Understanding (sessile/constrained) bubble and drop oscillations

The diffuse literature on drop oscillation is reviewed, with an emphasis on capillary wave oscillations of constrained drops. Based on the review, a unifying conceptual framework is presented for drop and bubble oscillations, which considers free and constrained drops/bubbles, oscillation of the surface or the bulk (i.e. center of mass) of the drop/bubble, as well as different types of restoring forces (surface tension, gravity, electromagnetic, etc). Experimental results (both from literature and from a new set of experiments studying sessile drops in cross flowing air) are used to test mathematical models from literature, using a novel whole profile analysis technique for the new experiments. The cause of oscillation (cross flowing air, vibrated surface, etc.) is seen not to affect oscillation frequency. In terms of models, simplified models are seen to poorly predict oscillation frequencies. The most advanced literature models are found to be relatively accurate at predicting frequency. However it is seen that no existing models are reliably accurate across a wide range of contact angles, indicating the need for advanced models/empirical relations especially for drops undergoing the lowest frequency mode of oscillation (the order 1 degree 1 non-axisymmetric ‘bending’ mode that corresponds to a lateral ‘rocking’ motion of the drop).     

Kinetic adsorption energy distributions of rough surfaces: a computational study

The adsorption energy distribution usually refers to localized monolayers of adsorbate at thermodynamic equilibrium. Many papers have been published that analyze its influence on adsorption isotherms, heats of adsorption, and adsorption kinetics. However, the adsorption energy distribution, in its classical thermodynamic equilibrium sense, may be not as useful as expected. This is because many important processes involving adsorption have dynamic character and reactant particles have a finite time for penetration of the adsorbent. The above suggests that some adsorption centers located in less accessible fragments of the surface can be invisible in a dynamic process. However, under conditions allowing the thermodynamic equilibrium such adsorption centers could noticeably contribute to the adsorption energy distribution. The aim of this work is to measure the adsorption energy distributions of special rough surfaces using a dynamic method. This method is based on the molecular dynamics simulation of an ideal gas flowing over a sample surface. The ideal gas particles penetrate the surface, and at the moment of collision of a gas particle with the surface the Lennard-Jones potential energy is calculated. This energy can be identified with the adsorption energy at a given point on the surface. The surfaces used in the calculations have been created using two surface growth models (i.e., random deposition and ballistic deposition). The application of these highly disordered surfaces enables us to draw some general conclusions about the properties of real surfaces that are usually far from any deterministic geometry.     

Modeling of wetting: a study of nanowetting at rough and heterogeneous surfaces

Molecular dynamics simulations were performed to study the behavior of nanoscale water droplets at solid surfaces. Simulations of droplets on heterogeneous patterned surfaces show that the relative sizes of the domains and the droplets play an important role as do the interactions between the solid and the liquid, particularly when the domain width is comparable to the droplet radius. For pillar surfaces, a transition is observed between the Wenzel and the Cassie and Baxter regimes with increasing pillar height. The effects of pillar width and the gap between the pillars were also examined. The simulations show clearly the importance of the detailed topography and composition of the solid surface.     

Desiccating colloidal sessile drop: dynamics of shape and concentration

Using lubrication theory, drying processes of sessile colloidal droplets on a solid substrate are studied. A simple model is proposed to describe temporal dynamics of both the shape of the drop and the volume fraction of the colloidal particles inside the drop. The concentration dependence of the viscosity is taken into account. It is shown that the final shapes of the drops depend on both the initial volume fraction of the colloidal particles and the capillary number. The results of our simulations are in a reasonable agreement with the published experimental data. Computations for the drops of aqueous solution of human serum albumin are presented.     

Particle and substrate charge effects on colloidal self-assembly in a sessile drop

By direct video monitoring of dynamic colloidal self-assembly during solvent evaporation in a sessile drop, we investigated the effect of surface charge on the ordering of colloidal spheres. The in situ observations revealed that the interaction between charged colloidal spheres and substrates affects the mobility of colloidal spheres during convective self-assembly, playing an important role in the colloidal crystal growth process. Both ordered and disordered growth was observed depending on different chemical conditions mediated by surface charge and surfactant additions to the sessile drop system. These different self-assembly behaviors were explained by the Coulombic and hydrophobic interactions between surface-charged colloidal spheres and substrates.     

