Analysis of the equilibrium droplet shape based on an ellipsoidal droplet model

Controllable Fabrication of Highly Ordered Spherical Microcavity Arrays by Replica Molding of In Situ Self-Emulsified Droplets

Ordered spherical hollow micro- and nanostructures hold great appeal in the fields of cell biology and optics. However, it is extremely challenging for standard lithography techniques to achieve spherical micro-/nanocavities. In this paper, we describe a simple, cost-effective, and scalable approach to fabricate highly ordered spherical microcavity arrays by replica molding of in situ self-emulsified droplets. The in situ self-emulsion involves a two-step process: discontinuous dewetting-induced liquid partition and interfacial tension-driven liquid spherical transformation. Subsequent replica molding of the droplets creates spherical microcavity arrays. The shapes and sizes of the microcavities can be easily modulated by varying the compositions of the droplet templates or utilizing an osmotically driven water permeation. To demonstrate the utility of this method, we employed it to create a spherical microwell array for the mass production of embryoid bodies with high viability and minimal loss. In addition, we also demonstrated the optical functions of the generated spherical microcavities by using them as microlenses. We believe that our proposed method will open exciting avenues in fields ranging from regenerative medicine and microchemistry to optical applications.

Numerical Investigation of Heat Transfer and Development in Spherical Condensation Droplets

This study establishes thermodynamic assumptions regarding the growth of condensation droplets and a mathematical formulation of droplet energy functionals. A model of the gas-liquid interface condensation rate based on kinetic theory is derived to clarify the relationship between condensation conditions and intermediate variables. The energy functional of a droplet, derived using the principle of least action, partially elucidates the inherent self-organizing growth laws of condensed droplets, enabling predictive modeling of the droplet's growth. Considering the effects of the condensation environment and droplet heat transfer mechanisms on droplet growth dynamics, we divide the process into three distinct stages, marked by critical thresholds of 105 nm3 and 1010 nm3. Our model effectively explains why the observed contact angle fails to reach the expected Wenzel contact angle. This research presents a detailed analysis of the factors affecting surface condensation and heat transfer. The predictions of our model have an error rate of less than 3% error compared to baseline experiments. Consequently, these insights can significantly contribute to and improve the design of condensation heat transfer surfaces for the phase-change heat sinks in microprocessor chips.

A generalized analytical energy balance model for evaluating agglomeration from a binary collision of wet particles

Agglomeration of wet particles, i.e., particles coated with a thin liquid layer, is a common phenomenon in many processes like fluidized bed combustion of low rank fuels. The availability of an agglomeration model that can evaluate the outcome of a binary collision between wet particles differing in solid particle properties, liquid layer thicknesses, and initial collision (impact) speeds is essential for obtaining a comprehensive understanding on the existing processes experiencing wet particle agglomeration or for a successful development of new processes with high chances of wet particle agglomeration. This study presents a generalized agglomeration model on the basis of energy conservation before and after collision when colliding wet particles may differ in solid particle properties, liquid layer thicknesses, and impact speeds. The model was established based on the approximate values of energy losses that may happen during the collision. It incorporates body forces, solid-solid contacting, liquid capillary, and viscous contributions, as well as the liquid bridge volume effect. Predictions of the new model for collision outcomes of identical wet particles were like those from an analytical energy balance model developed recently by the group for identical wet particles. We also validated the new model by experimental data from literature. The results of a collision direction analysis indicated that the direction often has a minimal effect on the collision outcome in many practical scenarios. The results of Monte Carlo uncertainty analyses with the new model revealed that proper estimations of impact speed, under capillary limiting conditions, and thickness of coating layers and asperity heights, under viscous limiting conditions, are critical for the realistic prediction of collision outcomes at impact speeds close to critical impact speed, i.e., the minimum particle speed required for the particles to rebound.

Shaping in the Third Direction: Self-Assembly of Convex Colloidal Photonic Crystals on an Optical Fiber Tip by Hanging Drop Method

High-quality convex colloidal photonic crystals can be grown on the tip of an optical fiber by self-assembly using the hanging drop method. They are convex-shaped, produce the diffraction of reflecting light with high efficiency (blazing colors), and have a high curvature. The convex colloidal crystals are easily detachable and, as free-standing objects, they are mechanically robust, allowing their manipulation and use as convex reflective diffraction devices in imaging spectrometers. Currently, the same characteristics are obtained by using gratings-based structures. The optical fiber/colloidal crystal interface is disordered; thus, no light diffraction can be registered. The ordering at this interface was highly increased by forming a polystyrene spacer on the optical fiber tip, which served as a self-assembly substrate for silica colloid, as a mechanical bond between the fiber and the crystal, and as a filler reservoir for an inverse-opal synthesis. The silica opal-like grown on the optical fiber tip can be transformed into a high-quality polystyrene (blazing colors) inverse-opal by using the polystyrene spacer as a filler. We found that the colloidal crystal axisymmetric self-assembles onto the optical fiber tip only if a maximum volume of the colloid drop is settled on a flat end of the polystyrene spacer.

