Drop Surface Research Articles

Influence of interface on nondeformable micropolar drop migration

Abstract In this article, an analytical approach is considered to study the issue of specifying Stokesian motion due to a micropolar sphere drop translating at a concentric instantaneous position within a spherical fluid–fluid interface that divides two immiscible fluids, one of which is bounded and the other is unbounded. Here, the focus is on the situation where there are two microstructure-related fluid phases (micropolar fluids) out of the three. The motion is considered to have low Reynolds numbers; thus, the drop’s surface and fluid–fluid interface have insignificant deformation. General solutions to the slow axisymmetric motion of the micropolar/viscous fluid in a spherical coordinate system are obtained based on a concentric position. Boundary conditions are fulfilled at the drop’s surface and the fluid–fluid interface. Findings indicate that the normalised hydrodynamic force increases monotonically as the droplet-to-interface radius ratio increases, acting on a moving micropolar sphere droplet and becoming unlimited when the drop’s surface touches the fluid–fluid interface. The numerical findings for the normalised force operating on the micropolar sphere droplet at different values of the suitable parameters are introduced in both graphical and tabular form. Our numerical findings are compared with the suitable data for the special cases stated in the literature. The current investigation of the study has practical applications in many domains of industrial, biological, medicinal, and natural processes, for example, liquid crystals, polymeric suspensions, muddy fluids, liquid–liquid extraction, raindrop formation, blood cells moving through a vein or artery, suspension rheology, sedimentation, and coagulation.

3D-3C measurements of flow reversal in small sessile drops in shear flow

Sessile drops play an important role in nature and the operation of many technical and biological systems as for instance fuel cells, cleaning processes, lab-on-a-chip devices and single-cell analysis. Nonetheless, their dynamic behavior in a shear flow is still not fully understood (e. g. detachment mechanism). Challenges exist regarding the precise simulation of two-phase flows as well as difficulties in conducting flow measurements with sufficient temporal resolution of more than 1 kHz. In this article, we present the first three-dimensional flow measurements in strongly oscillating drops stemming from a shear flow by using a monocular 3D localization microscope based on a Double-Helix Point Spread Function combined with Particle Tracking Velocimetry. The high temporal resolution and the large measurement volume - in terms of microscopy - make it possible to measure the time- and phase-averaged flow in small drops with Bond numbers (Bo) smaller than 1. Water drops were placed in an air flow channel and measurements were conducted for Reynolds numbers (Red) from about 750 to 1700. Our measurements show that the results of previous investigations for drops with Bo>1 concerning vortex pattern and flow reversal inside the drop apply for smaller drops as well. In addition, we are able to reveal the three-dimensional flow structure and multiple vortex-pattern in time and space. We discover a periodic 3D vortical flow pattern that corresponds to the first and second eigenfrequency of the drop. Moreover, we demonstrate the potential of adaptive optics to correct measurement errors stemming from time-varying light refraction when conducting measurements through the fluctuating drop surface, in particular for opaque substrates. The results may help in understanding the coupling of inner and outer flow for sessile drops in shear flow which allows for an analysis of the onset motion of these drops, i.e. drop removal. Removal of sessile drops plays a crucial role in many applications, which includes among other things the water management of fuel cells where small drops with Bo<1 predominantly occur.

Parametric oscillations of the sessile drop

Waves are formed on the surface of a sessile drop driven through substrate vibrations oriented at a slanting angle from the normal. A mathematical model is derived, which leads to an infinite system of coupled Mathieu equations governing the wave dynamics that are solved using Floquet theory. The spatial structure of the waves is described by the mode number pair $[\ell,m]$ , where $\ell$ and $m$ are the polar and azimuthal mode numbers, respectively. Limiting cases corresponding to horizontal and vertical vibrations are discussed with predictions agreeing well with prior literature. We focus our results on three drop motions – (1) harmonic $[1,1]$ rocking mode, (2) harmonic $[2,0]$ pumping mode, and (3) subharmonic rocking $[1,1]$ mode – as they depend upon the slanting angle, static contact angle, and contact-line conditions, which we assume to be either pinned or freely moving with fixed contact angle. New theoretical predictions are tested through experiments over a range of parameters, showing good agreement.

