Influence of Surface Wettability on Transport Mechanisms Governing Water Droplet Evaporation

Prediction and manipulation of the evaporation of small droplets is a fundamental problem with importance in a variety of microfluidic, microfabrication, and biomedical applications. A vapor-diffusion-based model has been widely employed to predict the interfacial evaporation rate; however, its scope of applicability is limited due to incorporation of a number of simplifying assumptions of the physical behavior. Two key transport mechanisms besides vapor diffusionevaporative cooling and natural convection in the surrounding gasare investigated here as a function of the substrate wettability using an augmented droplet evaporation model. Three regimes are distinguished by the instantaneous contact angle (CA). In Regime I (CA ≲ 60°), the flat droplet shape results in a small thermal resistance between the liquid–vapor interface and substrate, which mitigates the effect of evaporative cooling; upward gas-phase natural convection enhances evaporation. In Regime II (60 ≲ CA ≲ 90°), evaporative cooling at the interface suppresses evaporation with increasing contact angle and counterbalances the gas-phase convection enhancement. Because effects of the evaporative cooling and gas-phase convection mechanisms largely neutralize each other, the vapor-diffusion-based model can predict the overall evaporation rates in this regime. In Regime III (CA ≳ 90°), evaporative cooling suppresses the evaporation rate significantly and reverses entirely the direction of natural convection induced by vapor concentration gradients in the gas phase. Delineation of these counteracting mechanisms reconciles previous debate (founded on single-surface experiments or models that consider only a subset of the governing transport mechanisms) regarding the applicability of the classic vapor-diffusion model. The vapor diffusion-based model cannot predict the local evaporation flux along the interface for high contact angle (CA ≥ 90°) when evaporative cooling is strong and the temperature gradient along the interface determines the peak local evaporation flux

Continuous Oil–Water Separation Using Polydimethylsiloxane-Functionalized Melamine Sponge

The development of absorbent materials with high selectivity for oils and organic solvents is of great ecological importance for removing pollutants from contaminated water sources. We have developed a facile solution-immersion process for creating poly­dimethyl­siloxane (PDMS)-functionalized sponges for oil–water separation. Sponge materials with densities ranging from 8 to 26 mg/cm³ were investigated as candidate skeletons. After functionalization, the lowest-density melamine sponge exhibits superior superhydrophobic and superoleophilic properties, absorption capacity, oil–water selectivity, and absorption recyclability. Via suction through such a functionalized sponge, we have experimentally demonstrated that various kinds of oils can be continuously separated from immiscible liquid mixtures without any water uptake. The widely available raw materials (melamine sponge and PDMS solution) and simple synthesis steps yield a cost-effective and scalable process for fabrication of absorbent materials that can be readily adopted for the cleanup of oil spills and industrial chemical leakage of low-surface-tension solvents that are immiscible with water

Re-entrant Cavities Enhance Resilience to the Cassie-to-Wenzel State Transition on Superhydrophobic Surfaces during Electrowetting

Electrowetting-based droplet actuation has applications in digital microfluidics. Mobility of droplets on surfaces can be enhanced using structured superhydrophobic surfaces that offer inherently low adhesion to droplets in the Cassie state. However, these surfaces must be designed to prevent transition to the Wenzel state (in which droplets are immobile) at high electrowetting actuation voltages. The electrowetting behavior of cylindrical microposts and mushroom-shaped re-entrant microstructures, both of which afford excellent superhydrophobicity, is investigated and compared. A surface-energy-based model is employed to estimate the energy barrier for the Cassie-to-Wenzel transition and thus the electrowetting voltage required to initiate this transition. The mushroom structures are predicted to be more resilient to transition (i.e., transition occurs at a voltage that is up to 1.5 times higher) than microposts. Both types of microstructured surfaces are fabricated and electrowetting experiments performed to demonstrate that mushroom structures indeed inhibit the Cassie-to-Wenzel transition at voltages that induce such transition on the cylindrical microposts

Evaporation-Driven Micromixing in Sessile Droplets for Miniaturized Absorbance-Based Colorimetry