Structural Color from Cellulose Nanocrystals or Chitin Nanocrystals: Self-Assembly, Optics, and Applications

Widespread concerns over the impact of human activity on the environment have resulted in a desire to replace artificial functional materials with naturally derived alternatives. As such, polysaccharides are drawing increasing attention due to offering a renewable, biodegradable, and biocompatible feedstock for functional nanomaterials. In particular, nanocrystals of cellulose and chitin have emerged as versatile and sustainable building blocks for diverse applications, ranging from mechanical reinforcement to structural coloration. Much of this interest arises from the tendency of these colloidally stable nanoparticles to self-organize in water into a lyotropic cholesteric liquid crystal, which can be readily manipulated in terms of its periodicity, structure, and geometry. Importantly, this helicoidal ordering can be retained into the solid-state, offering an accessible route to complex nanostructured films, coatings, and particles. In this review, the process of forming iridescent, structurally colored films from suspensions of cellulose nanocrystals (CNCs) is summarized and the mechanisms underlying the chemical and physical phenomena at each stage in the process explored. Analogy is then drawn with chitin nanocrystals (ChNCs), allowing for key differences to be critically assessed and strategies toward structural coloration to be presented. Importantly, the progress toward translating this technology from academia to industry is summarized, with unresolved scientific and technical questions put forward as challenges to the community.

Apple-like Shape of Freezing Paraffin Wax Droplets and Its Origin

Paraffin wax stores energy in the form of latent heat at a nearly constant temperature during melting and releases this energy during solidification. This effect is used in industrial energy storage. At the same time, the possible deformation of even small volumes of material as a result of phase change is insufficiently studied. In this paper, the physical nature of such deformation, probably for the first time, is studied on the example of a droplet of paraffin wax. An unusual change in the shape of a melted droplet of paraffin wax placed on a relatively cold glass plate was observed in the laboratory experiments. As the droplet solidifies, its upper surface becomes nearly flat, and a dimple is formed in the center of this surface, making the droplet look like a fruit (pumpkins are more commonly shaped like this, but the authors prefer apples). A series of experiments, as well as physical and numerical modeling of the droplet's thermal state, taking into account the formation of a mushy zone between liquidus and solidus, made it possible to understand the role of gravity and gradual increase in viscosity and density of paraffin wax on changing the droplet shape and, in particular, to clarify the mechanism of formation of the dimple on its upper. It was shown that the mushy zone between the liquidus and solidus of the paraffin wax is responsible for the dimple formation.

Effect of gravity on the spreading of a droplet deposited by liquid needle deposition technique

This study represents an experimental investigation, complemented with a mathematical model, to decipher the effect of gravity on the spreading dynamics of a water droplet. For the theoretical discussion, an overall energy balance approach is adopted to explain the droplet spreading under both microgravity (μg) and terrestrial gravity condition. Besides explaining the mechanism of the droplet spreading under microgravity condition achieved during the parabolic flight, a technique with a detailed experimental set-up has also been developed for the successful deposition of droplet. A rational understanding is formulated through experimental investigation and theoretical analysis, which allows us to distinguish the transient variation of the spreading of a droplet, between microgravity and terrestrial gravity condition. The spreading of the droplet is predicted by the non-linear overall energy balance equation, which accounts for the operating parameters in the form of non-dimensional groups like Reynolds number ([Formula: see text]), Weber number (We) and Bond number (Bo). To distinctly identify the difference in the drop spreading at terrestrial and microgravity conditions, the Bo with transient gravitational field obtained through the on-board accelerometer is considered. The obtained theoretical results are further corroborated by experimental results which are obtained from the parabolic flight.

Predictions of the Wettable Parameters of an Axisymmetric Large-Volume Droplet on a Microstructured Surface in Gravity

In this study, a numerical model was developed to predict the wettable parameters of an axisymmetric large-volume droplet on a microstructured surface in gravity. We defined a droplet with the Bond number Bo>0.1 as a large-volume droplet. Bo was calculated by using the equation Bo=ρlgγlv3V4π23 where ρl is the density of liquid, γlv is the liquid-vapor interfacial tension, g is the gravity acceleration and V is the droplet volume. The volume of a large-volume water droplet was larger than 2.7 μL. By using the total energy minimization and the arc differential method of the Bashforth-Adams equation, we got the profile, the apparent contact angle and the contact circle diameter of an axisymmetric large-volume droplet in gravity on a microstructured horizontal plane and the external spherical surface. The predictions of our model have a less than 3% error rate when compared to experiments. Our model is much more accurate than previous ellipsoidal models. In addition, our model calculates much more quickly than previous models because of the use of the arc differential method of the Bashforth-Adams equation. It shows promise for use in the design and fabrication of microfluidic devices.

Pore-Level Multiphase Simulations of Realistic Distillation Membranes for Water Desalination

Membrane distillation (MD) is a thermally driven separation process that is operated below boiling point. Since the performance of MD modules is still comparatively low, current research aims to improve the understanding of the membrane structure and its underlying mechanisms at the pore level. Based on existing realistic 3D membrane geometries (up to 0.5 billion voxels with 39nm resolution) obtained from ptychographic X-ray computed tomography, the D3Q27 lattice Boltzmann (LB) method was used to investigate the interaction of the liquid and gaseous phase with the porous membrane material. In particular, the Shan and Chen multi-phase model was used to simulate multi-phase flow at the pore level. We investigated the liquid entry pressure of different membrane samples and analysed the influence of different micropillar structures on the Wenzel and Cassie-Baxter state of water droplets on rough hydrophobic surfaces. Moreover, we calculated the liquid entry pressure required for entering the membrane pores and extracted realistic water contact surfaces for different membrane samples. The influence of the micropillars and flow on the water-membrane contact surface was investigated. Finally, we determined the air-water interface within a partially saturated membrane, finding that the droplet size and distribution correlated with the porosity of the membrane.