Polymer-Mediated Crack Suppression in Deposit of Nanoellipsoids.

Uniform distribution of particles and crack suppression in dried particulate deposits are major challenges for applications in coating and printing technologies. To address this, we investigated the impact of the addition of a water-soluble polymer, poly(vinyl alcohol) (PVA), on the evaporative self-assembly and kinetics of crack formation in deposits of anisotropic colloids. The fluid flow inside the drying drop is significantly altered due to polymer-mediated adsorption of ellipsoids to the drop surface. The competition between outward capillary flow and Marangoni flow developed in the drying colloid-polymer dispersion drop dictates the distribution of particles in the final dried patterns. The deposits formed by drying drops of ellipsoids dispersed in PVA solutions show three distinct patterns depending on the PVA concentration. A transition from ring-like deposit to uniform deposition with intermittent cracks was observed for a critical PVA concentration of 0.3 wt %. Radial as well as annular cracks were observed in the case of no PVA, while only annular cracks were formed in the dried patterns as the PVA content increased, thus indicating the change of capillary stresses in the films. Analyses of the particle dynamics and deposition patterns confirmed the effectiveness of gelation-driven crack prevention. This method offers a facile and straightforward solution for obtaining crack-free coatings in drying-mediated colloidal nanoparticle assembly.

Water-Templated Growth of Interfacial Superglue Polymers for Tunable Thin Films and In Situ Fluid Encapsulation.

Thin polymer films (TPFs) are indispensable elements in numerous technologies ranging from liquid encapsulation to biotechnology to electronics. However, their production typically relies on wet chemistry involving organic solvents or chemical vapor deposition, necessitating elaborate equipment and often harsh conditions. Here, an eco-friendly, fast, and facile synthesis of water-templated interfacial polymers based on cyanoacrylates (superglues, CAs) that yield thin films with tailored properties is demonstrated. Specifically, by exposing a cationic surfactant-laden water surface to cyanoacrylate vapors, surfactant-modulated anionic polymerization produces a manipulable thin polymer film with a thickness growth rate of 8nmmin-1. Furthermore, the shape and color of the film are precisely controlled by the polymerization kinetics, wetting conditions, and/or exposure to patterned light. Using various interfaces as templates for film growth, including the free surface of drops and soap bubbles, the developed method advantageously enables in situ packaging of chemical and biological cargos in liquid phase as well as the encapsulation of gases within solidified bubbles. Simple, versatile, and biocompatible, this technology constitutes a potent platform for programmable coating and soft/smart encapsulation of fluids.

Solar evaporation of liquid marbles with Fe3O4/CNT hybrid nanostructures

HypothesisThrough the rational design of nanomaterial composites, broadband light harvesting and good thermal insulation can be achieved simultaneously to improve the efficiency of water evaporation. ExperimentSolar evaporation experiments were carried out on liquid marbles (LMs) coated with Fe3O4 nanoparticles, carbon nanotubes (CNTs) and hybrid nanomaterials (Fe3O4/CNTs) with different mass ratios of 2:1, 1:1 and 1:2. FindingThe results showed that the mixture of Fe3O4/CNTs enhances the light harvesting ability and solar interfacial evaporation performance. Fe3O4/CNT-LM at the mass ratio of 2:1 case provides the highest evaporation rate of 11.03 μg/s, which is about 1.22 and 1.34 times higher than that of Fe3O4 and CNT, respectively. This high performance is mainly due to the synergistic effect between Fe3O4 nanoparticles and CNTs, as the hybrid nanostructure significantly improves the both photothermal conversion and heat localization capability. Numerical simulation further supports that the composite can concentrate the electromagnetic field and heat at the phase-change interface. This leads to a rapid evaporation of the boundary region. This study provides a novel approach to a three-dimensional interface by assembling nanomaterials on the drop surface to enhance evaporation, which may have far-reaching implications for seawater desalination.

Shaping in the Third Direction: Colloidal Photonic Crystals with Quadratic Surfaces Self-Assembled by Hanging-Drop Method.

