Evaporation Dynamics of Surfactant-Laden Droplets on a Superhydrophobic Surface: Influence of Surfactant Concentration

Surfactant-laden sessile droplet evaporation plays a crucial role in a variety of omnipresent natural and technological applications, such as drying, coating, spray, and inkjet printing. Surfactant molecules can adsorb easily on interfaces and, hence, destructively ruin the useful gas-trapping wetting state (i.e., Cassie-Baxter, CB) of a drop on superhydrophobic (SH) surfaces. However, the influence of surfactant adsorption or concentration on evaporation modes has been rarely investigated so far. Here, we investigate the evaporation dynamics of aqueous didodecyldimethylammonium bromide (DDAB) sessile droplet on SH surfaces made of regular hydrophobic micropillars, with various dimensionless surfactant concentrations (C_S), primarily using experiments. We find that all drops initially form a CB state with a pinned base radius and evaporate in a mode of constant contact radius (CCR). Water and low-C_S (=0.02) drop subsequently evaporate with a constant contact angle (CCA) mode, followed by a CCR mode and, eventually, a mixed-mode. By contrast, high-C_S (of 0.25-1) droplets undergo a complex mixed mode, with rapidly increasing base radius, and finally a mixed mode, with slowly decreasing base radius and contact angle. The experimental data reveal that contact-angle-dependent evaporative mass flux, ṁ, collapses onto a nearly universal curve depending on C_S. For the low-C_S (of 0-0.25) drops, ṁ is lower and consistent with an evaporative cooling model, whereas high-C_S (of 0.5-1) droplets are consistent with a pure vapor-diffusive model. We further show that the critical C_S delineating these two evaporative models correlates with saturated surfactant adsorption on both liquid-solid and liquid-vapor interfaces.

Gibbsian Surface Thermodynamics

Gibbsian composite-system thermodynamics is the framework governing the equilibrium of composite systems, including systems that at equilibrium have more than one value of pressure because of the action of surface tension, semipermeable membranes, or fields, and thus cannot be treated as simple systems. J. W. Gibbs's paper that lays out composite-system thermodynamics, "On the Equilibrium of Heterogeneous Substances", communicated in two parts in 1876 and 1878, is widely regarded as one of the most important pieces of scientific literature of its century. Many scientists adopted and stressed the importance of Gibbsian thermodynamics. In 1960, H. B. Callen wrote a textbook that made Gibbsian composite-system thermodynamics more accessible to thermodynamicists. However, Callen's book left out Gibbs's work on curved fluid interfaces and did not treat the complicated nonideal systems of interest to today's thermodynamicists. In this Feature Article, I have attempted to convey in a comprehensive manner the framework of Gibbsian composite-system thermodynamics including in detail the treatment of systems with interface effects and with nonideal, multicomponent phases. This work lays out the relationships between important equilibrium equations including the following: the Gibbs-Duhem equation, the Gibbs adsorption equation, the Young-Laplace equation, the Young equation, the Cassie-Baxter equation, the Wenzel equation, the Kelvin equation, the Gibbs-Thompson equation, and the Ostwald-Freundlich equation, including nonideal and multicomponent forms. Equations of state that are often useful for Gibbsian composite-system thermodynamics are reviewed including adsorption isotherms and our own work on two semiempirical equations of state: the Elliott et al. form of the osmotic virial equation and the Shardt-Elliott-Connors-Wright equation for the temperature and composition dependence of surface tension. I summarize the work of our group developing Gibbisan composite-system thermodynamics including new equations for such things as the curvature-induced depression of the eutectic temperature or the removal of azeotropes by nanoscale fluid interface curvature. Gibbsian composite-system thermodynamics has broad applications in biotechnology, nanostructured materials, surface textures and coatings, microfluidics, nanoscience, atmospheric and environmental physics, among others.

Effect of a Cationic Surfactant on Droplet Wetting on Superhydrophobic Surfaces

We experimentally and theoretically examine the influence of a double-chain cationic surfactant, didodecyldimethylammonium bromide (DDAB), on the wetting states and contact angles on superhydrophobic (SH) surfaces made of hydrophobic microcylinders. We use two types of micropatterns of different surface roughness, r, and packing fraction, ϕ, and vary nine dimensionless surfactant concentrations (C_S), normalized by the critical micelle concentration (CMC), in the experiments. At low C_S, some of the surfactant-laden droplets are in a gas-trapping, Cassie-Baxter (CB) state on the high-roughness microstructures. In contrast, some droplets are in a complete-wetting Wenzel (W) state on the low-roughness microtextures. We found that the contact angle of CB drops can be well predicted using a thermodynamic model considering surfactant adsorption at the liquid-vapor (LV) and solid-liquid (SL) interfaces. At high C_S, however, all of the DDAB drops wet in a Wenzel mode. Based on a Gibbsian thermodynamic analysis, we find that for the two types of superhydrophobic surfaces used, the Wenzel state has the lowest thermodynamic energy and thus is more favorable theoretically. The CB state, however, is metastable at low C_S due to a thermodynamic energy barrier. The metastable CB wetting state becomes more stable on the SH microtextures with greater ϕ and r, in agreement with our experimental observations. Finally, we generalize this surface-energy analysis to provide useful designs of surface parameters for a DDAB-laden surfactant droplet on the SH surface with a stable and robust CB state.