Sessile Drop Method: Critical Analysis and Optimization for Measuring the Contact Angle of an Ion-Exchange Membrane Surface

The contact angle between a membrane surface and a waterdrop lying on its surface provides important information about the hydrophilicity/hydrophobicity of the membrane. This method is well-developed for solid non-swelling materials. However, ion-exchange membranes (IEMs) are gel-like solids that swell in liquids. When an IEM is exposed to air, its degree of swelling changes rapidly, making it difficult to measure the contact angle. In this paper, we examine the known experience of measuring contact angles and suggest a simple equipment that allows the membrane to remain swollen during measurements. An optimized protocol makes it possible to obtain reliable and reproducible results. Measuring parameters such as drop size, water dosing speed and others are optimized. Contact angle measurements are shown for a large number of commercial membranes. These data are supplemented with values from other surface characteristics from optical and profilometric measurements.

Analyzing light-structuring features of droplet lenses on liquid-repelling surfaces

The complete understanding of the formation of seemingly levitating droplets on liquid-repelling surfaces provides the basis for further development of applications requiring friction-free liquid transport. For the investigation of these droplets and, thereby, the underlying surface properties, standard techniques typically only reveal a fraction of droplet or surface information. Here, we propose to exploit the light-shaping features of liquid droplets when interpreted as thick biconvex elliptical lenses. This approach has the potential to decode a plethora of droplet information from a passing laser beam, by transforming the information into a structured light field. Here, we explore this potential by analyzing the three-dimensional intensity structures sculpted by the droplet lenses, revealing the transfer of the characteristics of the underlying liquid-repelling effect onto the light field. As illustrative complementary examples, we study droplet lenses formed on a non-wetting Taro (Colocasia esculenta) leaf surface and by the Leidenfrost effect on a heated plate. Our approach may reveal even typically "invisible" droplet properties as the refractive index or internal flow dynamics and, hence, will be of interest to augment conventional tools for droplet and surface investigation.

Equilibrium droplet shapes on chemically patterned surfaces: theoretical calculation, phase-field simulation, and experiments

HYPOTHESIS

Droplet wetting on a solid substrate is affected by the surface heterogeneity. Introducing patterned wettability on the solid substrate is expected to engender anisotropic wetting morphologies, thereby manipulating droplet wetting behaviors. However, when the droplet size is comparable with that of the surface heterogeneity, the wetting morphologies cannot be depicted by the quintessential Cassie's theory but should be possible to be predicted from the perspective of thermodynamics via surface energy minimization.

METHODS

Here, we investigate the equilibrium droplet shapes on chemically patterned substrates by using an analytical model, phase-field simulations, and experiments. The former two methods are sharp and diffuse interface treatments, respectively, which both are based on minimizing the free energy of the system. The experimental results are obtained by depositing droplets on chemically patterned glass substrates.

FINDINGS

Various anisotropic wetting shapes are found from the three methods. Excellent agreement is observed between different methods, showing the possibility to quantify the anisotropic wetting droplet morphologies on patterned substrates by present methods. We also address a series of non-rotationally symmetric droplet shapes, which is the first resport about these special wetting morphologies. Furthermore, we reveal the anisotropic wetting shapes in a quasi-equilibrium evaporation process.

Modelling Sessile Droplet Profile Using Asymmetrical Ellipses

Modelling the profile of a liquid droplet has been a mainstream technique for researchers to study the physical properties of a liquid. This study proposes a facile modelling approach using an elliptic model to generate the profile of sessile droplets, with MATLAB as the simulation environment. The concept of the elliptic method is simple and easy to use. Only three specific points on the droplet are needed to generate the complete theoretical droplet profile along with its critical parameters such as volume, surface area, height, and contact radius. In addition, we introduced fitting coefficients to accurately determine the contact angle and surface tension of a droplet. Droplet volumes ranging from 1 to 300 µL were chosen for this investigation, with contact angles ranging from 90° to 180°. Our proposed method was also applied to images of actual water droplets with good results. This study demonstrates that the elliptic method is in excellent agreement with the Young–Laplace equation and can be used for rapid and accurate approximation of liquid droplet profiles to determine the surface tension and contact angle.

Hydrodynamic constraints on the energy efficiency of droplet electricity generators

Electric energy generation from falling droplets has seen a hundred-fold rise in efficiency over the past few years. However, even these newest devices can only extract a small portion of the droplet energy. In this paper, we theoretically investigate the contributions of hydrodynamic and electric losses in limiting the efficiency of droplet electricity generators (DEG). We restrict our analysis to cases where the droplet contacts the electrode at maximum spread, which was observed to maximize the DEG efficiency. Herein, the electro-mechanical energy conversion occurs during the recoil that immediately follows droplet impact. We then identify three limits on existing droplet electric generators: (i) the impingement velocity is limited in order to maintain the droplet integrity; (ii) much of droplet mechanical energy is squandered in overcoming viscous shear force with the substrate; (iii) insufficient electrical charge of the substrate. Of all these effects, we found that up to 83% of the total energy available was lost by viscous dissipation during spreading. Minimizing this loss by using cascaded DEG devices to reduce the droplet kinetic energy may increase future devices efficiency beyond 10%.

