Transient volume of evaporating sessile droplets: 2/3, 1/1, or another power law?

Field driven evaporation kinetics of a sessile ferrofluid droplet on a soft substrate

We experimentally investigate the evaporation kinetics of a sessile ferrofluid droplet placed on a soft substrate in the presence of a time-dependent magnetic field. We use both bright field visualization techniques and μ-PIV analysis to gain qualitative as well as quantitative insights into the internal hydrodynamics of the droplet. The results show that the droplet evaporation rate is augmented significantly in the presence of a time-dependent magnetic field, attributed primarily to the enhanced internal flow advection. We show that the motion of the magnetic nanoparticles dictates the overall life-time of the evaporating ferrofluid droplet. At lower frequencies of the magnetic field, the magnetic nanoparticles move towards the magnet and agglomerate into a chain-like cluster formation, oriented according to the magnetic field lines. On the other hand, at higher frequencies, the magnetic nanoparticles do not have sufficient time to travel the whole characteristic length (droplet diameter). Consequently, we observe the presence of a critical frequency at which the perturbation time scale balances the advective time scale of the flow inside the droplet. We show that on account for this balance between the time scales, the droplet experiences a minimum life-time. Finally, we demonstrate that the evaporation kinetics of a ferrofluid droplet in the presence of a time-dependent magnetic field can be described through three distinguishable stages viz., the decreasing contact angle and variable radius zone, the decreasing contact angle and decreasing radius zone and the late mixed zone. The inferences drawn from this study could have far-reaching implications in fields ranging from biomedical engineering to surface patterning.

Investigation of Wettability, Drying and Water Condensation on Polyimide (Kapton) Films Treated by Atmospheric Pressure Air Dielectric Barrier Discharge

In this study, we report on the investigation of influence of air atmospheric pressure dielectric barrier discharge on polyimide (Kapton) films. It is shown that plasma treatment causes a significant increase of Kapton wettability that is connected with alterations of its chemical composition (oxidation) induced by dielectric barrier discharge. Observed variations in the wettability of Kapton were also found to be accompanied by changes in the dynamics of water droplets drying on plasma-treated Kapton, namely by the reduction of the constant contact angle phase of the droplet drying. This effect may be ascribed to the higher surface heterogeneity of plasma-treated Kapton that causes pinning of the edges of drying droplet on the Kapton surface. Finally, the differences in wettability induced by the plasma treatment led to a different way, how the water condensates on the Kapton surface: while the condensing water forms large amount of small droplets on untreated Kapton, much bigger water structures were found on the Kapton exposed to atmospheric plasma.

Theoretical Analysis of a Sessile Evaporating Droplet on a Curved Substrate with an Interfacial Cooling Effect

Sessile droplet evaporation is widely encountered in nature, and it has numerous applications in industrial and scientific communities; therefore, the accurate prediction of droplet evaporation has great significance in practical applications. In this paper, for the first time, a comprehensive theoretical model is built up for diffusion-controlled heat and mass transfer for sessile droplet evaporation on a curved substrate in toroidal coordinates. The evaporative mass transfer is coupled with the heat transfer across the gas-liquid droplet interface, as well as the heat transfer across the solid-liquid interface of the curved substrate. The effects of interfacial cooling and thermal conductivity of the droplet and substrate as well as their initial shapes on the droplet evaporation are provided in details. It is found that the evaporative flux usually increases sharply near the droplet edge due to the short distance for heat conduction from the substrate to the droplet; however, it can be reversed from sharp increasing to decreasing at a low thermal conductivity ratio k_R < 0.3 of the substrate over droplet or large initial droplet contact angle θ > 30°. The interfacial evaporative cooling effect can always suppress the droplet evaporation. The lifetime of evaporative droplet can be prolonged with the decreasing thermal conductivity ratio, increasing evaporative cooling number, and increasing initial droplet contact angle or tangential angle of a curved substrate. These findings may be of great significance in the applications of droplet evaporation on the curved substrate.

Analytical Model for Diffusive Evaporation of Sessile Droplets Coupled with Interfacial Cooling Effect

Current analytical models for sessile droplet evaporation do not consider the nonuniform temperature field within the droplet and can overpredict the evaporation by 20%. This deviation can be attributed to a significant temperature drop due to the release of the latent heat of evaporation along the air-liquid interface. We report, for the first time, an analytical solution of the sessile droplet evaporation coupled with this interfacial cooling effect. The two-way coupling model of the quasi-steady thermal diffusion within the droplet and the quasi-steady diffusion-controlled droplet evaporation is conveniently solved in the toroidal coordinate system by applying the method of separation of variables. Our new analytical model for the coupled vapor concentration and temperature fields is in the closed form and is applicable for a full range of spherical-cap shape droplets of different contact angles and types of fluids. Our analytical results are uniquely quantified by a dimensionless evaporative cooling number E_o whose magnitude is determined only by the thermophysical properties of the liquid and the atmosphere. Accordingly, the larger the magnitude of E_o, the more significant the effect of the evaporative cooling, which results in stronger suppression on the evaporation rate. The classical isothermal model is recovered if the temperature gradient along the air-liquid interface is negligible ( E_o = 0). For substrates with very high thermal conductivities (isothermal substrates), our analytical model predicts a reversal of temperature gradient along the droplet-free surface at a contact angle of 119°. Our findings pose interesting challenges but also guidance for experimental investigations.

