Sessile Droplet Research Articles

Experimental study of sessile droplet evaporation under the influence of substrate elastic deformation

Experimental study of sessile droplet evaporation under the influence of substrate elastic deformation

A Computational Investigation of the “Equivalent Substrates” in the Evaporation of Sessile Droplets

This paper investigates the coupled relationship between solid-phase temperature fields and droplet evaporation, focusing on the effects of substrate thermal conduction properties on droplet evaporation behavior. A mathematical model is developed to analyze the impacts of substrate thermal conductivity, thickness, and lower-surface temperature on evaporation rate, surface temperature, and evaporation flux. A dimensionless relative evaporation rate (HCs) is introduced to characterize the influence of substrate thermal conduction. Results show that increasing substrate thermal conductivity enhances droplet surface temperature and evaporation flux, thereby monotonically increasing evaporation rate until it approaches the rate of the evaporative cooling model. Conversely, increasing substrate thickness lengthens the heat transfer path, reducing heat conducted to the solid–liquid interface and decreasing evaporation rate. Changes in substrate lower-surface temperature significantly affect evaporation rate, but HCs remains nearly unaffected. The concept of equivalent substrates is proposed and verified through dimensionless analysis and simulations. It is found that different combinations of substrate thickness and thermal conductivity exhibit consistent effects on droplet evaporation, with minimal relative errors in evaporation rate and total heat transfer at the solid–liquid interface. This confirms the existence of the equivalent substrate phenomenon. Additionally, the effects of droplet properties, such as contact angle and evaporative cooling coefficient (Ec), on the equivalent substrate phenomenon are explored, revealing negligible impacts. These findings provide theoretical guidance for optimizing droplet evaporation processes in practical applications, such as micro/nanoscale thermal management systems.

Rigorous model of sessile droplet evaporation considering the kinetic factor

Rigorous model of sessile droplet evaporation considering the kinetic factor

Evaporation dynamics of wavy sessile droplets

We study the evaporation dynamics of non-thin non-spherical-cap (i.e. wavy) droplets. These droplets exhibit surface curvature that varies periodically with the polar angle, which profoundly influences their evaporation flux, internal flow dynamics, and the resultant deposition patterns upon complete evaporation. The droplet is considered quasi-static throughout its entire lifetime. The asymptotic expansions of the evaporation flux in the diffusion-limited model, and the induced internal inviscid flow of the droplets, are derived through asymptotic analysis. Under the assumption of small deformation amplitudes, the accuracies of these two expansions are validated numerically. Expanding upon these asymptotic results, we also investigate the surface density profile of the droplet deposition after it dries up. The results indicate that the freely moving contact line of the droplet leads to the deposited stain exhibiting a mountain-like morphology. The internal inviscid flow along with the non-spherical-cap shape eliminates the divergence of the deposited surface density profile at droplet’s centre. This work provides a theoretical basis for geometrically controlled sessile droplet evaporation, which may have practical applications in industry.

Numerical simulation of sessile droplet evaporation enhanced by corona wind

Numerical simulation of sessile droplet evaporation enhanced by corona wind

Experimental study on the evaporation characteristics of sessile droplets under different substrate materials and relative humidity

Abstract Based on the demand to enhance static phase change evaporation heat transfer, this research examines the evaporation behavior of sessile droplets exposed to shear flow within a compact wind tunnel. The results indicate that various factors, including substrate materials, substrate structures, relative humidity (RH), and droplet types, influence the evaporation of droplets affected by shear flow. The evaporation of droplets on copper substrates predominantly aligns with the Constant Contact Radius (CCR) model, exhibiting a higher evaporation rate. Elevated base structures can mitigate the effects of the boundary layer, facilitating faster evaporation of droplets at lower shear flow rates. Increasing relative humidity raises the vapor concentration in the air, thereby inhibiting droplet evaporation. Ethanol droplets under shear flow demonstrate a distinct behavior, with evaporation rates initially increasing before slightly decreasing. At low wind velocities, evaporation is predominantly driven by vapor concentration, while at high wind velocities, it is primarily limited by energy transfer. This research may provide valuable insights for utilizing shear flow to enhance liquid evaporation rates and improve heat transfer efficiency.

Effect of gravity-induced shape change on the diffusion-limited evaporation of thin sessile and pendant droplets

Effect of gravity-induced shape change on the diffusion-limited evaporation of thin sessile and pendant droplets

Asymmetric Deposits and Crack Formation during Desiccation of a Blood Droplet on an Inclined Surface.