Wetting of electrospun nylon-11 fibers and mats

Wetting of electrospun mats plays a huge role in tissue engineering and filtration applications. However, it is challenging to trace the interrelation between the wetting of individual nano-sized fibers and the macroscopic electrospun mat. Here we measured the wetting of different nylon-11 samples – solution-cast films, electrospun fibers deposited onto a substrate, and free-standing mats. With electrospun nylon-11 on aluminium foil, we traced the dependence of the wetting contact angle on the fibers' surface density (substrate coverage). When the coverage was low, the contact angle increased almost linearly with it. At ∼17–20% coverage, the contact angle achieved its maximum of 124 ± 7°, which matched the contact angle of a non-woven electrospun mat, 126 ± 2°. Our results highlight the importance of the outermost layer of fibers for the wetting of electrospun mats.

When the surface density of electrospun nylon-11 fibers on aluminium increases, it causes a two-stage change in the wetting behaviour.

The Shape of Heavy Droplets on Superhydrophobic Surfaces

An analytical model is developed to describe the shape of heavy droplets on solid surfaces with arbitrary wetting properties (corresponding to the contact angles ranging from 0 to 180°). This model, based on a surface of revolution by rotating two elliptic arcs, reduces to the ellipsoid model for a hydrophilic case. Experimental measurements are also conducted to verify the model. It shows that the mean curvature distribution of the developed model agrees well with that of real droplets on hydrophobic surfaces, even on superhydrophobic surfaces. For water droplets with a volume up to 1000 μL on superhydrophobic surfaces having a 162° contact angle, the errors of the predicted heights, maximum radius, and wetting radius using this model are less than 1.7%, which suggests the capability of this model in studying the wettability of heavy droplets. This model provides an accurate theoretical basis for designing and controlling the spread, transport, condensation, and evaporation of heavy droplets on superhydrophobic surfaces.

Moldless Printing of Silicone Lenses With Embedded Nanostructured Optical Filters

Optical lenses are among the oldest technological innovations (3000 years ago) and they have enabled a multitude of applications in healthcare and in our daily lives. The primary function of optical lenses has changed little over time; they serve mainly as a light-collection (e.g. reflected, transmitted, diffracted) element, and the wavelength and/or intensity of the collected light is usually manipulated by coupling with various external optical filter elements or coatings. This generally results in losses associated with multiple interfacial reflections, and increases the complexity of design and construction. In this work we introduce a change in this paradigm, by integrating both light-shaping and image magnification into a single lens element using a moldless procedure that takes advantage of the physical and optical properties of mesoporous silicon (PSi) photonic crystal nanostructures. Casting of a liquid poly(dimethyl) siloxane (PDMS) pre-polymer solution onto a PSi film generates a droplet with contact angle that is readily controlled by the silicon nanostructure, and adhesion of the cured polymer to the PSi photonic crystal allows preparation of lightweight (10 mg) freestanding lenses (4.7 mm focal length) with an embedded optical component (e.g. optical rugate filter, resonant cavity, distributed Bragg reflector). Our fabrication process shows excellent reliability (yield 95%) and low cost and we expect our lens to have implications in a wide range of applications. As a proof-of-concept, using a single monolithic lens/filter element we demonstrate: fluorescence imaging of isolated human cancer cells with rejection of the blue excitation light, through a lens that is self-adhered to a commercial smartphone; shaping the emission spectrum of a white light emitting diode (LED) to tune the color from red through blue; and selection of a narrow wavelength band (bandwidth 5 nm) from a fluorescent molecular probe.

Investigation of Single and Binary of “Sandwich” Type Convex Liquid Capillary Bridges, Stretched between Two Flat Surfaces (Experimental Approach)

The interest to monophasic liquid capillary bridges (CB) has a long history. These shapes are attractive not only because of their interesting surface properties but also because of the possibility of their behavior to be analytically predicted by the equations of differential geometry. In the current paper we extend our previous studies by implementation of an approach for prediction of liquid gravityless CB behavior during their quasi-static stretching. It was found, that a simple linear relation, h r m ~ ln R r m , is valid the case of good wetting, 0° ≤ θ ≤ 90°, where h is the height of CB, R is the radius at the contact surface, rm is the CB waist radius, and θ is the solid/liquid (static, receding) contact angle. We experimentally studied the geometrical properties evolution of monophasic cedar oil and water CBs between two glass plates during their quasi-static (stepwise with equilibration after each step for 1–2 min.) stretching. In addition, we investigated a binary CB of a new type, resembling “sandwich”. There, due to the stronger glass wetting by the water, the oil phase is adhered at the water/gas interface, partially engulfed with a tendency to stand in the zone around the waist (minimal surface energy). During the stretching, it tends to replace the water in the CB waist region. A simple mechanism for interaction of the two immiscible liquids leading to creation of “sandwich” like binary structures, is proposed. Experiments of capillary bridges (CB) stretching between two flat surfaces have been carried for all liquids at different volume proportions. The investigation is extended also to identification of CB profile generatrix shape. We experimentally found that for monophasic CB, it can be described by a circle during the quasi-static stretching. If the CB height is increased, before the rupture, the shape evolves consecutively to an ellipse, parabola, or possibly to a hyperbola. The investigated binary CB evolves a similar way. Conclusions are drawn and directions for further investigations are given.

