The structures of these models are modified by cascading the output features according to the physics involved. This distinctive approach results in better prediction of the evaporation kinetics than basic ML models. The models are trained by a large set of input parameters for the target variables: viz. droplet evaporation rate, velocity scale, and temperature drop in the solid and liquid domain. Finally, the performance of these ML models is assessed by comparing their predictions with that of physics-based, experimentally validated, numerical models. Results show that the inclusion of additional features obtained using feature engineering significantly improve the prediction performance of ML algorithms, and consistently accurate predictions of droplet evaporation kinetics are obtained. Among various algorithms considered here, the ANN outperforms in term of various error matrices for most of the cases, followed by XGB, and RF models. Also, the highest mean average error (MAE) yield by the ML models for evaporation rate, velocity scale and temperature drop in liquid remains within ∼12.5%. In the case of temperature drop for the solid, the MAE is considerably higher due to large variability of the same target variable. Overall, the work clearly shows that ML algorithms can be used to obtain physically consistent predictions for sessile droplet evaporation parameters.

PH effects on capture efficiency and deposition patterns in sessile droplet immunoassays: An XDLVO analysis.

Immunosensors are crucial for various applications, with capture efficiency and detection time as key performance parameters. Sessile droplets on functionalized substrates have demonstrated potential as micro-reactors for antibody-antigen binding, reducing detection time and analyte volume due to the presence of convective currents. Tuning the surface charges by adjusting buffer pH can modulate antigen capture efficiency. While the impact of pH has been studied on antibody-antigen binding in flow and non-flow systems, the use of sessile droplets and the specific impact of buffer pH on the capture efficiency of surface-functionalized antibodies remains understudied. Understanding how pH affects capture and deposition patterns is vital for optimizing immunosensor design. Additionally, the mechanisms governing internal flow within the droplet and dominant driving forces require further investigation. We investigated the effect of varying buffer pH on prostate-specific antigen (PSA) capture by anti-PSA functionalized polydimethylsiloxane substrates. Capture efficiency was measured using the Brown-Anson model applied to cyclic voltammetry, validated with electrochemical impedance spectroscopy. pH significantly influenced PSA capture by surface-immobilized anti-PSA IgG. The extended Derjaguin-Landau-Verwey-Overbeek theory explained the interplay between pH and internal flow. Micro-particle image velocimetry (PIV) confirmed internal flow, primarily driven by Marangoni flow from solute concentration gradients. Controlling buffer pH in biosensors offers higher capture efficiency and desired deposition patterns. These insights advance immunosensor design and hold potential for biomedical and diagnostic applications.

Phase-field-based lattice Boltzmann method for containerless freezing.

In this paper we first propose a phase-field model for the containerless freezing problems, in which the volume expansion or shrinkage of the liquid caused by the density change during the phase change process is considered by adding a mass source term to the continuum equation. Then a phase-field-based lattice Boltzmann (LB) method is further developed to simulate solid-liquid phase change phenomena in multiphase systems. We test the developed LB method by the problem of conduction-induced freezing in a semi-infinite space, the three-phase Stefan problem, and the droplet solidification on a cold surface, and the numerical results are in agreement with the analytical and experimental solutions. In addition, the LB method is also used to study the rising bubbles with solidification. The results of the present method not only accurately capture the effect of bubbles on the solidification process, but also are in agreement with the previous work. Finally, a parametric study is carried out to examine the influences of some physical parameters on the sessile droplet solidification, and it is found that the time of droplet solidification increases with the increase of droplet volume and contact angle.

NaClO3 Crystal Growth and Dissolution by Temperature Cycling in a Sessile Droplet

Sodium chlorate is the most popular compound used to study spontaneous symmetry breaking by means of crystallization. Therefore, it is important to know the behavior of the solid particles. NaClO3 crystal growth and dissolution are investigated in an aqueous sessile droplet subjected to numerous temperature cycles. On cooling, in addition to the classical formation of repeated elongated fluid inclusions, there is a reproducible appearance of prismatic fluid inclusions (PFIs) at the corners of single crystals. The underlying mechanism involves the complete termination of the (110) face growth and the propagation of the {100} faces, which can close the PFIs. This study reports that on heating, transient donut-like single crystals formed, which could lead to their segmentation, even without stirring the suspension. The systematic addition of other sodium salts with chlorine atoms at different oxidation states did not change these observations.

