Sessile Liquid Droplets Research Articles

A non-invasive capacitive sensor to investigate the Leidenfrost phenomenon: a proof of concept study

A volatile sessile liquid droplet or a sublimating solid manifests levitation on its own vapor when placed on a sufficiently heated surface, illustrating the Leidenfrost phenomenon. In this study, we introduce a non-invasive capacitance method for investigating this phenomenon, offering a potentially simpler alternative to existing optical techniques. The designed sensor features in-plane miniaturized electrodes forming a double-comb structure, also known as an interdigitated capacitor. Initially, the sensor’s capacitance is characterized for various distances between the sensor and a dielectric material. The influence of the sensor substrate material and the spacing between the electrodes on the sensor’s capacitance is also investigated. To demonstrate the feasibility of the method, a sublimating dry ice pellet is placed on the capacitive sensor, and its performance is evaluated. We present results for the dimensionless vapor layer thickness and the pellet’s lifetime at different substrate temperatures, derived from the capacitance output. The results are compared with Optical Coherence Tomography (OCT) data, serving as a benchmark. While the temporal evolution of the sensor’s output, variation in the dimensionless vapor layer thickness, and the lifetime of the dry ice pellet align with expected results from OCT, notable quantitative deviations are observed. These deviations are attributed to practical experimental limitations rather than shortcoming in the sensor’s working principle. Although this necessitates further investigation, the methodology presented in this paper can potentially serve as an alternative for the detection and measurement of Leidenfrost vapor layers.

Evaporation Process of Sessile Liquid Droplet and Layer in Steady State

Evaporation Process of Sessile Liquid Droplet and Layer in Steady State

Use of Heating Configuration to Control Marangoni Circulation during Droplet Evaporation

The present work presents a numerical study of the evaporation of a sessile liquid droplet deposited on a substrate and subjected to different heating configurations. The physical formulation accounts for evaporation, the Marangoni effect, conductive transfer in the support, radiative heating, and diffusion–convection in the droplet itself. The moving interface is solved using the Arbitrary Lagrangian–Eulerian (ALE) method. Simulations were performed using COMSOL Multiphysics. Different configurations were performed to investigate the effect of the heating conditions on the shape and intensity of the Marangoni circulations. A droplet can be heated by the substrate (different natures and thicknesses were tested) and/or by a heat flux supplied at the top of the droplet. The results show that the Marangoni flow can be controlled by the heating configuration. An upward Marangoni flow was obtained for a heated substrate and a downward Marangoni flow for a flux imposed at the top of the droplet. Using both heat sources generated two vortices with an upward flow from the bottom and a downward flow from the top. The position of the stagnation zone depended on the respective intensities of the heating fluxes. Controlling the circulation in the droplet might have interesting applications, such as the control of the deposition of microparticles in suspension in the liquid, the deposition of the solved constituent, and the enhancement of the evaporation rate.

Interference patterns produced by an evaporating droplet on a horizontal surface

We study dynamical Newton-ring like fringes created by interfering Fresnel reflections of an evaporating sessile liquid droplet, which acts as a miniature convex lens. We show that conventional thin-film interference theory cannot be applied to explain the physical phenomenon. Because of the large thickness and curvature of the liquid droplet, the geometrical light paths of the reflected beams become very complicated and can no longer be considered approximately collimated. This results in interference fringes of concentric circles with different directional motion depending on the observation plane. The change in the interference pattern as a function of time is demonstrated by both simulation and experiment. This investigation allows us to fully understand the formation of interference patterns of an optical system having arbitrary thickness and curvature. In addition, by analyzing the high-contrast dynamic rings, we demonstrate nanoscale sensitivity to surface height changes of an evaporating water drop.

Capillary-induced deformation of an initially stressed neoHookean solid: A sessile liquid droplet

The development in lab-on-a-chip and flexible electronics has attracted great interest to understand the fluid-structure interaction. In this work, we analyze the capillary-induced deformation of an initially stressed neoHookean solid with an axisymmetric, sessile droplet on the surface in the framework of the incremental deformation theory. The neoHookean material is subjected initially to uniformly biaxial loading (stretching or compressing). Using the incremental deformation theory and the concept of breadth, we derive an explicit solution of the normal displacement component of the surface of the initially stressed neoHookean solid, which consists of a scaling factor and a shape function. The scaling factor decreases with the increase of the biaxial stretch, leading to the decrease in the deformation induced by the sessile droplet. The initially biaxial compression of the neoHookean solid increases the scaling factor. There is a critical-initial compression loading, at which the surface deformation changes from convex shape to concave shape. Increasing the ratio of the breadth to the radius of the contact zone between the sessile droplet and the initially stressed neoHookean solid increases the maximum value of the shape function.

