Outer Droplet Research Articles

On the shape and size of liquid droplets on flat solid surfaces

This article introduces two dimensionless positive geometric parameters that characterize the shape of a liquid droplet on a flat solid surface, which formed by the surface tension. The first parameter, “shape coefficient” K, is defined by the ratio of volume to surface and is always >3 (3 is the space dimension). The second parameter, “holding limit” κ0, is defined by the fraction of osculating surface and K and is <1. The ratio of the surface tension energy of a droplet attached to a substrate in zero gravity to the energy of the same droplet floating in zero gravity is presented through these parameters as 1-(K-3)(κ0-κ)/3(1-κ0), where the material parameter κ (which appears in the Young equation κ=cosθ) indicates the decrease in liquid surface tension by the solid The relative energy of the surface tension, K and κ0, are explicitly expressed for a droplet of an elliptical rounded segment (ERS) shape through its eccentricity e, relative height χ, and relative rounding radius η. It is shown that the Young equation is a self-consistent (i.e., leading to η=0) minimum condition of the energy only in the spherical (e=0) case. The rounding, either inner or outer, is specified by the legs of a triangle with zero angles and the median as a slope line. The main result obtained is the proof that the outer rounded ERS weighty droplets with inflection points, due to weight and hydrostatic forces, cannot exist if their radii larger than 2-4 capillary length. This proscription is absent in zero gravity.

Generation and evolution of double emulsions in a circular microchannel

Double emulsions are attracting much attention from academic community and industry fields. Emerging microfluidics technology offered new ways to prepare unprecedentedly controllable double emulsions. Here a numerical simulation method, volume of fluid (VOF) technique, was adopted to study the generation and evolution of double emulsions in a circular microchannel, which is helpful for understanding the underlying physics of double emulsion preparation and optimizing the operation conditions. The flow pattern regions where double emulsions existed were found and classified according to dripping and jetting models of double emulsion generation. Velocity fields inside and outside double emulsions were investigated, and several distinct velocity vortexes were observed. Several characteristic parameters involving pressure distribution of fluids and deformation index of double emulsions were studied. At last, preparation of double emulsions with desired configurations, including same inner droplets engulfed by different outer droplets and same outer droplets encapsulating different inner droplets, were explored in depth.

Numerical simulation on free oscillation interfacial dynamics of single-core compound droplet driven by shell deformation

Compound droplets are often used as microcontainers in biomedical, material encapsulation, and so on, and a good understanding of their free oscillatory behavior is essential for controllable product preparation. Herein, the free oscillatory deformation behavior of single-core compound droplet induced by shell deformation is studied computationally using the volume-of-fluid (VOF) method. The effects of the inner droplet diameter, the outer droplet initial deformation and physical properties are considered. The results show that outer droplet oscillation has obvious periodicity and damping attenuation mechanism, and the inner droplet has two oscillation forms: large-deformation forced oscillation and small-deformation free oscillation. The oscillation period is positively correlated with the inertial force, while the damped attenuation mechanism is dominated by the viscous force, and the presence of the inner droplet and the increase of its diameter will enhance the inertial and viscous forces of the outer droplet. The deformation degree of the inner and outer droplet is related to the energy transfer between the two and the initial interfacial energy, which is generally greater for the outer droplet than for the inner droplet, but the larger diameter ratio makes the opposite situation, and the critical value lies between the diameter ratio of 0.625–0.75. The obtained results will provide the possibility to control the morphological structure of the compound droplets after preparation.