Enhanced evaporation and heat transfer of sessile droplets via coupling electric field and temperature field

Controllable evaporation of sessile droplets is essential in diverse applications, ranging from thermal management to chemical reactions and combustion. Despite considerable advances, further enhancement of droplet evaporation is still challenging. Here, an experimental system that couples uniform/non-uniform electric fields with temperature fields to enhance hydrophilic droplet evaporation is introduced. The electric field can generate Coulomb force by changing the redistribution of charges at the droplet interface, which enables highly flexible and precise control of the sessile droplet. By leveraging the uniform electric field, the droplet is stretched upwards, which increases the heat transfer thermal resistance and the vapor concentration near the droplet interface, leading to the deterioration of droplet evaporation. Whereas the application of a non-uniform electric field will flatten the droplets due to the shear effect of the corona wind on the droplet interface, and the reduction of the heat transfer thermal resistance of the droplets, as well as the vapor concentration near the interface, which promotes the droplet evaporation. The coupling of uniform electric and temperature fields could reverse the inhibition effect of droplet evaporation caused by a purely uniform electric field, and the maximum enhancement ratio reaches 5.11 times. The coupling of a non-uniform electric field and temperature field can enhance droplet evaporation up to 29.34 times. The corresponding numerical simulation study reveals the flow and temperature distribution inside the droplet. This research provides critical insights into the precise manipulation of droplet evaporation by applying an electric field.

Deformation of Sessile Droplets under a Gentle Shear Airflow.

Deformation of sessile droplets under shear flow is widespread in both nature and industry. Previous research focuses on the shedding process of sessile droplets under shear airflow, with insufficient attention paid to the droplet deformation before shedding. In this work, experimental studies on the deformation behaviors of sessile droplets under shear airflow are conducted to investigate the effects of airflow velocity and droplet volume on the tangential and normal droplet deformations. Scaling laws of the droplet deformations are established. The results show that the profile of sessile droplets changes under shear airflow with the topmost point exhibiting periodic oscillations in both tangential and normal directions. The oscillation period of the tangential deformation exceeds that of the normal deformation. The average tangential deformation of droplets increases with the increasing airflow velocity and droplet volume. The average normal deformation of droplets increases with the increasing airflow velocity and is influenced by the droplet volume at a higher airflow velocity. The contact angle on the windward side oscillates periodically, and its average value significantly decreases. The contact angle of droplets on the windward side decreases as the airflow velocity and droplet volume increase, while the contact angle on the leeward side remains almost unchanged. The average deformation of droplets in the tangential and normal directions is linearly related to the effective Weber number and the square of the effective Weber number. These findings could be used to predict the deformation of sessile droplets under shear airflows.

Intricate Evaporation Dynamics in Different Multidroplet Configurations.

We experimentally investigate the evaporation dynamics of an array of sessile droplets arranged in different configurations. Utilizing a customized goniometer, we capture side and top view profiles to monitor the evolution of height, spread, contact angle, and volume of the droplets. Our results reveal that the lifetime of a droplet array surpasses that of an isolated droplet, attributed to the shielding effect induced by neighboring droplets, which elevates the local vapor concentration, thereby reducing the evaporation rate. We found that lifetime increases as droplet separation distance decreases at a fixed configuration and substrate temperature. It is observed that the lifetimes increase with the number of droplets. We observe a decrease in lifetimes, following a power law trend, with increasing substrate temperature, with the shielding effect diminishing at higher substrate temperatures due to natural convective effects. We also observe a generalized behavior for the centrally placed droplet across various separation distances and substrate temperatures. This arises from different droplet configurations and substrate temperatures, which modify the local vapor concentration around the droplets without significantly impacting the contact line dynamics. Additionally, the experimental results are compared with a diffusion-based theoretical model that incorporates the evaporative cooling effect to predict the lifetime of the central droplet within the array. We observe that the theoretical model satisfactorily predicts the lifetime of the droplet at room temperature. However, for high-temperature cases, the model slightly overpredicts the evaporative lifetimes.

Dispersion of particles in a sessile droplet evaporating on a heated substrate

A coupled volume-of-fluid (VOF) and discrete element model (DEM) is developed and used to study the dispersion of particles in an evaporating pinned sessile droplet on a heated substrate. Fully resolved simulations of evaporating droplets are performed to study the effects of substrate temperature and the Marangoni stresses to study the fluid flow and temperature distribution within the droplet. The fluid flow inside the evaporating droplets is used to predict the behavior of particles, studying the effect of relative particle density and the aforementioned effects on the particle dispersion within the droplet. This study shows that the presence of Marangoni stresses significantly affects the flow and temperature distribution inside the droplet, which, in turn, influences the dispersion of particles in the droplet. The fluid velocity induced by the Marangoni stresses is nearly two orders of magnitude larger than the velocity generated by capillary flow as a result of evaporation, promoting a strong convective mixing within the droplet, while working to equilibrate the temperature distribution at the interface. In the absence of Marangoni stresses, the dispersion of particles is governed by the competing effects of adsorption by the downward-moving interface as a result of evaporation, and particle sedimentation under the influence of gravity. However, both these effects become less dominant in the presence of a flow induced by the Marangoni stresses, causing the particles to initially move toward the apex of the droplet along the interface and, subsequently, toward a stagnation point on the interface.