Shaping and transporting diamagnetic sessile drops

Electromagnetic fields are commonly used to control small quantities of fluids in microfluidics and digital microfluidics. Magnetic control techniques are less well studied than their electric counterparts, with only a few investigations into liquid diamagnetism. The ratio of magnetic to surface energy (magnetic Bond number B m ) is an order of magnitude smaller for diamagnetic drops ( B m ≈ - 0.3 at 1.2 T applied field) than for paramagnetic drops ( B m ≈ 9.0 at 1.2 T applied field). This weaker interaction between the magnetic field and the diamagnetic drop has led to the phenomenon being overlooked in digital microfluidics. Here, we investigate shaping and transport of diamagnetic drops using magnetostatic fields. Our findings highlight how diamagnetic fluids can be used as a novel tool in the toolbox of microfluidics and digital microfluidics.

Colour compound lenses for a portable fluorescence microscope

In this article, we demonstrated a handheld smartphone fluorescence microscope (HSFM) that integrates dual-functional polymer lenses with a smartphone. The HSFM consists of a smartphone, a field-portable illumination source, and a dual-functional polymer lens that performs both optical imaging and filtering. Therefore, compared with the existing smartphone fluorescence microscope, the HSFM does not need any additional optical filters. Although fluorescence imaging has traditionally played an indispensable role in biomedical and clinical applications due to its high specificity and sensitivity for detecting cells, proteins, DNAs/RNAs, etc., the bulky elements of conventional fluorescence microscopes make them inconvenient for use in point-of-care diagnosis. The HSFM demonstrated in this article solves this problem by providing a multifunctional, miniature, small-form-factor fluorescence module. This multifunctional fluorescence module can be seamlessly attached to any smartphone camera for both bright-field and fluorescence imaging at cellular-scale resolutions without the use of additional bulky lenses/filters; in fact, the HSFM achieves magnification and light filtration using a single lens. Cell and tissue observation, cell counting, plasmid transfection evaluation, and superoxide production analysis were performed using this device. Notably, this lens system has the unique capability of functioning with numerous smartphones, irrespective of the smartphone model and the camera technology housed within each device. As such, this HSFM has the potential to pave the way for real-time point-of-care diagnosis and opens up countless possibilities for personalized medicine.

Solvodynamic Printing As A High Resolution Printing Method

Printing techniques are becoming increasingly prevalent in modern manufacturing. However, its biggest drawback is the limit in printing resolution. In this paper, we present solvodynamic printing as a novel printing system which aims to improve print resolution by incorporating an additional immiscible carrier solvent into the ink delivery system. The resolution is improved due to the solvent-solvent interactions between the ink and the carrier solvent which alter the contact angle of the ink on the substrate and limit the printed feature size. We demonstrate the proof of concept of solvodynamic printing by printing silver nanoparticle inks on a polyethylene naphthalate substrate. Silver nanoparticle tracks with widths of 35.2 ± 7.0 μm were achieved using a 300 μm nozzle. This is equivalent to 11.7 ± 2.3% of the nozzle diameter. The result shows great potential in solvodynamic printing as not many modern printing techniques can achieve such nozzle to feature size ratios.

Numerical Simulation of Sessile Droplet Spreading and Penetration on Porous Substrates

Numerical simulation is performed for sessile droplet spreading and penetration on porous surfaces in this study. The volume of the fluid model is used to accurately track the droplet deformation, and the pressure implicit split operator algorithm is presented to calculate the coupling of the droplet pressure and velocity. The effects of droplet characteristics, porous media characteristics, and the wettability of liquid/porous media on sessile droplet spreading and permeation are investigated in detail. The studied problem can be characterized by four control parameters: the Bond number, Darcy number, static equilibrium contact angle, and ratio between the initial diameter of the droplet and the particle diameter in the porous substrate. The numerical simulations show that droplet spreading and penetration are competitive with each other and dependent on the above four dimensionless parameters. The results obtained in this work are of benefit to provide deep insights into the dynamic behavior of sessile droplet on porous substrates.

Gibbsian Thermodynamic Study of Capillary Meniscus Depth

In the presence of gravity or other external fields, liquid surface curvature deviates from a spherical shape and the surface configuration can be found by numerical integration of the Young–Laplace equation and the typical initial point for integration is the apex of the interface. The meniscus shape in large Bond number systems, which have the central portion of the interface flattened, cannot be determined with the apex as the initial point for integration. Here we find the depth of capillary menisci by considering an initial point for integration to be at the three-phase-contact-line (TPCL) and evaluate the curvature at the TPCL by free energy analysis and inspect the effect of different parameters on the interface shape. A new parameter—which is the deviation of equilibrium curvature at the TPCL from the spherical shape (SR)—is introduced and inspected and it was found that at a Bond number of 13 the maximum deviation, approximately 0.8 of spherical curvature, takes place while for large enough Bond numbers the curvature at the three-phase contact line is near the spherical shape (0.95 < SR < 1). A potential application of this approach is to measure the capillary rise at the TPCL to find the surface tension in high Bond number systems such as those with low surface/interfacial tensions.