The transients in the evaporation of sessile liquid droplets and the applicability of the steady-state approximation

The initial transients in the droplet evaporation (i.e., the transient processes immediately after the droplet is placed on the substrate) has been investigated first both numerically and experimentally. The results show that, during the initial stage of droplet evaporation, the vapor concentration changes monotonically when approaching its steady-state while the temperature changes nonmonotonically. The initial transient times needed for the vapor concentration and for the temperature to change from their initial values to the steady-state values are almost the same, and the ratio between the initial transient time and the droplet drying time is mainly determined by the properties of the liquid, not by the underlying substrate or by the pressure of the surrounding atmosphere. The duration of the initial transients is in general longer than the duration of the process transients which denotes the adjustment of the vapor concentration and the temperature to the change in the droplet shape as the evaporation proceeds. Furthermore, a quantitative criterion for evaluating the applicability of the steady-state approximation in the droplet evaporation is obtained, indicating that the approximation is more reasonable for liquids with a lower saturated vapor concentration. The criterion is corroborated experimentally and may contribute to the body of knowledge concerning the droplet evaporation.

Engineering Micropatterned Surfaces for Controlling the Evaporation Process of Sessile Droplets

Controlling the evaporation process of a droplet is of the utmost importance for a number of technologies. Also, along with the advances of microfabrication, micropatterned surfaces have emerged as an important technology platform to tune the wettability and other surface properties of various fundamental and applied applications. Among the geometrical parameters of these micropatterns, it is of great interest to investigate whether the arrangement of the patterns would affect the evaporation process of a sessile liquid droplet. To address this question, we fabricated four microhole arrays with different arrangements, quantified by the parameter of “eccentricity”. The results suggested that, compared to smooth substrates, the evaporation mode was not only affected by engineering the microhole arrays, but also by the eccentricity of these micropatterns. The values of contact angle hysteresis (CAH) were used to quantify and test this hypothesis. The CAH could partially explain the different evaporation modes observed on the microhole arrays with zero and non-zero values of eccentricity. That is, on microhole arrays with zero eccentricity, CAH of water droplets was comparatively low (less than 20 ° ). Consistently, during the evaporation, around 60% of the life span of the droplet was in the mixed evaporation mode. Increasing the eccentricity of the microhole arrays increases the values of CAH to above 20 ° . Unlike the increasing trend of CAH, the evaporation modes of sessile droplets on the microhole array with non-zero values of eccentricity were almost similar. Over 75% of the life span of droplets on these surfaces was in constant contact line (CCL) mode. Our findings play a significant role in any technology platform containing micropatterned surfaces, where controlling the evaporation mode is desirable.

Evaporation model for a sessile liquid droplet with variable temperature

Studies of the changes in the mass and the geometry of the sessile tiny droplet have been performed. The droplet was evaporated on a hot medium with variable temperatures. Based on the “CCR” (constant contact radius) model, a new theoretical model predicting the relationship between the mass and the geometry of the evaporating droplet when ambient temperature is changing, has been built. A solution is given when temperature changing is the linear function of the time. Measurements of the mass change of the desulfurization wastewater droplet in TGA have been conducted. The contact angle, the contact diameter and the height were detected by a visualization method. The results show that the diameter of the 0.5 μL droplet decreases little at the first stage and then plummets rapidly. This trend is rarely affected by the change of the temperature. Also, the TGA results show that, ranging of the setting temperature increasing rate from 15 °C/min to 45 °C/min and of the volume from 0.5 μL to 2.5 μL, the mass change function, G(t), is almost equal to the geometric function, F(θ). This means the theoretical model has great accuracy and validation for the prediction.

Thermodynamic Analysis of Adsorption and Line-Tension Contributions to Contact Angles of Small Sessile Droplets

Relations for the contact angles of sessile liquid droplets with axially symmetric or cylindrical shapes and different equilibrium sizes have been considered using a general thermodynamic approach. For a multicomponent system comprising a liquid droplet, a vapor–gas medium, and a solid substrate, influence of dependence of the surface tension on the chemical potentials related to equilibrium droplet size (i.e., the effect of adsorption) and the effect of size-dependent line tension on the contact angles have been discussed. It has been shown that, for an axially symmetric sessile droplet, the effects of adsorption and line tension are, in the general case, comparable and manifest themselves already at the first order with respect to the droplet curvature. For a cylindrical droplet, the effect of adsorption is observed already in the first order with respect to the droplet curvature, while the influence of the line tension manifests itself only in the second order and is governed by the droplet-size dependence of the line tension.