We study the combined effect of varying droplet volume and inclination angles on the desiccation patterns left behind evaporating sessile droplets of human blood. We systematically varied the droplet volume in a range of [1-10 μL] and inclination angles between [0-70°]. Microstructural characterization of the deposits was performed using optical microscopy and surface profilometry. On a horizontal surface, typical deposits of toroidal shape with cracks oriented in radial and azimuthal directions were observed. With an increase in the droplet volume and inclination, the interplay between the gravitational and surface tension effects leads to an asymmetric liquid-vapor interface shape, resulting in a differential evaporative mass flux pattern across the interface. Subsequently, we observe elongation of the overall desiccation patterns along with asymmetric mass deposits between the advancing and receding fronts. As a consequence, the crack morphology on the two fronts exhibits pronounced differences. The distinct regimes of asymmetric mass deposits and crack morphology were quantitatively examined as a characteristic of varying droplet volume and inclinations, parametrized in terms of the mean radial crack spacing and width. These findings are qualitatively analyzed by a first-order theoretical model that is based on the energy conservation principle incorporating the release of mechanical stress energy by contraction of the deposit at the last stage of the desiccation process and the consumed surface energy upon formation of the new surfaces during crack evolution.

Emergence of metachronal waves in a chain of symmetrically beating filaments

Recent experiments show that metachronal waves (MCWs) can emerge from a chain of symmetrically beating nematodes aligned at the edge of sessile droplets. Our study, employing a coupled elastohydrodynamic model of active filaments, elucidates that a misalignment caused by a tilt against the bounding wall disrupts the synchronization and generates a constant time lag between adjacent filaments, giving rise to MCWs. The MCWs, enhancing the fluid circulation, achieve their maximum thermodynamic efficiency over the same range of tilt angles observed in the nematode experiments. Published by the American Physical Society 2025

Preservation of wetting ridges using field-induced plasticity of magnetoactive elastomers.

Preservation of wetting ridges using field-induced plasticity of magnetoactive elastomers.

Line tension from dual-geometry sessile droplet measurements: Combining contact-angle size-dependence data for axisymmetric and cylindrical droplets to determine the line tension.

We perform a thermodynamic analysis of various contributions to the size dependence of the contact-angle cosine for both axisymmetric and cylindrical sessile droplets. This shows that a commonly used method to determine the line tension from the slope of the contact-angle cosine dependence on the three-phase contact-line curvature (for axisymmetric droplets) provides a certain combination of the line tension, the adsorptions at the three interfaces, and the macroscopic contact angle. To extract the contribution related to the contact line in the leading order and determine the line tension, we propose a simple technique using droplet-size dependences of the contact angle for axisymmetric and cylindrical droplets under the same conditions.

Azimuthal Variation of Apparent Contact Angles on Structured Surfaces Featuring Micrometric Ramps, Pyramids and Staggered Cubes at Two Different Inherent Wettabilities.

As new manufacturing methods enable manufacturing of microstructured surfaces with varying structure geometries, questions remain on some effects on the wetting behavior and the resulting apparent contact angles. In this study, we report the manufacturing process using 3D Direct Laser Writing (3D-DLW) and hot embossing for Poly methyl methacrylate (PMMA) surfaces with micrometric pyramids, cubes on a staggered grid and two types of ramped structures. We measure the azimuthal variation of the apparent contact angle of sessile droplets on the surfaces. Using plasma polymerization or no treatment of the surfaces, two different inherent wettabilities are studied. We find that while all structure types cause an azimuthal variation of the apparent contact angle, pinning at the ramp tops increases the contact angle more strongly on one side. On pyramid structures, pinning lines can occur on the structure axes and diagonals similarly. For cubes on a hexagonal grid, the strongest contact angle increases are observed along the primary structure axes, where pinning is preferred while smaller peaks are seen on the secondary axes at 60 and 120° to the primary axis.

An Extended Height‐Function Method for 3D VOF Simulations of Wetting Phenomena on Super‐Hydrophilic and Hydrophobic Surfaces

ABSTRACTAn extended height‐function (HF) method that can be consistently utilized for 3D volume of fluid (VOF) simulations of wetting phenomena on super‐hydrophilic and super‐hydrophobic surfaces, is proposed. First, the standard HF method is briefly explained. Then, 2D and 3D HF methods that reflect the contact angles reported so far are described, with their limitations discussed. Finally, specific treatments of contact line identification and HF construction reflecting the contact angle boundary condition, required to overcome such limitations, are presented in detail. Numerical tests for a sessile droplet reveal that the contact line identification and HF construction are conducted appropriately with respect to the imposed contact angles ranging from to in the proposed numerical scheme. Additionally, the present method shows approximately first‐ or second‐order convergence of the curvature at the contact line for a wide range of contact angles. Moreover, simulations of droplet spreading driven by surface tension reveal that the proposed method can reasonably reproduce the behavior of a droplet reaching an equilibrium state defined by an imposed contact angle.

Modeling of the evaporation process of a pair of sessile droplets on a heated substrate

Sessile droplet evaporation is a complex process that involves both mass and heat transfer at the liquid/vapor interface. This process has many practical applications, including cooling microprocessors, and improving heat exchanger efficiency. This work builds upon a previously developed point source model for purely diffusive evaporation, expanding it to account for the effect of heated substrates on the evaporation behavior of a pair of sessile water droplets. Experimental investigations were carried out at various substrate temperatures and droplet separation distances to assess the validity of the diffusive model under these conditions. Results show that as the substrate temperature increases, convection becomes a more prominent factor alongside diffusion, enhancing the evaporation rate. When the temperature difference between the substrate and the ambient is small, diffusion dominates, but as this difference grows, natural convection plays a significant role. It is found that for Ra · L/d < 400, the evaporation rate is governed mainly by diffusion. Likewise, for Ra · L/d > 2400, the contribution of convection and diffusion stabilizes. An empirical correlation was developed to predict evaporation rates, accounting for both diffusion and convection. The proposed correlation shows excellent agreement with experimental data across different conditions, making it a valuable tool for predicting droplet evaporation rates on heated surfaces and its applications in thermal management systems.