Calculation of apparent contact angle for sessile droplets on structured hydrophobic surfaces based on dynamic of contact line during droplet formation

The sessile-droplet method is widely used to characterize surface wettability, however, the measured apparent contact angle (APCA) is usually a non-unique value between the advancing and receding contact angles, which seems hardly to be predicted by the classical Cassie-Baxter model. Thus, a reliable calculation model for APCAs of sessile droplets on structured hydrophobic surfaces is needed to guide the structural design of functional hydrophobic surfaces. Focusing on the force and motion analysis of the contact line during the formation process of sessile droplets, a theoretical model was developed to calculate the APCA of the droplet on hydrophobic surfaces featured with square micropillar arrays. The present model considers the synergistic effect of the droplet shape and the contact-line pinning on the APCA. Compared with the Cassie-Baxter model, the APCAs calculated by the proposed model agree better with the experimental data. This study shows that APCA is generally more susceptible to advancing contact angle, which is not significantly different on structured hydrophobic surfaces with different dimensions, resulting in the inability of APCA to accurately characterize surface wettability. As a complement, receding-contact-angle and adhesion-force measurements, which can reflect the effects of structural dimensions, are recommended to be adopted to characterize surface wettability.

Interphase-Controlled Inkjet Printing of MicroInlaid OLEDs: Effects of Solvent- and Solute-Polymer Interactions.

Inkjet printing, a highly promising technique for the cost-effective fabrication of large-scale organic light-emitting devices (OLEDs), typically necessitates the intricate alignment of precisely patterned insulating layers. Recently, we introduced a unique single-step inkjet printing process that produces well-patterned microinlaid spots of functional compounds through insulating polymer layers. This approach exploits lateral phase separation between the solute of functional compounds and the polymer, allowing the simultaneous spatial etching of the polymer and the infilling of the solute using a single inkjet-printed sessile droplet. Here, we demonstrate that the interaction between the solvent and polymer, as well as the solute and polymer, critically determines the precision and efficiency of printing. This is particularly evident when using either the insulating poly(vinylpyridine) isomer of poly(4-vinylpyridine) (P4VP) or poly(2-vinylpyridine) (P2VP) with chloroform as a solvent, which allows for a detailed examination of these interactions based on certain solubility parameters. Micro-Raman spectroscopy reveals that the self-organizing capability of the microinlaid spots with P4VP is superior to that with P2VP. This is due to the fact that P2VP shows higher affinity to the solvent and causes imperfect phase separation as compared to P4VP. As a result, a performance evaluation demonstrates enhanced device performance for inkjet-printed green micro-OLEDs with P4VP, exhibiting a higher external quantum efficiency of 3.3% compared to that of 2.3% achieved with P2VP. These findings elucidate the important roles of solvent-polymer and solute-polymer interactions in the inkjet printing process, leading to interfacial control of inkjet printing technique for the cost-effective production of high-performance and high-resolution micro-OLEDs.

A novel phase-field lattice Boltzmann framework for diffusion-driven multiphase evaporation

Heat transfer and phase change phenomena, particularly diffusion-driven droplet evaporation, play pivotal roles in various industrial applications and natural processes. Despite advancements in computational fluid dynamics, modeling multiphase flows with large density ratios remains challenging. In this study, we developed a robust and stable conservative Allen–Cahn-based phase-field lattice Boltzmann method to solve the flow field equations. This method is coupled with the finite difference discretization of vapor species transport equation and the energy equation. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius–Clapeyron correlation. Our approach is capable of simulations under real physical conditions and is compatible with graphics processing unit architecture, making it ideal for large-scale industrial simulations. Three validation test cases are conducted to demonstrate the consistency of the presented model, including simulations of Stefan flow, the evaporation of suspended droplets containing water, acetone, and ethanol in the air, and the evaporation of a water sessile droplet on a flat surface. The results show that the model is able to predict the behavior and characteristics of each case accurately. Notably, our numerical results exhibit a maximum relative error of approximately 1% in simulations of Stefan flow. In the case of suspended droplet evaporation, the observed maximum difference between the calculated wet bulb temperatures and those derived from psychrometric charts is approximately 0.9 K. Moreover, our analysis of the sessile droplet reveals a good agreement between the results obtained by our model for the evaporative mass flux and those obtained from the existing models in the literature for different contact angles.

Contact angle calculations for argon and water sessile droplets on planar lyophilic and lyophobic surfaces within molecular dynamics modeling

There exist many ways to calculate the contact angle of a sessile droplet on a planar surface on the basis of molecular modeling data, and the result may depend on the chosen approach. This paper presents molecular dynamics simulations of argon and water sessile droplets on simple model and more complex atomistic substrates. Several approaches for calculating contact angles are described. These approaches are based on an analysis of instantaneous droplet’s configurations and averaged density profiles. The latter are analyzed using density cutoffs and the Sobel filters. Parameters of the interaction between the planar surface and the fluid are being tuned in order to consider model lyophilic and lyophobic substrates. Dependences of the contact angle on the strength of interaction between the fluid and the substrate and on the droplet size are obtained. The apparent line tensions for the observed sessile droplets are evaluated.