Hysteresis of Contact Angle of Sessile Droplets on Deformable Substrates: Influence of Disjoining Pressure

Liquid droplet placed on a deformable / soft substrate causes the substrate to deform. Combined action of capillary pressure and surface forces, which act in the vicinity of the apparent three-phase contact line and substrate's elasticity determine both the liquid shape and the substrate deformation. A theory of contact angle hysteresis of sessile liquid droplets on deformable/soft substrate is developed in terms of disjoining pressure isotherm, Πh, which accounts for the action of surface forces in the vicinity of the contact line. Minimum of excess free energy of the droplet on deformable substrate results in two interconnected equations for droplet and deformed substrate shapes in terms of disjoining pressure isotherm. A simplified s-shaped disjoining pressure isotherm, which allows direct calculations of static advancing/receding contact angles on deformable substrates, is adopted. Elasticity of the substrate is assumed to obey a simple Winkler's model for elastic surfaces. The obtained results are in agreement with the contact angle hysteresis theory developed earlier for non-deformable substrates. Calculated values of both advancing and receding contact angles for droplets on deformable substrate depend on droplet volume (which has a direct experimental confirmation). Advancing and receding contact angles of droplets on deformable substrates are lower as compared with those on a non-deformable substrate. The results of the derived model on hysteresis of contact angle on deformable substrates qualitatively agree with known experimental observations.

Coalescence of droplets on micro-structure patterned hydrophobic planar solid surfaces

The motion and coalescence of sessile liquid droplets on patterned solid surfaces are investigated systematically in terms of the liquid and substrate surface properties.

Expressions for the evaporation of sessile liquid droplets incorporating the evaporative cooling effect

The evaporation along the surface of pinned, sessile droplets is investigated numerically by using the combined field approach. In the present model, the evaporative cooling at the droplet surface which leads to a reduction in the evaporation is taken into account. Simple, yet accurate analytical expressions for the local evaporation flux and for the total evaporation rate of sessile droplets are obtained. The theoretical analyses indicate that the reduction in the evaporation becomes more pronounced as the evaporative cooling number Ec increases. The results also reveal that the variation of total evaporation rate with contact angle will change its trend as the intensity of the evaporative cooling changes. For small values of Ec, the total evaporation rate increases with the contact angle, the same as predicted by Deegan et al. and by Hu and Larson in their isothermal models in which the evaporative cooling is neglected. Contrarily, when the evaporative cooling effect is strong enough, the total evaporation rate will decrease as the contact angle increases. The present theory is corroborated experimentally, and found in good agreement with the expressions proposed by Hu and Larson in the limiting isothermal case.

Droplet on an elastic substrate: Finite Element Method coupled with lubrication approximation

Sessile liquid droplets deposited on soft substrates may cause substrate deformation. The substrate elasticity affects the apparent contact angle and the spreading dynamics of the sessile drop. In the present work, a model for description of a droplet on an elastic substrate is developed using the disjoining pressure concept. A Finite Element Method for the elasticity problem in a substrate is coupled with lubrication approximation for the modelling of droplet spreading. The disjoining pressure model allows an independent definition of contact angle and the thickness of the adsorbed layer. Simulations are performed to quantify the influence of mechanical properties, the substrate size and the parameters of the disjoining pressure model on the substrate deformation and apparent contact angle. It is shown that the dimensionless substrate deformation peak height scales with the dimensionless parameter σsinθ/(Ea), and the solid angle appearing in the deformed substrate near the apparent cotact line scales with σ/(Ea), where σ denotes the surface tension, E is the Young modulus, θ is the apparent contact angle and a is a width of the region in which the disjoining pressure plays an important role.

Floating mechanism of a small liquid marble

Flotation of small solid objects and liquid droplets on water is critical to natural and industrial activities. This paper reports the floating mechanism of liquid marbles, or liquid droplets coated with hydrophobic microparticles. We used X-ray computed tomography (XCT) to acquire cross-sectional images of the floating liquid marble and interface between the different phases. We then analysed the shape of the liquid marble and the angles at the three-phase contact line (TPCL). We found that the small floating liquid marbles follow the mechanism governing the flotation of solid objects in terms of surface tension forces. However, the contact angles formed and deformation of the liquid marble resemble that of a sessile liquid droplet on a thin, elastic solid. For small liquid marbles, the contact angle varies with volume due to the deformability of the interface.

Combined effects of underlying substrate and evaporative cooling on the evaporation of sessile liquid droplets

The evaporation of pinned, sessile droplets resting on finite thickness substrates was investigated numerically by extending the combined field approach to include the thermal properties of the substrate. By this approach, the combined effects of the underlying substrate and the evaporative cooling were characterized. The results show that the influence of the substrate on the droplet evaporation depends largely on the strength of the evaporative cooling. When the evaporative cooling is weak, the influence of substrate is also weak. As the strength of evaporative cooling increases, the influence of the substrate becomes more and more pronounced. Further analyses indicated that it is the cooling at the droplet surface and the temperature dependence of the saturation vapor concentration that relate the droplet evaporation to the underlying substrate. This indicates that the evaporative cooling number, Ec, can be used to identify the influence of the substrate on the droplet evaporation. The theoretical predictions by the present model are compared and found to be in good agreement with the experimental measurements. The present work may contribute to the body of knowledge concerning droplet evaporation and may have applications in a wide range of industrial and scientific processes.