Improvement of interfacial tension measurement using a captive bubble in conjunction with axisymmetric drop shape analysis (ADSA)

Axisymmetric drop shape analysis (ADSA) is a method to measure surface tension using drop or bubble profiles. Combining ADSA with a captive bubble configuration (ADSA-CB) facilitates pulmonary surfactant related studies. The accuracy of ADSA-CB is crucially dependent on the quality of the bubble profile extracted from the raw image. In the previous version of ADSA-CB, a global thresholding method was used to segment the bubble profile. However, that technique is of limited accuracy for images with noise and/or lack of contrast. In this paper, a new generation of ADSA-CB using the Canny edge detector was developed. To obtain better results, a novel edge smoothing technique, termed axisymmetric liquid fluid interfaces-smoothing (ALFI-S), was introduced and incorporated with the Canny edge detector to extract bubble profiles. The performance of the new version of ADSA-CB was evaluated using captive bubble images under different conditions. The results suggest that the new methodology is capable of producing accurate surface tension values under a variety of circumstances.     

Axisymmetric drop shape analysis-constrained sessile drop (ADSA-CSD): a film balance technique for high collapse pressures

Collapse pressure of insoluble monolayers is a property determined from surface pressure/area isotherms. Such isotherms are commonly measured by a Langmuir film balance or a drop shape technique using a pendant drop constellation (ADSA-PD). Here, a different embodiment of a drop shape analysis, called axisymmetric drop shape analysis-constrained sessile drop (ADSA-CSD) is used as a film balance. It is shown that ADSA-CSD has certain advantages over conventional methods. The ability to measure very low surface tension values (e.g., <2 mJ/m2), an easier deposition procedure than in a pendant drop setup, and leak-proof design make the constrained sessile drop constellation a better choice than the pendant drop constellation in many situations. Results of compression isotherms are obtained on three different monolayers: octadecanol, dipalmitoyl-phosphatidyl-choline (DPPC), and dipalmitoyl-phosphatidyl-glycerol (DPPG). The collapse pressures are found to be reproducible and in agreement with previous methods. For example, the collapse pressure of DPPC is found to be 70.2 mJ/m2. Such values are not achievable with a pendant drop. The collapse pressure of octadecanol is found to be 61.3 mJ/m2, while that of DPPG is 59.0 mJ/m2. The physical reasons for these differences are discussed. The results also show a distinctive difference between the onset of collapse and the ultimate collapse pressure (ultimate strength) of these films. ADSA-CSD allows detailed study of this collapse region.     

Triple-line behavior and wettability controlled by nanocoated substrates: influence on sessile drop evaporation

In this article, we investigate the influence of the surface properties of substrates on the evaporation process. Using various nanocoatings, it is possible to modify the surface properties of substrates, such as the roughness and the surface energy, while maintaining constant thermal properties. Experiments are conducted under atmospheric conditions with five fluids (methanol, ethanol, propanol, toluene and water) and four coatings (PFC, PTFE, SiOC, and SiO(x)). The various combinations of these fluids and coatings allow for a wide range of drop evaporation properties to be studied: the dynamics of the triple line, the volatility of fluids, and a large range of wettabilities (from 17 to 135°). The experimental data are in very good quantitative agreement with existing models of quasi-steady, diffusion-driven evaporation. The experimental results show that the dynamics of the evaporative rate are proportional to the dynamics of the wetting radius. Thus, the models succeed in describing the evaporative dynamics throughout the evaporation process regardless of the behavior of the triple line. Moreover, the use of various liquids reveals the validity of the models regardless of their volatility. The results also confirm the recent finding of a universal relation for the time evolution of the drop mass, independent of the drop size and initial contact angle. Finally, this study highlights the separate and coupled roles of the triple line and the wettability on the sessile drop evaporation process. Data reveal that the more wet and pinned a drop, the shorter the evaporation time.     

Multicomponent analysis: Comparison of various graphical and numerical methods

The performance of several graphical (zero-crossing and derivative quotient spectra with standardized divisor) and numerical methods (MULTIC and PLS) for the resolution of binary and ternary mixtures of species is compared. Numerical methods were found to be specially suited to multicomponent analysis, particularly for mixtures containing more than two analytes with highly overlapped spectra. The results obtained by using the compared methods to analyse various synthetic mixtures of acetylsalicylic acid, caffeine and thiamine were quite consistent and errors in the simultaneous quantification of the analytes amounted to less than 5% in all instances.     

Comparison of methods for numerical differentiation

Numerical differentiation can uncover hidden features in chemical data, but the limitations of the technique used should be understood. A method based on fitting data to a quadratic polynomial gives good signal-to-noise ratios, but systematically low derivative intensities. Central difference methods are more accurate but less tolerant of noise.     

