Ion-Specific Bubble Coalescence Dynamics in Electrolyte Solutions.

Bubble coalescence time scale is important in applications such as froth flotation, food and pharmaceutical industries, and two-phase thermal management. The time scale of coalescence is sensitive to the dissolved ions. In this study, we investigate the evolution of a thin electrolyte film between a bubble and a hydrophilic substrate during coalescence. We present a thin-film equation-based numerical model that accounts for the dependence of the surface tension gradient and electric double layer (EDL) on the concentration of ions at the air-liquid interface. The influence of Marangoni stresses and the EDL on the hydrodynamics of drainage determines the coalescence time scale. We show that the electrolytes, such as NaCl, Na2SO4, and NaI retard coalescence, in contrast to HCl and HNO3 that have little effect on the coalescence time scale. We also show that the drainage of the electrolyte films with higher concentrations is retarded due to increased Marangoni stresses at the air-water interface. The slow drainage triggers an early formation of the dimple in the thin film, thus trapping more fluid within, which further decreases the drainage rate. For a hydrophilic substrate, EDL along with van der Waals for a given concentration governs the final dynamics of thin films, eventually resulting in a stable thin layer of the electrolyte between the bubble and the substrate. The stabilizing thickness reduces by an order of magnitude as the NaCl concentration increases from 0.01 to 10 mM. For Na2SO4 solution, the film is stabilized at a smaller thickness due to higher valency cations resulting in higher screening of the EDL repulsion.

Generality of Evaporative Crystal Liftoff on Heated Hydrophobic Substrates.

Scaling or mineral fouling occurs due to the presence of dissolved minerals in water. Scaling is problematic in numerous industrial and household plumbing applications where water is used. The current methods of scale removal often utilize harsh chemicals that are not environmentally friendly. The evaporation of a saline droplet provides a platform to study the role of the substrate in the dynamics of crystallization during scaling. In the present work, we show out-of-plane growth of crystal deposits during the evaporation of saline droplets of aqueous potassium chloride on a heated smooth and microtextured hydrophobic substrate. These out-of-plane deposits, termed as "crystal legs", are in minimal contact with the substrate and can be easily removed from the substrate. The out-of-plane evaporative crystallization of saline droplets of different initial volumes and concentrations is observed irrespective of the chemistry of the hydrophobic coating and the crystal habits investigated. We attribute this general behavior of crystal legs to the growth and stacking of smaller crystals (size ∼10 µm) between the primary crystals toward the end of evaporation. We show that the rate at which the crystal legs grow increases with an increase in the substrate temperature. A mass conservation model is applied to predict the leg growth rate, which agrees well with the experiments.

Patterns during Evaporative Crystallization of a Saline Droplet.

In the present work, we investigate the influence of substrate wettability and crystal morphology on the evaporative crystallization of saline droplets. On a superhydrophilic substrate, the evaporative crystals formed during the drying of a saline droplet of aqueous potassium nitrate are observed to be long and needle-shaped, oriented along the substrate. The crystal deposits form a flower-shaped pattern when the initial contact angle of the droplet increases to ∼72°. The orientation of the crystals along the triple contact line of the droplet controls the self-amplifying creeping growth of the salt crystals that eventually determines the overall evaporative patterns. The crystals change from being needle-shaped to globular salt deposits as the volume of liquid available for crystallization reduces. We demonstrate that the arrangement of the crystal with respect to the substrate and the droplet-air interface governs the rate of evaporation, growth, and morphology of the crystals.

Evaporation-Based Low-Cost Method for the Detection of Adulterant in Milk.

Adulteration of milk poses a severe health hazard, and it is crucial to develop adulterant-detection techniques that are scalable and easy to use. Water and urea are two of the most common adulterants in commercial milk. Detection of these adulterants is both challenging and costly in urban and rural areas. Here we report on an evaporation-based low-cost technique for the detection of added water and urea in milk. The evaporative deposition is shown to be affected by the presence of adulterants in milk. We observe a specific pattern formation of nonvolatile milk solids deposited at the end of the evaporation of a droplet of unadulterated milk. These patterns alter with the addition of water and urea. The evaporative deposits are dependent on the concentrations of water and urea added. The sensitivity of detection of urea in milk improves with the dilution of milk with water. We show that our method can be used to detect a urea concentration as low as 0.4% in milk. Based on the detection level of urea, we present a regime map that shows the concentration of urea that can be detected at different extents of dilution of milk.