High-quality, 3D-shaped, SiO2 colloidal photonic crystals (ellipsoids, hyperboloids, and others) were fabricated by self-assembly. They possess a quadratic surface and are wide-angle-independent, direction-dependent, diffractive reflection crystals. Their size varies between 1 and 5 mm and can be achieved as mechanical-resistant, free-standing, thick (hundreds of ordered layers) objects. High-quality, 3D-shaped, polystyrene inverse-opal photonic superstructures (highly similar to diatom frustules) were synthesized by using an inside infiltration method as wide-angle-independent, reflective diffraction objects. They possess multiple reflection bands given by their special architecture (a torus on the top of an ellipsoid) and by their different sized holes (384 nm and 264 nm). Our hanging-drop self-assembly approach uses setups which deform the shape of an ordinary spherical drop; thus, the colloidal self-assembly takes place on a non-axisymmetric liquid/air interface. The deformed drop surface is a kind of topological interface which changes its shape in time, remaining as a quality template for the self-assembly process. Three-dimensional-shaped colloidal photonic crystals might be used as devices for future spectrophotometers, aspheric or freeform diffracting mirrors, or metasurfaces for experiments regarding space-time curvature analogy.

Bubbling up in a Lab-on-a-Chip: A gravity-driven approach to the formation of polyelectrolyte multilayer capsules and foams

The generation of multi-functional capsules often requires the sequential deposition of different components on the surface of bubbles or drops. Batch-based methods lack fine control over the capsule sizes, including risk of fusion, and cannot ensure identical environments for each capsule. To overcome these issues, different micro/milli-fluidic methods have been developed in the past. However, a major challenge remains in combining an explicit and flexible control over the capsule generation and their residence time in the different solutions within the same device. Using for the first time the example of bubbles covered by layers of oppositely charged polyelectrolytes (PSS/PAH), we introduce an original millifluidic Lab-on-a-Chip device with two novel functions: (1) Size and separation of the bubbles are tuned at constant flow conditions via gas injection through a movible, circular dispense tip into the cross-flow of a rectangular channel. We provide a detailed exploration of the bubbling parameters together with physical justification of the observations. (2) The device exploits gravity to make the generated bubbles rise between horizontally stacked millifluidic chips containing each the controlled flow of a specific polyelectrolyte solution. In analogy with electric circuits, we show how the flow resistance of each chip can be adapted such that bubbles move smoothly between them while avoiding undesired mixing of the solutions. We show first examples of obtained multilayer capsules and discuss their peculiar features, in particular, their outstanding stability with respect to coalescence and dissolution. While our methods use polyelectrolyte assembly on bubbles, they can be readily transferred to other types of solutions or even to drops and particles.

From weakly to strongly nonlinear viscous drop shape oscillations: An analytical and numerical study

Nonlinear axisymmetric shape oscillations of a Newtonian drop in a vacuum are investigated using two different theoretical methods, for fundamental interest and for the significance of the oscillations in transport processes across the drop surface. The extended discontinuous Galerkin method is contrasted to the weakly nonlinear theory. While the former allows large drop surface deformation amplitudes to be analyzed with high precision and drop volume errors below 0.11% even at the largest deformations, the latter provides analytical insight into the origin of quasiperiodic time behavior of the oscillations and reveals the oscillation modes coupled in the nonlinear motion. Results from both methods for moderate initial deformation amplitudes at modes of initial drop deformation m=2, 3, and 4 are in excellent agreement, showing the time asymmetry of the oscillation and the decrease of the oscillation frequency with increasing deformation amplitude. The Fourier power spectra for the first oscillation period exhibit decreased dominant frequencies as compared to the linear results as well as the mode coupling as nonlinear effects. The numerical method is used to compute the oscillatory and damping behavior of viscous drops, as well as the interconversion of kinetic and surface energies during the oscillations at strong initial deformations. Published by the American Physical Society 2024

P‐103: Ultra Fine Drop Volume Measurement Technic using Chromatic Confocal Sensor(CCS) for Quantum Dot Inkjet Printing Process

In this study, ultra fine drop (&lt;10pl) volume measurement technics were developed using chromatic confocal sensor(CCS). A printing pattern was printed on the substrate by printing equipment, and each sensor measures the height of the drop surface and by integrating them, the drop volume could be determined. To evaluate its performance, measurement accuracy, and the repeatability was determined. The measurement accuracy can be obtained by comparing the same drop volume measured by the confocal microscope. For the measurement repeatability, the same drop volume was measured for several times and its maximum and minimum value was used to determine. As a result, CCS showed a good measurement performance with measurement accuracy of more than 0.90 (R 2 in least square) and measurement repeatability of over 0.95.