Volume evolution of small sessile droplets evaporating in stick-slip mode

This work is aimed at developing a simple and efficient predictive model and revealing the volume evolution behavior of small sessile droplets evaporating in stick-slip (SS) mode, covering a wide range of initial (θ_{0}) and receding (θ_{rec}) contact angles (0^{∘}<θ_{rec}≤θ_{0}<180^{∘}). For this purpose, simple closed-form expressions for the evolutions of the contact angle and contact radius of droplets evaporating in SS mode are first developed, and are then validated with the experimental data in the literature. With the proposed expressions, the volume evolutions of evaporating droplets with different θ_{0} and θ_{rec} are predicted and analyzed. The results show that on a hydrophilic surface (θ_{0}≤90^{∘}), the volume evolution of droplets in SS mode always occurs in a way between the constant contact radius (CCR) and constant contact angle (CCA) modes (i.e., two extreme modes); however, on a hydrophobic surface (θ_{0}>90^{∘}), as θ_{rec} increases from 0 to θ_{0}, the volume evolution of droplets in SS mode first departs from the CCR mode, then approaches the SS mode with θ_{rec}=90^{∘}, and finally returns to the CCA mode. More interestingly, the initially identical droplets evaporating on hydrophobic surfaces with different receding contact angles (θ_{rec}=90^{∘}±Δθ) can even have approximately the same volume evolution behavior. It is also found that the widely accepted 2/3 law is applicable only for volume evolution of droplets in SS mode with large initial contact angle or small contact angle hysteresis, with the predicted deviation less than 1.5% for θ_{0}≥150^{∘} or θ_{0}≥50^{∘} when θ_{0}-θ_{rec}≤15^{∘}. Finally, a physical interpretation for the volume evolution behaviors of droplets in SS mode is proposed.

Stick-Jump (SJ) Evaporation of Strongly Pinned Nanoliter Volume Sessile Water Droplets on Quick Drying, Micropatterned Surfaces

We present an experimental study of stick-jump (SJ) evaporation of strongly pinned nanoliter volume sessile water droplets drying on micropatterned surfaces. The evaporation is studied on surfaces composed of photolithographically micropatterned negative photoresist (SU-8). The micropatterning of the SU-8 enables circular, smooth, trough-like features to be formed which causes a very strong pinning of the three phase (liquid-vapor-solid) contact line of an evaporating droplet. This is ideal for studying SJ evaporation as it contains sequential constant contact radius (CCR) evaporation phases during droplet evaporation. The evaporation was studied in nonconfined conditions, and forced convection was not used. Micropatterned concentric circles were defined having an initial radius of 1000 μm decreasing by a spacing ranging from 500 to 50 μm. The droplet evaporates, successively pinning and depinning from circle to circle. For each pinning radius, the droplet contact angle and volume are observed to decrease quasi-linearly with time. The experimental average evaporation rates were found to decrease with decreasing pining radii. In contrast, the experimental average evaporation flux is found to increase with decreasing droplet radii. The data also demonstrate the influence of the initial contact angle on evaporation rate and flux. The data indicate that the total evaporation time of a droplet depends on the specific micropattern spacing and that the total evaporation time on micropatterned surfaces is always less than on flat, homogeneous surfaces. Although the surface patterning is observed to have little effect on the average droplet flux-indicating that the underlying evaporation physics is not significantly changed by the patterning-the total evaporation time is considerably modified by patterning, up to a factor or almost 2 compared to evaporation on a flat, homogeneous surface. The closely spaced concentric circle pinning maintains a large droplet radius and small contact angle from jump to jump; the result is a large evaporation rate leading to faster evaporation.

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 droplets on strongly hydrophobic substrates

The manner in which the extreme modes of droplet evaporation (namely, the constant contact radius and the constant contact angle modes) become indistinguishable on strongly hydrophobic substrates is described. Simple asymptotic expressions are obtained which provide good approximations to the evolutions of the contact radius, the contact angle, and the volume of droplets evaporating in the extreme modes for a wide range of hydrophobic substrates. As a consequence, on strongly hydrophobic substrates it is appropriate to use the so-called "2/3 power law" to extrapolate the lifetimes of droplets evaporating in the constant contact radius mode as well as in the constant contact angle mode.