Anomalous contact angle hysteresis of a captive bubble: advancing contact line pinning

Contact angle hysteresis of a sessile drop on a substrate consists of continuous invasion of liquid phase with the advancing angle (θ(a)) and contact line pinning of liquid phase retreat until the receding angle (θ(r)) is reached. Receding pinning is generally attributed to localized defects that are more wettable than the rest of the surface. However, the defect model cannot explain advancing pinning of liquid phase invasion driven by a deflating bubble and continuous retreat of liquid phase driven by the inflating bubble. A simple thermodynamic model based on adhesion hysteresis is proposed to explain anomalous contact angle hysteresis of a captive bubble quantitatively. The adhesion model involves two solid–liquid interfacial tensions (γ(sl) > γ(sl)′). Young’s equation with γ(sl) gives the advancing angle θ(a) while that with γ(sl)′ due to surface rearrangement yields the receding angle θ(r). Our analytical analysis indicates that contact line pinning represents frustration in surface free energy, and the equilibrium shape corresponds to a nondifferential minimum instead of a local minimum. On the basis of our thermodynamic model, Surface Evolver simulations are performed to reproduce both advancing and receding behavior associated with a captive bubble on the acrylic glass.     

Interfacial tension of liquids from the height and contact angle of a single sessile drop

The height of a sessile drop of liquid when placed on a smooth solid surface increases as the drop volume increases, until it reaches a limiting value for a very large drop. The magnitude of the height and the contact angle depends on the different physical properties of the system. A large value for the contact angle is often associated with a large value for height and vice versa. From the data of measured limiting height, Z _Θ ^∞ and contact angle,Θ, the surface or interfacial tension,γ, can be estimated using the following equation: $$\gamma = \Delta \rho \cdot g \cdot (Z_\Theta ^\infty )^2 /2(1 - \cos (\Theta ))$$ whereΔ? is the density difference between the sessile drop and that of its surrounding medium,g is the gravitational force of acceleration. In this study, the magnitude ofγ of water for various systems is estimated. These values agree with the literature values. Furthermore, the values ofγ for various liquid₁/ solid/liquid₂ systems agree with data from other methods. Thus, the above equation is valid for different liquid-solid systems. It is further shown that very accurate measurements of contact angle,Θ, can be carried out for systems in which Z _Θ Δ _? andγ are known. The variation ofΘ with the height and volume of the sessile drop is analyzed for different systems.     

Dynamics of a disturbed sessile drop measured by atomic force microscopy (AFM)

A new method for studying the dynamics of a sessile drop by atomic force microscopy (AFM) is demonstrated. A hydrophobic microsphere (radius, r ～ 20-30 μm) is brought into contact with a small sessile water drop resting on a polytetrafluoroethylene (PTFE) surface. When the microsphere touches the liquid surface, the meniscus rises onto it because of capillary forces. Although the microsphere volume is 6 orders of magnitude smaller than the drop, it excites the normal resonance modes of the liquid interface. The sphere is pinned at the interface, whose small (<100 nm) oscillations are readily measured with AFM. Resonance oscillation frequencies were measured for drop volumes between 5 and 200 μL. The results for the two lowest normal modes are quantitatively consistent with continuum calculations for the natural frequency of hemispherical drops with no adjustable parameters. The method may enable sensitive measurements of volume, surface tension, and viscosity of small drops.     

Variational approach to wetting problems: Calculation of a shape of sessile liquid drop deposited on a solid substrate in external field

Analysis of the shape of sessile drops pinned to a solid substrate and exposed to the external potential is presented. Explicit expressions describing the drops’ shape are obtained with a calculus of variations for 2D and 3D wetting problems. The presented approach is applicable for analysis of electrowetting problems, the study of vibrated and centrifuged drops.     

Molecular dynamics simulation study of interaction between model rough hydrophobic surfaces

We study some aspects of hydrophobic interaction between molecular rough and flexible model surfaces. The model we use in this work is based on a model we used previously (Eun, C.; Berkowitz, M. L. J. Phys. Chem. B 2009, 113, 13222-13228), when we studied the interaction between model patches of lipid membranes. Our original model consisted of two graphene plates with attached polar headgroups; the plates were immersed in a water bath. The interaction between such plates can be considered as an example of a hydrophilic interaction. In the present work, we modify our previous model by removing the charge from the zwitterionic headgroups. As a result of this procedure, the plate character changes: it becomes hydrophobic. By separating the total interaction (or potential of mean force, PMF) between plates into the direct and the water-mediated interactions, we observe that the latter changes from repulsive to attractive, clearly emphasizing the important role of water as a medium. We also investigate the effect of roughness and flexibility of the headgroups on the interaction between plates and observe that roughness enhances the character of the hydrophobic interaction. The presence of a dewetting transition in a confined space between charge-removed plates confirms that the interaction between plates is strongly hydrophobic. In addition, we notice that there is a shallow local minimum in the PMF in the case of the charge-removed plates. We find that this minimum is associated with the configurational changes that flexible headgroups undergo as the two plates are brought together.     