Estimating sliding drop width via side-view features using recurrent neural networks

High speed side-view videos of sliding drops enable researchers to investigate drop dynamics and surface properties. However, understanding the physics of sliding requires knowledge of the drop width. A front-view perspective of the drop is necessary. In particular, the drop’s width is a crucial parameter owing to its association with the friction force. Incorporating extra cameras or mirrors to monitor changes in the width of drops from a front-view perspective is cumbersome and limits the viewing area. This limitation impedes a comprehensive analysis of sliding drops, especially when they interact with surface defects. Our study explores the use of various regression and multivariate sequence analysis (MSA) models to estimate the drop width at a solid surface solely from side-view videos. This approach eliminates the need to incorporate additional equipment into the experimental setup. In addition, it ensures an unlimited viewing area of sliding drops. The Long Short Term Memory (LSTM) model with a 20 sliding window size has the best performance with the lowest root mean square error (RMSE) of 67 µm. Within the spectrum of drop widths in our dataset, ranging from 1.6 to 4.4 mm, this RMSE indicates that we can predict the width of sliding drops with an error of 2.4%. Furthermore, the applied LSTM model provides a drop width across the whole sliding length of 5 cm, previously unattainable.

Infrared Spectral Emissivity Dynamics of Surfaces Under Water Condensation

AbstractWater condensation on a surface strongly affects its effective emissivity, especially in the atmospheric window, a wavelength range essential for outdoor applications related to energetically passive cooling and heating. The evolution of emissivity of a silicon surface during dropwise and filmwise water deposition is studied. The evolution of the spectral radiative properties shows that the increase in effective emissivity due to the growth of a droplet pattern is steeper than for a growing water film of equivalent thickness. The change of surface emissivity takes place in the first moments of condensation where droplets as small as 10 µm drastically impact the reflectance of the pristine surface. The upper limit of effective emissivity is reached for a droplet radius or film thickness of 50 µm. During dropwise condensation, effective emissivity is weighted by the drop surface coverage and then remains within an asymptotic maximum value of 0.8, while in case of filmwise condensation, it is shown to reach 0.9 corresponding to water emissivity. Micrometer‐scale spatially‐resolved infrared spectral images enable to correlate the spatial variation of spectral properties to the droplet size and localization. Such findings are of interest to the implementation of moisture‐controlled emissivity tuning and radiative sky‐coolers for dew harvesting.

Spontaneous Rise of Hydrogen Microbubbles in Interfacial Gas Evolution Reaction.

Liquid organic hydrogen carrier is a promising option for the transport and storage of hydrogen as a clean energy source. This study examines the stability and behavior of organic drops immobilized on a substrate during an interfacial hydrogen-evolution reaction (HER) at the drop surface and its surrounding aqueous solution. Hydrogen microbubbles form within the drop and rise to the drop apex. The growth rate of the hydrogen in-drop bubble increases with the concentration of the reactant in the surrounding medium. The drop remains stable till the buoyancy acting on the in-drop bubble is large enough to overcome the capillary force and the external viscous drag. The bubble spontaneously rises and carries a portion drop liquid to the solution surface. These spontaneous rising in-drop bubbles are detected in measurements using a high-precision sensor placed on the upper surface of the aqueous solution, reversing the settling phase from phase separation in the reactive emulsion. The finding from this work provides new insights into the behaviors of drops and bubbles in many interfacial gas evolution reactions in clean technologies.