Molecular Motors Govern Liquidlike Ordering and Fusion Dynamics of Bacterial Colonies

Bacteria can adjust the structure of colonies and biofilms to enhance their survival rate under external stress. Here, we explore the link between bacterial interaction forces and colony structure. We show that the activity of extracellular pilus motors enhances local ordering and accelerates fusion dynamics of bacterial colonies. The radial distribution function of mature colonies shows local fluidlike order. The degree and dynamics of ordering are dependent on motor activity. At a larger scale, the fusion dynamics of two colonies shows liquidlike behavior whereby motor activity strongly affects surface tension and viscosity.

Modeling of Droplet Impact onto Polarized and Nonpolarized Dielectric Surfaces

This paper is concerned with simulation of the droplet impact on a dielectric surface, referred to as the dynamic electrowetting-on-dielectric (DEWOD). In particular, we seek to shed more light on the fundamental processes occurring during the impact of an electrically conducting droplet onto a dielectric surface with and without an applied voltage. The liquid in the droplet is an ionic conductor (a leaky dielectric). This work employs an approach based on Cahn-Hilliard-Navier-Stokes (CHNS) modeling. The simulations are validated by predicting the equilibrium contact angle, droplet oscillations, and charge density estimation. Then, four cases of droplet impact are studied, namely, the impact onto a surface with no voltage applied and the impacts onto the surfaces with 2, 4, and 6 kV applied. The modeling results of water droplet impact allow for direct comparison with the experimental results reported by Lee et al. [ Langmuir 2013, 29, 7758]. The results reveal the electric field, the body forces acting on the droplet, the velocity and pressure fields inside and outside the droplet, as well as the free charge density and the electric energy density. The model predicts the droplet shape evolution (e.g., the spreading distance over the surface and the rebound height) under different conditions that are consistent with the experimental observations. Thus, our findings provide new qualitative and quantitative insights into the droplet manipulation that can be used in novel applications of the DEWOD phenomenon.

Numerical Study for a Large-Volume Droplet on the Dual-Rough Surface: Apparent Contact Angle, Contact Angle Hysteresis, and Transition Barrier

The profile, apparent contact angle (ACA), contact angle hysteresis (CAH), and wetting state transmission energy barrier (WSTEB) are important static and dynamic properties of a large-volume droplet on the hierarchical surface. Understanding them can provide us with important insights into functional surfaces and promote the application in corresponding areas. In this paper, we establish three theoretical models (models 1-3) and the corresponding numerical methods, which were obtained by the free energy minimization and the nonlinear optimization algorithm, to predict the profile, ACA, CAH, and WSTEB of a large-volume droplet on the horizontal regular dual-rough surface. In consideration of the gravity, the energy barrier on the contact circle, the dual heterogeneous structures and their roughness on the surface, the models are more universal and accurate than the previous models. It showed that the predictions of the models were in good agreement with the results from the experiment or literature. The models are promising to become novel design approaches of functional surfaces, which are frequently applied in microfluidic chips, water self-catchment system, and dropwise condensation heat transfer system.

The Self-Assembly of Cellulose Nanocrystals: Hierarchical Design of Visual Appearance

By controlling the interaction of biological building blocks at the nanoscale, natural photonic nanostructures have been optimized to produce intense coloration. Inspired by such biological nanostructures, the possibility to design the visual appearance of a material by guiding the hierarchical self-assembly of its constituent components, ideally using natural materials, is an attractive route for rationally designed, sustainable manufacturing. Within the large variety of biological building blocks, cellulose nanocrystals are one of the most promising biosourced materials, primarily for their abundance, biocompatibility, and ability to readily organize into photonic structures. Here, the mechanisms underlying the formation of iridescent, vividly colored materials from colloidal liquid crystal suspensions of cellulose nanocrystals are reviewed and recent advances in structural control over the hierarchical assembly process are reported as a toolbox for the design of sophisticated optical materials.

The measurement of the surface energy of solids using a laboratory drop tower

This work presents a technique for the study and measurement of the interfacial energies of solid-liquid-gas systems. The instrument and the evaluation method for the measurements obtained by it, allow the analysis of the energy changes of sessile drops submitted to microgravity. A mathematical model based on the thermodynamic of wetting is applied to evaluate the interfacial energies as a function of the drop shape changes due to the effect of the release of gravitation during the experiment. The presented model bases on the thermodynamic equilibrium of the interfaces and not on the balance of bi-dimensional tensors on the contour line. For this reason, the model does not follow Young's equation as the current surface wetting characterization techniques usually do.

Drops on a Superhydrophobic Hole Hanging On under Evaporation

Drops with larger volumes placed over a superhydrophobic (SH) surface with a hole do not fall through unless they are evaporated to a size that is small enough. This feature offers the ability to preconcentrate samples for biochemical analysis. In this work, the influence of pinning on the behavior of drops placed on a 0.1 mm thick SH substrate with a 2 mm diameter hole as they evaporated was investigated. With 16 μL of water dispensed, the sessile drop component volume was initially higher than that of the overhanging drop component and maintained this until the later stages where almost identical shapes were attained and full evaporation was achieved without falling off the hole. With 15 μL of water dispensed, the volume of the sessile drop was initially higher than that of the overhanging drop component but the liquid body was able to squeeze through the hole after 180 s due to the contact line not having sufficient pinning strength when it encountered the edge of the hole. This resulted in the liquid body either falling through the hole or remaining pinned with an oval-like shape. When it did not fall-off, the liquid body had volume and contact angle characteristics for the sessile drop and overhanging drop components that were reversed. In the later stages, however, nearly identical shapes were again attained and full evaporation was achieved without falling off the hole. The effects of pinning, despite the substrate being SH, offer another path toward achieving practical outcomes with liquid bodies without the need for chemical surface functionalization. Similarities and differences could be seen in the behavior of a sessile drop on a SH plate that was inclined at 30° to the horizontal and evaporated.