Bubble-Induced Rupture of Droplets on Hydrophobic and Lubricant-Impregnated Surfaces.

Bursting of bubbles is ubiquitous with numerous applications ranging from spraying of pesticides, drug delivery, and inkjet printing to forming emulsions. Understanding the parameters that influence the dynamics of bubble rupture is crucial to design systems with improved performance. Here, we experimentally investigate the behavior of air-bubble-induced rupture of a sessile droplet placed on hydrophobic and lubricant-impregnated surfaces (LIS). We demonstrate that the bubble dynamics inside a sessile droplet and subsequent rupture of the thinning film is dependent on the nature of the underlying substrate and the thermodynamic state of the droplet on the substrate. The growth of the bubble is shown to be dependent on the contact angle hysteresis of water and air on the substrate and the presence of a cloaking oil film around the water droplet. On a plain and textured surface with a high contact angle hysteresis, bubble-induced rupture initiates at the apex of the droplet. In the case of LIS that offers negligible pinning forces, the bubble-induced rupture of liquid shell initiates near the triple contact line. The dynamics of rupture of droplets placed on LIS is shown to be dependent on the viscosity of the impregnating and cloaking lubricant.

Evaporative Crystallization of Spirals.

Spiral motifs are pervasive in nature, art, and technology due to their functional property of providing compact length. Nature is particularly adept at spiral patterning, and yet, the spirals observed in seashells, hurricanes, rams' horns, flower petals, etc. all evolve via disparate physical mechanisms. Here, we present a mechanism for the self-guided formation of spirals from evaporating saline drops via a coupling of crystallization and contact line dynamics. These patterns are in contrast to commonly observed patterns from evaporation of colloidal drops, which are discrete (rings, concentric rings) or continuous (clumps, uniform deposits) depending on the particle shape, contact line dynamics, and evaporation rate. Unlike the typical process of drop evaporation where the contact line moves radially inward, here, a thin film pinned by a ring of crystals ruptures radially outward. This motion is accompanied by a nonuniform pinning of the contact line due to crystallization, which generates a continuous propagation of pinning and depinning events to form a spiral. By comparing the relevant timescales of evaporation and diffusion, we show that a single dimensionless number can predict the occurrence of these patterns. These insights on self-guided crystallization of spirals could be used to create compact length templates.

Photothermal trap utilizing solar illumination for ice mitigation.

Ice buildup is an operational and safety hazard in wind turbines, power lines, and airplanes. Traditional deicing methods, including mechanical and chemical means, are energy-intensive or environmentally unfriendly. Superhydrophobic anti-icing surfaces, while promising, can become ineffective due to frost formation within textures. We report on a "photothermal trap"-a laminate applied to a base substrate-that can efficiently deice by converting solar illumination to heat at the ice-substrate interface. It relies on the complementing properties of three layers: a selective absorber for solar radiation, a thermal spreader for lateral dispersal of heat, and insulation to minimize transverse heat loss. Upon illumination, thermal confinement at the heat spreader leads to rapid increase of the surface temperature, thereby forming a thin lubricating melt layer that facilitates ice removal. Lateral heat spreading overcomes the unavoidable shadowing of certain areas from direct illumination. We provide a design map that captures the key physics guiding illumination-induced ice removal. We demonstrate the deicing performance of the photothermal trap at very low temperatures, and under frost and snow coverage, via laboratory-scale and outdoor experiments.

Evaporative Crystallization in Drops on Superhydrophobic and Liquid-Impregnated Surfaces.