Self-shaping of triglyceride and alkane drops: Similarities and differences

Small emulsion drops typically exhibit spherical shape at positive interfacial tension due to the energy minimization principle. However, in a series of studies (Denkov et al., Nature, 2015, 528, 392–395; Cholakova et al., Nature Phys., 2021, 17, 1050–1055) we showed that alkane droplets stabilized by appropriate saturated long-chain surfactants may spontaneously change their shape upon cooling, morphing into various polyhedra; hexagonal, tetragonal and triangular platelets; rod-like particles and even synthetic swimmers. These deformations are governed by the formation of thin plastic rotator phases adjacent to the drop surface. Although alkanes have numerous industrial applications, they cannot be used in food and pharma related products, in which most often triglyceride molecules are employed. The possibility for self-shaping of triglyceride drops has been demonstrated, but the detailed understanding of the process is currently missing. In the present study, we performed model experiments aimed to reveal the conditions under which the triglyceride emulsion drops may change their shape upon cooling. We show that most of the various non-spherical shapes known for alkanes can be reproduced with triglyceride droplets providing that the surfactant adsorption layer freezes before the nucleation of the oily molecules inside the drops. By comparing the behavior of triglyceride and alkane droplets, we draw unified picture and provide guiding principles which can be used for selection of appropriate surfactants enabling the spontaneous shape deformations upon cooling of oily drops of different chemical compositions.

Plastocapillarity: Partial and full Newtonian drop embedding into immiscible yield stress substrates

HypothesisRecent advances have been made in elastocapillarity; reversible 3D deformations of solid substrates with low elastic moduli from the surface tension of deposited drops. This study explores permanent deformations caused by liquid drops on immiscible yield stress substrates. We hypothesize that the substrate's rheological properties play a major role in determining the shape and stability of the drop-substrate interface, and govern partial or full embedding into the substrate. ExperimentsSubstrate yield stress magnitudes are modified through altering the mixture ratios of petroleum jelly to paraffin oil. Water drops are deposited on substrates and deformation profiles of the deformed interface are quantified. FindingsAbove a critical Bingham-Capillary number, which characterizes the ratio of yield stress magnitude to surface tension, deposited water drops deform the substrate surface permanently, but minimally. Below this value, drops become increasingly embedded as the substrate yield stress magnitude decreases, with larger indentation depths and increased circumferential ridge heights. With sufficiently low yield stress magnitudes, where surface tension forces dominate over yield stress forces, the plastically deformed ridges fully encapsulate the liquid drop surface, resulting in full drop embedding within the substrate. These results advance knowledge of interfacial wetting on soft yield stress substrates and has implications for binary fluids, functional materials, and new drug delivery systems.

Cavitation and jetting from shock wave refocusing near convex liquid surfaces

We study the physical mechanisms behind the ejection of a liquid jet from a curved free surface, specifically a free-falling water drop. The jet is produced after a spherical shock wave emitted from a micro-explosion created by a focused laser pulse is refocused on the opposite side of its source. The analysis of high-speed videos of the liquid jet formation revealed that it originates from a larger, prolate cavitation bubble created by the strong tension produced after the reflection of the original wave on the air–liquid interface. The shock wave propagation and jet formation are modeled separately with finite volume simulations in OpenFOAM. Initially we study the pressure evolution inside the drop by comparing the numerical simulations with the distribution of bubbles nucleated after the passage of the negative pressure wave. The jet formation dynamics is explained by comparing the experiments with numerical results. The jet velocity is higher if the laser focus is closer to the drop surface.

Bounce and contact mode regimes for drop impact on smooth surfaces: The influence of gas kinetics and electrostatics

When liquid drops impact on solid surfaces, an air layer forms in between the drop and the surface, acting as a cushion to mitigate the impact. In this work, we focus on delineating the bounce and contact mode regimes of impacting drops on smooth surfaces, specifically discerning whether drops rebound from the air layer or make contact with the solid surfaces, and pinpointing the precise contact modes between the drop and solid surfaces by resolving the gas film evolution and rupture. Our simulation model incorporates gas kinetics and electrostatics effects, both of which have been validated by experiments documented in the literature or theoretical models regarding thin film instabilities. We undertake a comprehensive review and categorization of the contact modes and elucidate how they change under different conditions of impact velocities, ambient pressures, and electric field intensities. We also provide some perspectives on the regime map for the lubricated surfaces, which contains an unresolved issue that the critical Weber number for bouncing-wetting transition is significantly reduced compared to the solid smooth surfaces like mica. These insights have noteworthy practical implications offering guidance for a wide range of scenarios, from normal-pressure environments to low-pressure conditions at high altitudes, encompassing high electric field conditions such as nanogenerators as well as low electric field conditions resembling glass surfaces with static electricity.