Evolutionary modeling and mechanistic analysis of the impact dynamics between free-falling droplets and a sessile droplet on an anisotropic surface

Evolutionary modeling and mechanistic analysis of the impact dynamics between free-falling droplets and a sessile droplet on an anisotropic surface

Collision of immiscible droplets on a solid surface

While the impact of a single drop on a surface has been extensively studied, the more complex scenario of a drop impacting a sessile drop, particularly when the two liquids are immiscible, remains relatively unexplored. This study employs a multiple-relaxation-time phase-field lattice Boltzmann model to numerically investigate the impact of an immiscible droplet onto a sessile droplet. The findings show that compared to the better-known case of miscible impact, immiscible impact exhibits reduced spreading on the substrate. A key determinant of impact outcome is the interfacial tension between the droplets, quantified by the spreading factor. Simulations across varying spreading factors reveal different outcomes: droplet sticking, bouncing, engulfment of the sessile by the impacting droplet, and vice versa. Furthermore, the maximum spreading exhibits a dependence on the Weber number and contact angle, analogous to miscible impact. Liquid property mismatches, particularly density disparities, significantly influence the impact dynamics, while viscosity variations have a lesser effect. Finally, the study examines off-center impact and demonstrates the influence of initial misalignment on the impact dynamics.

Sessile and suspended droplets on a biphilic surface in the presence of natural convection: Experimental studies and modeling

New experimental and modeling results, referring to heating and evaporation of sessile and pendant water droplet on a biphilic surface, are presented. Two modeling approaches are used: one based on the previously developed variable density model in which the droplet shape in the presence of gravity is described by the Bashforth–Adams equation, and the other based on ANSYS Fluent. It is shown that the results predicted by both approaches almost coincide in the absence of gravity, which can be considered as verification of both approaches. The predictions of both approaches are shown to be close to experimental results for pendant droplets. For sessile droplets, however, both approaches tend to under-predict experimental data. The difference in model predictions, taking and not taking into account the effect of natural convection, is shown not to exceed 3% for the experimental conditions under consideration.

Multistep Phase Transition and Molecular Reaction of Plasmonic Nanoparticles at the Three-Phase Contact Line of an Evaporating Sessile Droplet

Multistep Phase Transition and Molecular Reaction of Plasmonic Nanoparticles at the Three-Phase Contact Line of an Evaporating Sessile Droplet

The effect of particle–substrate adsorption on the deposition of particles from a thin evaporating sessile droplet

A mathematical model for the evaporation of, the flow within, and the deposition from, a thin, pinned sessile droplet undergoing either spatially uniform or diffusion-limited evaporation is formulated and analysed. Specifically, we obtain explicit expressions for the concentration of particles within the bulk of the droplet, and describe the behaviour of the concentration of particles adsorbed onto the substrate as well as the evolution of the masses within the bulk of the droplet, adsorbed onto the substrate, and in the ring deposit that can form at the contact line. In particular, we show that the presence of particle–substrate adsorption suppresses the formation of a ring deposit at the contact line for spatially uniform, but not for diffusion-limited, evaporation. However, in both scenarios, the final adsorbed deposit is more concentrated near to the contact line of the droplet when radial advection due to evaporation dominates particle–substrate adsorption, but is more concentrated near to the centre of the droplet when particle–substrate adsorption dominates radial advection due to evaporation. In addition, in an appendix, we investigate the formation of a ring deposit at the contact line for a rather general form of the local evaporative flux, and show that the presence of particle–substrate adsorption suppresses the formation of the ring deposit that can otherwise occur when the local evaporative flux is non-singular at the contact line.

Soft Wetting Ridge Rotation in Sessile Droplets and Capillary Bridges.

We investigate the deformation of soft solid layers in the presence of sessile droplets or capillary bridges. Unlike models that assume Young's law governs the contact angle, we incorporate the surface tension balance at the contact line to analyze the rotation of the wetting ridge and the corresponding change in the contact angle. Our findings reveal that the rotation direction of the wetting ridge aligns with the sign of the Laplace pressure. Interestingly, although a softer solid layer typically decreases the contact angle for sessile droplets, a negative Laplace pressure in a hydrophilic capillary bridge pulls the solid-liquid interface, leading to an increased contact angle. A hydrophilic capillary bridge would be expected to move from thicker regions of a soft layer to thinner areas, exhibiting behavior opposite that of a sessile droplet. The interplay between soft layer deformation and contact angle modulation provides valuable insights into controlling droplet motion through elastocapillarity.