Spline Based Shape Prediction and Analysis of Uniformly Rotating Sessile and Pendant Droplets

Prediction and analysis of the shapes of liquid-vapor interface of droplets under the influence of external forces is critical for various applications. In this regard, a geometric model that can capture the macroscopic shape of the liquid-vapor interface in tandem with the subtleties near the contact line, particularly in the regime where the droplet shape deviates significantly from the idealized spherical cap geometry, is desirable. Such deviations may occur when external forces such as gravity or centrifugal dominate over the surface tension force. Here we use vector parametrized cubic spline representation for axisymmetric fluid-fluid interfaces along with a novel thermodynamic free energy minimization based heuristic to determine the shape of liquid-vapor interface of droplets. We show that the current scheme can easily predict the shapes of sessile and pendant droplets under the action of centrifugal force over a broad range of surface contact angle values and droplet sizes encountered in practical applications. Finally, we show that the cubic spline based modeling approach makes it convenient to perform the inverse analysis as well, i.e., predict interfacial properties from the shape of a droplet under the action of various types of external forces including gravity and centrifugal. We believe that this versatile modeling approach can be extended to model droplet shapes under various other external forces including electric and acoustic. In addition, the simple shape analysis approach is also promising for the development of inexpensive interfacial analysis tools such as surface tensiometers.

Empirical Formulae in Correlating Droplet Shape and Contact Angle

In contact angle measurements, direct identification of the contact angles from images taken from a goniometer suffers from errors caused by optical scatterings. Contact angles can be more accurately identified by the height and width of the droplet. Spherical dome is a simple model used to correlate the contact angles to the droplet shape; however, it features intrinsic errors caused by gravity-induced shape deformation. This paper demonstrates a simple method of obtaining an empirical formula, determined from experiments, to correct the gravity-induced error in the spherical dome model for contact angle calculations. A series of contact angles, heights, and surface contact widths are simultaneously collected for a large amount of samples, and the contact angles are also calculated using the spherical dome model. The experimental data are compared with those obtained from the spherical dome model to acquire an empirical formula for contact angles. Compared with the spherical dome model, the empirical formula can reduce the average errors of the contact angle from –16.3 % to 0.18 %. Furthermore, the same method can be used to correct the gravity errors in the spherical dome for the volume (calculated by height and width), height (calculated by contact angle and volume), and width (calculated by contact angle and volume), and the spherical dome errors can be reduced from –20.9 %, 24.6 %, and –4.8 % to 2 %, –0.13 %, and –0.6 %, respectively. Our method is generic and applicable for all kinds of solvent and substrates, and the derived empirical formulae can be directly used for water droplets on any substrate.

An algorithm for selecting the most accurate protocol for contact angle measurement by drop shape analysis

In this study, an error analysis is performed to study real water drop images and the corresponding numerically generated water drop profiles for three widely used static contact angle algorithms: the circle- and ellipse-fitting algorithms and the axisymmetric drop shape analysis-profile (ADSA-P) algorithm. The results demonstrate the accuracy of the numerically generated drop profiles based on the Laplace equation. A significant number of water drop profiles with different volumes, contact angles, and noise levels are generated, and the influences of the three factors on the accuracies of the three algorithms are systematically investigated. The results reveal that the above-mentioned three algorithms are complementary. In fact, the circle- and ellipse-fitting algorithms show low errors and are highly resistant to noise for water drops with small/medium volumes and contact angles, while for water drop with large volumes and contact angles just the ADSA-P algorithm can meet accuracy requirement. However, this algorithm introduces significant errors in the case of small volumes and contact angles because of its high sensitivity to noise. The critical water drop volumes of the circle- and ellipse-fitting algorithms corresponding to a certain contact angle error are obtained through a significant amount of computation. To improve the precision of the static contact angle measurement, a more accurate algorithm based on a combination of the three algorithms is proposed. Following a systematic investigation, the algorithm selection rule is described in detail, while maintaining the advantages of the three algorithms and overcoming their deficiencies. In general, static contact angles over the entire hydrophobicity range can be accurately evaluated using the proposed algorithm. The ease of erroneous judgment in static contact angle measurements is avoided. The proposed algorithm is validated by a static contact angle evaluation of real and numerically generated water drop images with different hydrophobicity values and volumes.