Mineral-fouling induced corrosion and deterioration of marine vessels, aircraft, and coastal structures is due in part from structural intrusion of crystals grown from ocean-generated saline drops. As such, much work has explored surface treatments that induce hydrophobicity or introduce barriers for antifouling and corrosion prevention; however, the efficacy of these strategies will be altered by the underlying substrate texture. Here, we study the behavior of evaporating saline drops on superhydrophobic and liquid-impregnated surfaces as a function of surface texture. On superhydrophobic surfaces, four disparate regimes (which are not observed for particle-laden drops) emerge as a function of the substrate solid fraction: Cassie-pinning, Cassie-gliding, Cassie-Wenzel transition, and Wenzel. These regimes control the morphology of the resultant crystal deposits. In contrast to the superhydrophobic surfaces, spreading liquid-impregnated surfaces demonstrate minimal influence of solid fraction on evaporative crystallization. The area, area localization, timescale of evaporation, and deposit morphology are all normalized by the presence of the lubricating layer, thus introducing an efficient method of eliminating crystal "coffee rings" as well as reducing the potential for fouling and corrosion.

Crystallization-Induced Fouling during Boiling: Formation Mechanisms to Mitigation Approaches.

Boiling is significantly altered by the presence of dissolved salts. In particular, salts whose solubility decreases with temperature have the tendency to crystallize and adhere to the heat transfer surface and adversely affect the thermal performance. Scaling due to the precipitation of such salts poses serious operational and safety challenges in several practical applications, including heat exchangers, pipelines, and desalination. Here, we study the effect of dissolved salts on the dynamics of pool boiling and its impact on the heat transfer coefficient and critical heat flux (CHF). We find that even undersaturated conditions can lead to crystallization and scale buildup on the boiling surface and dramatically lower heat transfer performance. For example, the CHF for a salt solution that is 75% of the saturation concentration is found to be at least 2 times lower than that for deionized water. Using simultaneous high-speed optical and infrared imaging, we determine the interdependence between crystallization-induced scale formation and bubble evolution dynamics, including bubble nucleation, growth, and departure. We find that salt crystallizes in a "coffee-ring" pattern due to evaporation at the contact line of the bubble. On the basis of the role of the microlayer and triple contact line on scale formation, we propose manipulating surface wettability as a means to avoid scale formation and the associated decrease in the heat transfer coefficient. Surfaces with hybrid wettability are demonstrated as a means to mitigate the reduction in the heat transfer coefficient and CHF in the presence of dissolved salts.

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.

Droplet evaporation on heated hydrophobic and superhydrophobic surfaces.

The evaporation characteristics of sessile water droplets on smooth hydrophobic and structured superhydrophobic heated surfaces are experimentally investigated. Droplets placed on the hierarchical superhydrophobic surface subtend a very high contact angle (∼160°) and demonstrate low roll-off angle (∼1°), while the hydrophobic substrate supports corresponding values of 120° and ∼10°. The substrates are heated to different constant temperatures in the range of 40-60 °C, which causes the droplet to evaporate much faster than in the case of natural evaporation without heating. The geometric parameters of the droplet, such as contact angle, contact radius, and volume evolution over time, are experimentally tracked. The droplets are observed to evaporate primarily in a constant-contact-angle mode where the contact line slides along the surface. The measurements are compared with predictions from a model based on diffusion of vapor into the ambient that assumes isothermal conditions. This vapor-diffusion-only model captures the qualitative evaporation characteristics on both test substrates, but reasonable quantitative agreement is achieved only for the hydrophobic surface. The superhydrophobic surface demonstrates significant deviation between the measured evaporation rate and that obtained using the vapor-diffusion-only model, with the difference being amplified as the substrate temperature is increased. A simple model considering thermal diffusion through the droplet is used to highlight the important role of evaporative cooling at the droplet interface in determining the droplet evaporation characteristics on superhydrophobic surfaces.

Buoyancy-induced on-the-spot mixing in droplets evaporating on nonwetting surfaces.