How Surfactants Affect Droplet Wetting on Hydrophobic Microstructures

Surfactants, as amphiphilic molecules, adsorb easily at interfaces and can detrimentally destroy the useful, gas-trapping wetting state (Cassie-Baxter, CB) of a drop on superhydrophobic surfaces. Here, we provide a quantitative understanding of how surfactants alter the wetting state and contact angle of aqueous drops on hydrophobic microstructures of different roughness (r) and solid fraction (ϕ). Experimentally, at low surfactant concentrations (C), some drops attain a homogeneous wetting state (Wenzel, W), while others attain the CB state whose large contact angles can be predicted by a thermodynamic model. In contrast, all of our high-C drops attain the Wenzel state. To explain this observed transition, we consider the free energy and find that, theoretically, for our surfaces the W state is always preferred, while the CB state is metastable at low C, consistent with experimental results. Furthermore, we provide a beneficial blueprint for stable CB states for applications exploiting superhydrophobicity.

Solid-Liquid-Liquid Wettability of Surfactant-Oil-Water Systems and Its Prediction around the Phase Inversion Point

Surfactant-oil-water (SOW) systems are important for numerous applications, including hard surface cleaning, detergency, and enhanced oil-recovery applications. There is limited literature on the wettability of solid-liquid-liquid (SLL) systems around the surfactant phase inversion point (PIP), and the few references that exist point to wettability inversion accompanying the microemulsion (μE) phase inversion. Despite the significance of this phenomenon and the extreme changes in contact angles, there are no models to predict SLL wettability as a function of proximity to the PIP. Recent works on SLL wettability in surfactant-free systems suggest that SLL contact angles can be predicted with an extension of Neumann's equation of state (e-EQS) if the interfacial tension (IFT or γ_o-w) is known and if there is a good estimate for the interfacial energy between the wetting phase and the surface (γ_{S-wetting liquid}). In this work, IFT predictions for SOW systems around the PIP were obtained via the combined hydrophilic-lipophilic difference (HLD) and net-average-curvature (NAC) framework. To test the hypothesis that the combined HLD-NAC + e-EQS can predict wettability inversion around the PIP, with a given γ_S-μE, the contact angles (measured through the light oil phase, θ_O) for the μE of sodium dihexyl sulfosuccinate-toluene-saline water system were measured on high surface free energy (SFE) materials (glass, stainless steel, and mica) and on polytetrafluoroethylene (low SFE) around the PIP. Considering that at the PIP, most systems have a contact angle of 90°, an estimated γ_S-μE = 1/4γ_o-w@PIP was found to be suitable for the systems considered in this work and for systems presented in the literature. The largest deviations between the predictions and the experimental values were found in the positive HLD range (surfactant in the light oil phase). Although there is room for improvement, this framework can estimate the wetting behavior of SOW systems starting solely from formulation parameters.

Solid-liquid-liquid wettability and its prediction with surface free energy models

Understanding wettability in solid-liquid-liquid (SLL or immersed) systems is important for numerous applications. However, predicting SLL wetting behavior on smooth surfaces has received little attention. The objective of this work was to explore alternatives to predict SLL wettability. To this end, we first present a review of solid surface free energy (σ_S) data obtained from solid-liquid-air (SLA) contact angle (θ_L^a) data and a summary of available SLL contact angle data for selected materials. Next, the existing surface free energy models for SLA systems are discussed in terms of their applicability to predict wettability of SLL systems. Finally, the SLL wettability of toluene drops on glass, mica, stainless steel and PTFE immersed in equilibrated Toluene-water-isopropyl alcohol (IPA) solutions was determined via contact angle (θ_O) measurements through the oil phase using the inverted sessile drop method over a wide range of interfacial tensions (γ_o-aq). The results were plotted as γ_o-aq·cosθ_O vs. γ_o-aq, showing a smooth wetting transition from water-wetting to oil-wetting with decreasing γ_o-aq for glass and stainless steel. Mica remained water-wetting, while PTFE oil-wetting. The Geometric (GM) and Harmonic (HM) mean approaches, and the Equation-of-State (EQS), originally developed for SLA systems, were extended to SLL systems. The extended GM and HM approaches could fit the SLL behavior after fitting the dispersive and polar contributions of the solid surface free energy (σ_S^d, σ_S^p), which required additional SLA θ_L^a measurements using PTFE as the reference surface. However, attempts at predicting θ_O for systems with high γ_o-aq resulted in significant deviations, a problem linked to the high σ_S^d values required to fit the wettability of low γ_o-aq systems (toluene-water-IPA). The extended EQS (e-EQS) method produced reasonable predictions of γ_o-aq·cosθ_O for all the available experimental and literature data. The e-EQS method required fitting one of the interfacial energy terms (γ_S-L). For low surface energy materials, such as PTFE, the γ_S-o value should be fitted. For high surface energy materials, the γ_S-aq should be fitted instead. The fitted values of γ_S-o for PTFE and γ_S-aq for glass were consistent with the values obtained from Young's equation applied to SLA data.