Evaporation of a sessile liquid droplet from the shear or flexural surfaces of a quartz tuning fork

A piezoelectric quartz tuning fork (QTF) has been used to investigate the evaporation of a sessile water droplet with nanogram sensitivity. A water droplet is placed on one facet of a QTF tine and the changes in the resonance frequency and dissipation factor, which are related to the changes in mass and viscous damping, respectively, are measured in situ during the evaporation. Depending on the facet of the QTF tine on which the water droplet is placed, the changes in the frequency and dissipation factor arise in different vibration modes: the flexural or shear modes. The shear mode measurement is affected by the penetration depth, so changes in the frequency and dissipation factor are observed only when the water droplet is sufficiently thin, whereas the changes in the flexural mode measurements are observed during the entire evaporation process. When a droplet of polystyrene nanoparticle suspension is evaporated from the flexural surface, the concentration of the nanoparticle suspension can be determined from the difference in mass between the initial droplet and the dry nanoparticles. In contrast, changes in the physical properties of the suspension are obtained in situ from the evaporation from the shear surface. These results demonstrate that QTFs are useful tools for the investigation of the evaporation of suspensions from solid surfaces.

Vibrational Modes of Elongated Sessile Liquid Droplets

Vibrations of small (microliter) sessile liquid droplets were studied using a simple optical deflection technique. The droplets were made to elongate in one direction by taking advantage of the anisotropic wetting of the liquids on structured diffraction grating surfaces. They were vibrated by applying a puff of nitrogen gas. Motion of the droplets was monitored by scattering laser light from their surfaces. The scattered light was collected using a photodiode, and the resulting time-dependent intensity signals were Fourier-transformed to obtain the vibrational response of the drops. The vibrational spectra of elongated sessile drops were observed to contain two closely spaced peaks. A simple model that considers the frequency of capillary wave fluctuations on the surfaces of the drops was used to show that the vibrational frequencies of these peaks correspond to standing wave states that exist along the major and minor profile lengths of the droplets.

Numerical simulation of natural convection in a sessile liquid droplet

Heat transfer in a sessile liquid droplet was studied with numerical methods. A computer code was developed for solving the problem of convection in an axisymmetric hemispherical droplet and in a spherical layer as well. The problem of establishing an equilibrium state in a droplet was solved using several variables: temperature, stream function, and vorticity. Simulation was performed for droplets of water, ethyl alcohol, and model liquids. Variable parameters: intensity of heat transfer from droplet surface, Rayleigh and Marangoni dimensionless criteria, and the characteristic temperature difference. It was revealed that the curve of convective flow intensity versus heat transfer intensity at droplet surface has a maximum. A dual-vortex structure was obtained in a stationary hemispherical profile of liquid droplet for the case of close values for thermocapillary and thermogravitational forces. Either thermocapillary or thermogravitational vortex might be dominating phenomena in the flow structure.

Resonant properties of sessile droplets; contact angle dependence of the resonant frequency and width in glycerol/water mixtures

A simple optical deflection technique was used to monitor the vibrations of small (microlitre) sessile droplets of glycerol/water mixtures when a puff of air was used to apply an impulse to the drops. A photodiode was used to detect time dependent variations in the intensity of laser light that was reflected from the droplets. The intensity variations obtained from droplets with masses in the range 0.0005–0.03 g were Fourier transformed to obtain information about the resonant properties (frequency and width of the resonance). These experiments were performed on a range of different substrates where the three phase contact angle formed by the droplets varied between 38 ± 2° and 160 ± 4°. This was repeated for droplets with glycerol compositions ranging from 10% to 75%. The measured resonant frequency values were found to be in good agreement with a recently developed 1-D theory of vibrations in sessile droplets which considers standing wave states around the meridonal profile length of the droplet. The widths of the resonances were also compared with modified theories which predict the influence of substrate effects, surface contamination effects and bulk viscous effects on the damping of capillary waves at the free surface of the droplets. These experiments indicate that the dominant source of damping in sessile liquid droplet is due to bulk viscous effects but that for small contact angles damping due to the droplet/substrate interaction becomes more important.

Droplets evaporation: Problems and solutions

The evaporation of single droplets and sprays into gaseous atmosphere and the evaporation of sessile liquid droplets on solid substrates are here considered. We argue that if thermodynamics is augmented with Derjaguin’s (disjoining/conjoining) pressure to handle phenomena in a vicinity of the three-phase contact line, problems like the singularity of the evaporation flux and of the viscous stress at the three-phase contact line of a sessile droplet are ruled out.