Ultralow interfacial tensions of aqueous two-phase systems measured using drop shape

Aqueous solutions of different polymers can separate and form aqueous two-phase systems (ATPS). ATPS provide an aqueous, biocompatible, and mild environment for separation and fractionation of biomolecules. The interfacial tension between the two aqueous phases plays a major role in ATPS-mediated partition of biomolecules. Because of the structure of the two aqueous phases, the interfacial tensions between the phases can be 3-4 orders of magnitude smaller than conventional fluid-liquid systems: ∼1-100 μJ/m(2) for ATPS compared to ∼72 mJ/m(2) for the water-vapor interface. This poses a major challenge for the experimental measurements of reproducible interfacial tension data for these systems. We address the need for precise determination of ultralow interfacial tensions by systematically studying a series of polymeric ATPS comprising of polyethylene glycol (PEG) and dextran (DEX) as the phase-forming polymers. Sessile and pendant drops of the denser DEX phase are formed within the immersion PEG phase. An axisymmetric drop shape analysis (ADSA) is used to determine interfacial tensions of eight different ATPS. Specific criteria are used to reproducibly determine ultralow interfacial tensions of the ATPS from pendant and sessile drops. Importantly, for a given ATPS, pendant drop and sessile drop experiments return values within 0.001 mJ/m(2) indicating reliability of our measurements. Then, the pendant drop technique is used to measure interfacial tensions of all eight ATPS. Our measured values range from 0.012 ± 0.001 mJ/m(2) to 0.381 ± 0.006 mJ/m(2) and vary with the concentration of polymers in equilibrated phases of ATPS. Measurements of ultralow interfacial tensions with such reproducibility will broadly benefit studies involving partition of different biomolecules in ATPS and elucidate the critical effect of interfacial tension.

Final state of a perturbed liquid film inside a container under the effect of solid-liquid molecular forces and gravity

We investigate theoretically the possible final stationary configurations that can be reached by a laterally confined uniform liquid film inside a container. The liquid is under the action of gravity, surface tension, and the molecular interaction with the solid substrate. We study the case when the container is in an upright position as well as when it is turned upside down. The governing parameters of the problem are the initial thickness of the film, the size of the recipient that contains the liquid, and a dimensionless number that quantifies the relative strength of gravity with respect to the molecular interaction. The uniform film is always a possible final state and depending on the value of the parameters, up to three different additional final states may exist, each one consisting in a droplet surrounded by a thin film. We derive analytical expressions for the energy of these possible final configurations and from these we analyze which state is indeed reached. A uniform thin film may show three different behaviors after a perturbation: The system recovers its initial shape after any perturbation, the fluid evolves towards a drop (if more than one is possible, it tends toward that with the thinnest precursor film) for any perturbation, or the system ends as a uniform film or a drop depending on the details of the perturbation.

Evaporation of droplets of surfactant solutions

The simultaneous spreading and evaporation of droplets of aqueous trisiloxane (superspreader) solutions onto a hydrophobic substrate has been studied both experimentally, using a video-microscopy technique, and theoretically. The experiments have been carried out over a wide range of surfactant concentration, temperature, and relative humidity. Similar to pure liquids, four different stages have been observed: the initial one corresponds to spreading until the contact angle, θ, reaches the value of the static advancing contact angle, θad. Duration of this stage is rather short, and the evaporation during this stage can be neglected. The evaporation is essential during the next three stages. The next stage after the spreading, which is referred to herein as the first stage, takes place at constant perimeter and ends when θ reaches the static receding contact angle, θr. During the next, second stage, the perimeter decreases at constant contact angle θ = θr for surfactant concentration above the critical wetting concentration (CWC). The static receding contact angle decreases during the second stage for concentrations below CWC because the concentration increases due to the evaporation. During the final stage both the perimeter and the contact angle decrease. In what follows, we consider only the longest stages I and II. The developed theory predicts universal curves for the contact angle dependency on time during the first stage, and for the droplet perimeter on time during the second stage. A very good agreement between theory and experimental data has been found for the first stage of evaporation, and for the second stage for concentrations above CWC; however, some deviations were found for concentrations below CWC.

A robust polynomial fitting approach for contact angle measurements

Polynomial fitting to drop profile offers an alternative to well-established drop shape techniques for contact angle measurements from sessile drops without a need for liquid physical properties. Here, we evaluate the accuracy of contact angles resulting from fitting polynomials of various orders to drop profiles in a Cartesian coordinate system, over a wide range of contact angles. We develop a differentiator mask to automatically find a range of required number of pixels from a drop profile over which a stable contact angle is obtained. The polynomial order that results in the longest stable regime and returns the lowest standard error and the highest correlation coefficient is selected to determine drop contact angles. We find that, unlike previous reports, a single polynomial order cannot be used to accurately estimate a wide range of contact angles and that a larger order polynomial is needed for drops with larger contact angles. Our method returns contact angles with an accuracy of <0.4° for solid-liquid systems with θ < ~60°. This compares well with the axisymmetric drop shape analysis-profile (ADSA-P) methodology results. Above about 60°, we observe significant deviations from ADSA-P results, most likely because a polynomial cannot trace the profile of drops with close-to-vertical and vertical segments. To overcome this limitation, we implement a new polynomial fitting scheme by transforming drop profiles into polar coordinate system. This eliminates the well-known problem with high curvature drops and enables estimating contact angles in a wide range with a fourth-order polynomial. We show that this approach returns dynamic contact angles with less than 0.7° error as compared to ADSA-P, for the solid-liquid systems tested. This new approach is a powerful alternative to drop shape techniques for estimating contact angles of drops regardless of drop symmetry and without a need for liquid properties.