Governing Influence of Thermodynamic and Chemical Equilibria on the Interfacial Properties in Complex Fluids

We propose a comprehensive analysis and a quasi-analytical mathematical formalism to predict the surface tension and contact angles of complex surfactant-infused nanocolloids. The model rests on the foundations of the interaction potentials for the interfacial adsorption-desorption dynamics in complex multicomponent colloids. Surfactant-infused nanoparticle-laden interface problems are difficult to deal with because of the many-body interactions and interfaces involved at the meso-nanoscales. The model is based on the governing role of thermodynamic and chemical equilibrium parameters in modulating the interfacial energies. The influence of parameters such as the presence of surfactants, nanoparticles, and surfactant-capped nanoparticles on interfacial dynamics is revealed by the analysis. Solely based on the knowledge of interfacial properties of independent surfactant solutions and nanocolloids, the same can be deduced for complex surfactant-based nanocolloids through the proposed approach. The model accurately predicts the equilibrium surface tension and contact angle of complex nanocolloids available in the existing literature and present experimental findings.

Effects of interplay of nanoparticles, surfactants and base fluid on the surface tension of nanocolloids

A systematically designed study has been conducted to understand and demarcate the degree of contribution by the constituting elements to the surface tension of nanocolloids. The effects of elements such as surfactants, particles and the combined effects of these on the surface tension of these complex fluids are studied employing the pendant drop shape analysis method by fitting the Young-Laplace equation. Only the particle has shown an increase in the surface tension with particle concentration in a polar medium like DI water, whereas only a marginal effect of particles on surface tension in weakly polar mediums like glycerol and ethylene glycol has been demonstrated. Such behaviour has been attributed to the enhanced desorption of particles to the interface and a theory has been presented to quantify this. The combined particle and surfactant effect on the surface tension of a complex nanofluid system showed a decreasing behaviour with respect to the particle and surfactant concentration with a considerably feeble effect of particle concentration. This combined colloidal system recorded a surface tension value below the surface tension of an aqueous surfactant system at the same concentration, which is a counterintuitive observation as only the particle results in an increase in the surface tension and only the surfactant results in a decrease in the surface tension. The possible physical mechanism behind such an anomaly happening at the complex fluid air interface has been explained. Detailed analyses based on thermodynamic, mechanical and chemical equilibrium of the constituents and their adsorption-desorption characteristics as extracted from the Gibbs adsorption analysis have been provided. The present paper conclusively explains several physical phenomena observed, yet hitherto unexplained, in the case of the surface tension of such complex fluids by segregating the individual contributions of each component of the colloidal system.

CONTACT INSTABILITY OF NON-PLANAR ELASTOMERIC SURFACES

Contact surfaces between non-planar elastomers widely present in the industrial and biomedical fields, such as corrugated mats and biological fillers. Probing out the mechanical instability of these contact surfaces could greatly contribute to the efficiency, safety and durability of the related structures. In this paper, we numerically studied the contact instability of non-planar elastomeric surfaces with typical projections (i.e., circular and triangle projections) by proposing an instability criterion and using the finite element method. Moreover, we studied the effects of several key factors (e.g., the geometrical parameters and the friction coefficients of the surfaces) on the critical force of the mechanical instability. It is found that with comparable geometric sizes, the surface with circular projections is more effective to enhance the contact stability than that with triangle projections. A larger slope and curvature radius result in weaker stability while a larger friction coefficient plays a positive role for the stability. However, with increasing friction coefficient, the maximum force presents smaller and smaller changes and further improvement of contact stability mainly depends on the changes of the number of projections. These investigations may improve the understanding of the mechanical instability of non-planar elastomeric surfaces and contribute to achieve better designs of related structures.