Surface modification of poly (ethylene terephthalate) using imidazolium-based ionic liquids

Ionic liquids (ILs), with their unique characteristics, are widely known as new alternatives for solvents and catalysts used in various chemical reactions. Due to their extensive range of applications and environmental compatibility, they are suitable options for treating fibrous substrates. In this regard, this paper focuses on investigating the possibility of poly (ethylene terephthalate) surface modification via imidazolium-based ILs. Surface modification was carried out under different process conditions by varying the temperature and the catalyst. The possibility of treating samples in the IL solution for the second time was also examined. Moreover, the effect of the modification on the dyeing of polyester with disperse dye without carrier at 100 °C was studied. The samples’ wettability properties were investigated through several test methods by measuring vertical wicking height, wetting time, drop contact angle, surface resistivity and absorption of methylene blue dye. The chemical and physical changes of the modified samples were also evaluated via scanning electron microscopy images, Fourier-transform infrared spectroscopy (FTIR) spectra and mechanical tests. Results demonstrate that treatment with [BMIM]Cl and [BMIM]Br induces morphological changes on the fibre surface, creating grooves and voids. FTIR analysis and Methylene blue staining test confirm the formation of hydroxyl and carboxyl groups, enhancing the fabric's hydrophilicity and dyeability. Wettability tests reveal that increased water absorption leads to reduced electrical resistivity. Mechanical tests indicate a slight reduction in tensile strength attributed to surface roughness.

Effect of the angle of wedge-shaped hydrophilic patterns on drop evaporation and contact line behaviour: A lattice Boltzmann study

Hypothesis:Angular hydrophilic patterns can manipulate the drop morphology for applications like inkjet-printing. It is hypothesized that such patterns can also affect the contact line behaviour and evaporation rate of drops in a dynamic way, further affecting the quality of depositions. Here, the effect of the angular region is quantified using a wedge-shaped pattern. Experiments:The pseudo-potential multicomponent lattice Boltzmann (LB) model is used for the diffusion-limited (isothermal) evaporation of pinned liquid drops from wedge-shaped hydrophilic patterns. Findings:The contact line unpins the earliest at the apex region of the smallest wedge angles due to a pronounced difference between the local and overall contact angles. The difference reduces linearly with increasing wedge angles, leading to their delayed unpinning. The evaporative flux along the contact line is initially independent of the contact angle but reduces sharply near the unpinning angle. The variation of flux across wedge angles depends more on unpinning timings, as maximum flux values did not differ significantly. The evaporation rate is dynamic, with the smaller wedge angles initially exhibiting a higher evaporation rate because of larger drop surface areas, while the larger wedge angles dominate later owing to the delayed unpinning and retaining larger drop surface areas.

Effect of Surface Renewal on the Drop Size Distribution in Dropwise Condensation within a Hybrid Surface

The description of liquid drop growth and drop distribution are two key models in evaluating the thermal performance of dropwise condensation (DWC) heat transfer. The drop size distribution describes the growth process of small drops by direct condensation and large drops by coalescence. The present work investigates the effect of surface renewal and coalescence intensities of DWC within a hybrid surface. Additionally, it examines the validity of the current empirical expression of the drop size distribution that is developed for DWC without considering surface renewal and coalescence intensities. The simulation work illustrates the drop growth process and surface renewal as drops depart and merge with neighboring film regions. The simulation results show that in hybrid DWC, the area fraction occupied by drops (f) lies between 0.28 to 0.296 for the ratio of maximum drop diameter to DWC region width (RD) from 0.125 to 1 and a total temperature drop (∆T) of 2, 4, and 8 ℃. Thus, the drop population is less sensitive to RD, and an average f of 0.288 is generalized. On the other hand, the surface renewal for DWC within the hybrid surface shows improvement for RD &gt; 0.5 with the highest enhancement of 64 to 85% taking place at RD = 1, mainly due to the merging effect. In addition, results for drop size distribution profiles of DWC within the hybrid surface are characterized by a lower population of large drops and a higher population of small drops than full DWC. Additionally, the constant exponent (n) in the literature’s empirical expression is replaced by a polynomial series as a function of drop effective and maximum radii. The impact of surface renewal on coalescence intensity is presented in a relatively steeper slope on the logarithmic scale.