We investigate hitherto-unexplored flow characteristics inside a sessile droplet evaporating on heated hydrophobic and superhydrophobic surfaces and propose the use of evaporation-induced flow as a means to promote efficient "on-the-spot" mixing in microliter-sized droplets. Evaporative cooling at the droplet interface establishes a temperature gradient that induces buoyancy-driven convection inside the droplet. An asymmetric single-roll flow pattern is observed on the superhydrophobic substrate, in stark contrast with the axisymmetric toroidal flow pattern that develops on the hydrophobic substrate. The difference in flow patterns is attributed to the larger height-to-diameter aspect ratio of the droplet (of the same volume) on the superhydrophobic substrate, which dictates a single asymmetric vortex as the stable buoyancy-induced convection mode. A scaling analysis relates the observed velocities inside the droplet to the Rayleigh number. On account of the difference in flow patterns, Rayleigh numbers, and the reduced solid-liquid contact area, the flow velocity is an order of magnitude higher in droplets evaporating on a superhydrophobic substrate as compared to hydrophobic substrates. Flow velocities in all cases are shown to increase with substrate temperature and droplet size: The characteristic time required for mixing of a dye in an evaporating sessile droplet is reduced by ∼8 times on a superhydrophobic surface when the substrate temperature is increased from 40 to 60 °C. The mixing rate is ∼15 times faster on the superhydrophobic substrate compared to the hydrophobic surface maintained at the same temperature of 60 °C.

Assessment of water droplet evaporation mechanisms on hydrophobic and superhydrophobic substrates.

Evaporation rates are predicted and important transport mechanisms identified for evaporation of water droplets on hydrophobic (contact angle ~110°) and superhydrophobic (contact angle ~160°) substrates. Analytical models for droplet evaporation in the literature are usually simplified to include only vapor diffusion in the gas domain, and the system is assumed to be isothermal. In the comprehensive model developed in this study, evaporative cooling of the interface is accounted for, and vapor concentration is coupled to local temperature at the interface. Conjugate heat and mass transfer are solved in the solid substrate, liquid droplet, and surrounding gas. Buoyancy-driven convective flows in the droplet and vapor domains are also simulated. The influences of evaporative cooling and convection on the evaporation characteristics are determined quantitatively. The liquid-vapor interface temperature drop induced by evaporative cooling suppresses evaporation, while gas-phase natural convection acts to enhance evaporation. While the effects of these competing transport mechanisms are observed to counterbalance for evaporation on a hydrophobic surface, the stronger influence of evaporative cooling on a superhydrophobic surface accounts for an overprediction of experimental evaporation rates by ~20% with vapor diffusion-based models. The local evaporation fluxes along the liquid-vapor interface for both hydrophobic and superhydrophobic substrates are investigated. The highest local evaporation flux occurs at the three-phase contact line region due to proximity to the higher temperature substrate, rather than at the relatively colder droplet top; vapor diffusion-based models predict the opposite. The numerically calculated evaporation rates agree with experimental results to within 2% for superhydrophobic substrates and 3% for hydrophobic substrates. The large deviations between past analytical models and the experimental data are therefore reconciled with the comprehensive model developed here.

Nanotextured superhydrophobic electrodes enable detection of attomolar-scale DNA concentration within a droplet by non-faradaic impedance spectroscopy.

Label-free, rapid detection of biomolecules in microliter volumes of highly diluted solutions (sub-femtomolar) is of essential importance for numerous applications in medical diagnostics, food safety, and chem-bio sensing for homeland security. At ultra-low concentrations, regardless of the sensitivity of the detection approach, the sensor response time is limited by physical diffusion of molecules towards the sensor surface. We have developed a fast, low cost, non-faradaic impedance sensing method for detection of synthetic DNA molecules in DI water at attomolar levels by beating the diffusion limit through evaporation of a micro-liter droplet of DNA on a nanotextured superhydrophobic electrode array. Continuous monitoring of the impedance of individual droplets as a function of evaporation time is exploited to dramatically improve the sensitivity and robustness of detection. Formation of the nanostructures on the electrode surface not only increases the surface hydrophobicity, but also allows robust pinning of the droplet contact area to the sensor surface. These two features are critical for performing highly stable impedance measurements as the droplet evaporates. Using this scheme, the detection limit of conventional non-faradaic methods is improved by five orders of magnitude. The proposed platform represents a step-forward towards realization of ultra-sensitive lab-on-chip biomolecule detectors for real time point-of-care application. Further works are however needed to ultimately realize the full potential of the proposed approach to appraise biological samples in complex buffer solutions rather than in DI water.