Experimental and theoretical investigations of evaporation of sessile water droplet on hydrophobic surfaces

Experiments of sessile water droplet evaporation on both polydimethylsiloxane (PDMS) and Teflon surfaces were conducted. All experiments begin with constant contact area mode (the initial contact angle is greater than 90°), switch to constant contact angle mode and end with mixed mode. Based on the assumptions of spherical droplet and uniform concentration gradient, theoretical analyses for both constant contact area and constant contact angle modes are made and theoretical solutions are derived accordingly, especially a theoretical solution of contact angle is presented first for CCR stage with any value of the initial contact angle. Moreover, comparisons between the theoretical solutions and experimental data of contact angle in CCR stage demonstrate the validity of the theoretical solution and it would help for a better understanding and application of water droplet on solid surfaces, which is quite often encountered in lab-on-a-chip, polymerase chain reaction (PCR) and other micro-fluidics devices.     

Reversible and irreversible adsorption of particles on homogeneous surfaces

The kinetics of localized reversible and irreversible adsorption of interacting particles on homogeneous surfaces was analysed. Asymptotic analytical equations were derived for the surface blocking parameter B(0), and for adsorption kinetics and adsorption isotherms in the limit of low and high surface concentrations. It was found that the geometrical blocking effect was much more pronounced than the Langmuir model predicts, especially for high surface concentrations and low ionic strengths of suspensions.The new adsorption isotherm formulated indicates that for a large adsorption constant, K_a, the equilibrium surface concentration becomes proportional to K^−1/3_a, whereas in the Langmuir model this quantity is approached as K⁻¹_a (for K_a ≫I). In the case of irreversible adsorption the theoretical predictions were experimentally tested by applying the direct microscope observation method. Monodisperse suspensions of negatively charged latex particles were used in these experiments with silanized mica sheets as the adsorbing surface. Our theoretical predictions were quantitatively confirmed, indicating that the Langmuir model is not appropriate for describing localized adsorption of particles on homogeneous surfaces.     

Experimental investigation of bubble and drop formation at submerged orifices

The aim of this study was to investigate bubble/drop formation at a single submerged orifice in stagnant Newtonian fluids and to gain qualitative understanding of the formation mechanism. The effects of various governing parameters were studied. Formation behavior of bubbles and drops in Newtonian aqueous solutions were investigated experimentally under different operating conditions with various orifices. The results show that the volume of the detached dispersed phase (bubble or drop) increases with the viscosity of the continuous phase (or dispersion medium), surface tension, orifice diameter, and dispersed phase flow rate. A PIV system was employed to measure the velocity flow field quantitatively during the bubble/drop formation, giving interesting information useful for the elucidation of the fundamental formation process at the orifice. It was revealed that the orifice shape strongly influences the size of the bubble formed. Furthermore, based on a simple mass balance, a general correlation successfully predicting both bubble and drop sizes has been proposed.     

Adsorption of semiflexible block copolymers on homogeneous surfaces

We present the results of extensive numerical off-lattice Monte Carlo simulations of semiflexible block-copolymer chains adsorbed onto flat homogeneous surfaces. We have compared the behavior of several chain structures, such as homopolymers, diblocks, (A(alpha)B(alpha)) block copolymers, and random heteropolymers. In all the cases studied, we have found the adsorption process to be favored with an increase of the chain rigidity. Particularly, the adsorption of diblock structures becomes a two-step process characterized by two different adsorbing temperatures that depend on the chain stiffness kappa, the chain length N, and the adsorbing energies epsilon(A) and epsilon(B). This twofold adsorbing process changes to a single one for copolymers of reduced block size alpha. Each block of the stiff copolymer chain is found to satisfy the classical scaling laws for flexible chains, however, we found the scaling exponent phi to depend on the chain stiffness. The measurement of the radius of gyration exhibits a typical behavior of a polymer chain composed of Nl(p) blobs whose persistence length follows l(p) approximately (kappa/k(B)T)(0.5) for large stiff chains.