We demonstrate the use of an evaporating, sessile droplet on a nonwetting substrate as a miniature micromixing device to conduct sample–dye reactions for absorbance-based colorimetry. The nonwetting substrate supports buoyancy-induced mixing inside the droplet for rapid completion of the measurement. The Bradford assay is used as a proof of concept, where a protein-containing sample is reacted with a reagent dye to measure the protein concentration. Viability of absorbance measurement through the droplet is first established using droplets in which the reactants are mixed prior to their deposition onto the substrate. In a second set of experiments involving in situ mixing, the reagent is directly added to a sessile droplet of the protein-containing sample, allowing the reactants to mix while the absorbance is being measured. Interplay between buoyancy-induced mixing, protein–reagent reaction, and protein adsorption onto the substrate leads to a complex temporal absorbance measurement signal. Videos corresponding to the signal data show that each of these mechanisms dominates during different phases of droplet evolution, causing a signal pattern containing peaks and valleys having a strong monotonic trend with the protein concentration. Overall, the second absorbance peak at which the reaction nears completion is the most sensitive to sample concentration. Heating of the substrate is demonstrated to dramatically speed up the mixing process. These protein concentration measurements, obtained with a simpler system and low reactant volumes, demonstrate that this droplet micromixing concept is a viable alternative to microtiter plates for colorimetric applications

Evaporation-Driven Micromixing in Sessile Droplets for Miniaturized Absorbance-Based Colorimetry

We demonstrate the use of an evaporating, sessile droplet on a nonwetting substrate as a miniature micromixing device to conduct sample–dye reactions for absorbance-based colorimetry. The nonwetting substrate supports buoyancy-induced mixing inside the droplet for rapid completion of the measurement. The Bradford assay is used as a proof of concept, where a protein-containing sample is reacted with a reagent dye to measure the protein concentration. Viability of absorbance measurement through the droplet is first established using droplets in which the reactants are mixed prior to their deposition onto the substrate. In a second set of experiments involving in situ mixing, the reagent is directly added to a sessile droplet of the protein-containing sample, allowing the reactants to mix while the absorbance is being measured. Interplay between buoyancy-induced mixing, protein–reagent reaction, and protein adsorption onto the substrate leads to a complex temporal absorbance measurement signal. Videos corresponding to the signal data show that each of these mechanisms dominates during different phases of droplet evolution, causing a signal pattern containing peaks and valleys having a strong monotonic trend with the protein concentration. Overall, the second absorbance peak at which the reaction nears completion is the most sensitive to sample concentration. Heating of the substrate is demonstrated to dramatically speed up the mixing process. These protein concentration measurements, obtained with a simpler system and low reactant volumes, demonstrate that this droplet micromixing concept is a viable alternative to microtiter plates for colorimetric applications

Evaporation-Driven Micromixing in Sessile Droplets for Miniaturized Absorbance-Based Colorimetry

We demonstrate the use of an evaporating, sessile droplet on a nonwetting substrate as a miniature micromixing device to conduct sample–dye reactions for absorbance-based colorimetry. The nonwetting substrate supports buoyancy-induced mixing inside the droplet for rapid completion of the measurement. The Bradford assay is used as a proof of concept, where a protein-containing sample is reacted with a reagent dye to measure the protein concentration. Viability of absorbance measurement through the droplet is first established using droplets in which the reactants are mixed prior to their deposition onto the substrate. In a second set of experiments involving in situ mixing, the reagent is directly added to a sessile droplet of the protein-containing sample, allowing the reactants to mix while the absorbance is being measured. Interplay between buoyancy-induced mixing, protein–reagent reaction, and protein adsorption onto the substrate leads to a complex temporal absorbance measurement signal. Videos corresponding to the signal data show that each of these mechanisms dominates during different phases of droplet evolution, causing a signal pattern containing peaks and valleys having a strong monotonic trend with the protein concentration. Overall, the second absorbance peak at which the reaction nears completion is the most sensitive to sample concentration. Heating of the substrate is demonstrated to dramatically speed up the mixing process. These protein concentration measurements, obtained with a simpler system and low reactant volumes, demonstrate that this droplet micromixing concept is a viable alternative to microtiter plates for colorimetric applications

Limitations of the Axially Dispersed Plug-Flow Model in Predicting Breakthrough in Confined Geometries