Droplet evaporation dynamics on a superhydrophobic surface with negligible hysteresis.

We report on experiments of droplet evaporation on a structured superhydrophobic surface that displays very high contact angle (CA ∼ 160 deg), and negligible contact angle hysteresis (<1 deg). The droplet evaporation is observed to occur in a constant-contact-angle mode, with contact radius shrinking for almost the entire duration of evaporation. Experiments conducted on Teflon-coated smooth surface (CA ∼ 120 deg) as a baseline also support an evaporation process that is dominated by a constant-contact-angle mode. The experimental results are compared with an isothermal diffusion model for droplet evaporation from the literature. Good agreement is observed for the Teflon-coated smooth surface between the analytical expression and experimental results in terms of the total time for evaporation, transient volume, contact angle, and contact radius. However, for the structured superhydrophobic surface, the experiments indicate that the time taken for complete evaporation of the droplet is greater than the predicted time, across all droplet volumes. This disparity is attributed primarily to the evaporative cooling at the droplet interface due to the high aspect ratio of the droplet and also the lower effective thermal conductivity of the substrate due to the presence of air gaps. This hypothesis is verified by numerically evaluating the temperature distribution along the droplet interface. We propose a generalized relation for predicting the instantaneous volume of droplets with initial CA > 90 deg, irrespective of the mode of evaporation.

Hybrid surface design for robust superhydrophobicity.

Surfaces may be rendered superhydrophobic by engineering the surface morphology to control the extent of the liquid-air interface and by the use of low-surface-energy coatings. The droplet state on a superhydrophobic surface under static and dynamic conditions may be explained in terms of the relative magnitudes of the wetting and antiwetting pressures acting at the liquid-air interface on the substrate. In this paper, we discuss the design and fabrication of hollow hybrid superhydrophobic surfaces which incorporate both communicating and noncommunicating air gaps. The surface design is analytically shown to exhibit higher capillary (or nonwetting) pressure compared to solid pillars with only communicating air gaps. Six hybrid surfaces are fabricated with different surface parameters selected such that the Cassie state of a droplet is energetically favorable. The robustness of the surfaces is tested under dynamic impingement conditions, and droplet dynamics are explained using pressure-based transitions between Cassie and Wenzel states. During droplet impingement, the effective water hammer pressure acting due to the sudden change in the velocity of the droplet is determined experimentally and is found to be at least 2 orders of magnitude less than values reported in the literature. The experiments show that the water hammer pressure depends on the surface morphology and capillary pressure of the surface. We propose that the observed reduction in shock pressure may be attributed to the presence of air gaps in the substrate. This feature allows liquid deformation and hence avoids the sudden stoppage of the droplet motion as opposed to droplet behavior on smooth surfaces.

Dynamics of droplet motion under electrowetting actuation.

The static shape of droplets under electrowetting actuation is well understood. The steady-state shape of the droplet is obtained on the basis of the balance of surface tension and electrowetting forces, and the change in the apparent contact angle is well characterized by the Young-Lippmann equation. However, the transient droplet shape behavior when a voltage is suddenly applied across a droplet has received less attention. Additional dynamic frictional forces are at play during this transient process. We present a model to predict this transient behavior of the droplet shape under electrowetting actuation. The droplet shape is modeled using the volume of fluid method. The electrowetting and dynamic frictional forces are included as an effective dynamic contact angle through a force balance at the contact line. The model is used to predict the transient behavior of water droplets on smooth hydrophobic surfaces under electrowetting actuation. The predictions of the transient behavior of droplet shape and contact radius are in excellent agreement with our experimental measurements. The internal fluid motion is explained, and the droplet motion is shown to initiate from the contact line. An approximate mathematical model is also developed to understand the physics of the droplet motion and to describe the overall droplet motion and the contact line velocities.