This paper examines the ability of the axially dispersed plug-flow model to accurately predict breakthrough in adsorbent beds confined by rigid walls. The axially dispersed plug-flow model is used to independently extract mass transfer and axial-dispersion coefficients from breakthrough experiments via centerline and mixed-exit concentration measurements, respectively. Four experimental cases are considered: breakthrough of carbon dioxide (CO2) and water (H2O), in two cylindrical beds of zeolite 13X (NaX) each. The extracted axial-dispersion coefficients are compared to predictions from existing correlations which are widely used to predict mechanical dispersion in packed beds. We show that such correlations grossly underpredict the apparent axial dispersion observed in the bed because they do not account for the effects of wall channeling. The relative magnitudes of wall-channeling effects are shown to be a function of the adsorption/adsorbate pair and geometric confinement (i.e., bed size). We show that while the axially dispersed plug-flow model fails to capture all the physics of breakthrough when non-plug-flow conditions prevail in the bed, it can still be used to accurately extract mass transfer coefficients using intrabed concentration measurements

Marangoni Convection in Evaporating Organic Liquid Droplets on a Nonwetting Substrate

We quantitatively characterize the flow field inside organic liquid droplets evaporating on a nonwetting substrate. A mushroom-structured surface yields the desired nonwetting behavior with methanol droplets, while use of a cooled substrate (5–15 °C) slows the rate of evaporation to allow quasi-static particle image velocimetry. Visualization reveals a toroidal vortex within the droplet that is characteristic of surface tension-driven flow; we demonstrate by means of a scaling analysis that this recirculating flow is Marangoni convection. The velocities in the droplet are on the order of 10–45 mm/s. Thus, unlike in the case of evaporation on wetting substrates where Marangoni convection can be ignored for the purpose of estimating the evaporation rate, advection due to the surface tension-driven flow plays a dominant role in the heat transfer within an evaporating droplet on a nonwetting substrate because of the large height-to-radius aspect ratio of the droplet. We formulate a reduced-order model that includes advective transport within the droplet for prediction of organic liquid droplet evaporation on a nonwetting substrate and confirm that the predicted temperature differential across the height of the droplet matches experiments

Marangoni Convection in Evaporating Organic Liquid Droplets on a Nonwetting Substrate

We quantitatively characterize the flow field inside organic liquid droplets evaporating on a nonwetting substrate. A mushroom-structured surface yields the desired nonwetting behavior with methanol droplets, while use of a cooled substrate (5–15 °C) slows the rate of evaporation to allow quasi-static particle image velocimetry. Visualization reveals a toroidal vortex within the droplet that is characteristic of surface tension-driven flow; we demonstrate by means of a scaling analysis that this recirculating flow is Marangoni convection. The velocities in the droplet are on the order of 10–45 mm/s. Thus, unlike in the case of evaporation on wetting substrates where Marangoni convection can be ignored for the purpose of estimating the evaporation rate, advection due to the surface tension-driven flow plays a dominant role in the heat transfer within an evaporating droplet on a nonwetting substrate because of the large height-to-radius aspect ratio of the droplet. We formulate a reduced-order model that includes advective transport within the droplet for prediction of organic liquid droplet evaporation on a nonwetting substrate and confirm that the predicted temperature differential across the height of the droplet matches experiments

Measurement and Prediction of the Heat of Adsorption and Equilibrium Concentration of CO₂ on Zeolite 13X

Adsorption isotherms are reported for pure carbon dioxide on zeolite 13X (also called zeolite NaX) pellets over a temperature range of 0 to 200 °C and a pressure range of 0.001 to 100 kPa. These pure-component equilibria are fit with Langmuir, Toth, two-site Langmuir, and three-site Langmuir models, both with and without temperature dependence being included in the saturation capacity. The agreement between fitted and measured isotherms is shown to increase with increasing number of available fitting parameters in the model, with the constant-saturation, two-site Langmuir isotherm providing the best balance between agreement with the measurements and model complexity. The isosteric heats of adsorption are measured across a temperature range from 10 to 200 °C using differential scanning calorimetry. The measured heats of adsorption decrease with increasing CO₂ loading but show little variation with temperature. The measurements are shown to agree with predicted heats of adsorption derived from the fitted Langmuir and Toth isotherms (via the Clausius–Clapeyron equation); the heats of adsorption predicted using the more complex multisite Langmuir models suffer from nonphysical artifacts