Study on the interfacial dynamics of free oscillatory deformation and breakup of single-core compound droplet

Compound droplets are usually taken as microcontainers for biomedical and material encapsulation applications in which a good understanding of the free oscillatory deformation and breakup behavior is essential. In this work, the dynamics of free oscillatory deformation and breakup of a single-core compound droplet with an initial ellipsoidal shell was investigated numerically using the volume-of-fluid method. The effects of droplet diameter and the outer droplet initial deformation parameter are considered. Four outcomes are identified: oscillatory deformation, separation, separation breakup, and breakup. The evolution of the kinetic energy and pressure field of the compound droplet for the four typical outcomes is also analyzed in detail. A clear boundary exists between the first and the latter three outcomes (initial deformation parameters of 0.600–0.773), while the critical factor for the latter three outcomes is the inner and outer droplet diameter ratio. The oscillatory deformation is characterized by the inner and outer droplet undergoing a finite deformation and subsequent oscillatory behavior, with the maximum deformation of the inner and outer droplets being related to the energy transfer between the two, and the outer droplet being a periodic decaying oscillation, while the inner droplet is a large deformation oscillation interspersed with a small deformation oscillation. Separation, separation breakup, and breakup are characterized by breakup at the inner or outer interface during deformation; separation and breakup times are largely dependent on droplet diameter and the initial deformation parameter of the outer droplet; and the neck width at separation is also analyzed in detail.

Solidification of a hollow sessile droplet under forced convection

This study presents a front-tracking-based numerical analysis of the forced convection solidification of a sessile droplet on a cooling surface. The droplet, a hollow (or compound) droplet with an encapsulated gas core, undergoes a liquid-to-solid phase change in its shell. This phase change starts from the surface. Meanwhile, the surrounding gas, which is characterized by its Reynolds number Re and temperature, moves toward the droplet parallel to the axis of symmetry. When the temperature of the forced flow is below the solidification value (i.e., cold-forced convection), increasing the strength of the forced flow shortens the solidification process. In contrast, increasing the Re number of a hot-forced convection system prolongs solidification. In other words, an increase in the forced flow temperature causes the entire liquid shell to solidify more slowly. Thinner shells require more time to solidify completely than thicker ones. The forced flow does not influence the formation of an apex at the top of the outer droplet surface. The aforementioned apex results from volume expansion. The effects of other parameters, for example, the capillary number and the morphologies of the droplet and cooling surface, are also determined.

Laser-induced deformation and fragmentation of droplets in an array

Droplet–droplet interactions is ubiquitous in various applications ranging from medical diagnostics to enhancing and optimizing liquid jet propulsion. We employ an experimental technique where the laser pulse interacts with a micron-sized droplet and causes optical breakdown. The interaction of a nanosecond laser pulse and an isolated spherical droplet is accurately controlled and manipulated to influence the deformation and fragmentation of an array of droplets. We elucidate how the fluid dynamic response (such as drop–drop and shock–drop interactions) of an arrangement of droplets can be regulated and optimally shaped by laser pulse energy and its interplay with the optical density of liquid target. A new butterfly type breakup is revealed, which is found to result in controlled and efficient fragmentation of the outer droplets in an array. The spatio-temporal characteristics of a laser-induced breakdown dictate how shock wave and central droplet fragments can influence outer droplets. The incident laser energy and pulse width employed in this work are representative of diverse industrial applications such as surface cleaning, nano-lithography, microelectronics, and medical procedures such as intraocular microsurgery.

Novel glass capillary microfluidic devices for the flexible and simple production of multi-cored double emulsions

HypothesisDouble emulsions with many monodispersed internal droplets are required for the fabrication of multicompartment microcapsules and tissue-like synthetic materials. These double emulsions can also help to optically resolve different coalescence mechanisms contributing to double emulsion destabilization. Up to date microfluidic double emulsions are limited to either core–shell droplets or droplets with eight or less inner droplets. By applying a two-step jet break-up within one setup, double emulsion droplets filled with up to several hundred monodispersed inner droplets can be achieved. ExperimentsModular interconnected CNC-milled Lego®-inspired blocks were used to create two separated droplet break-up points within coaxial glass capillaries. Inner droplets were formed by countercurrent flow focusing within a small inner capillary, while outer droplets were formed by co-flow in an outer capillary. The size of inner and outer droplets was independently controlled since the two droplet break-up processes were decoupled. FindingsWith the developed setup W/O/W and O/W/O double emulsions were produced with different surfactants, oils, and viscosity modifiers to encapsulate 25–400 inner droplets in each outer drop with a volume percentage of inner phase between 7% and 50%. From these emulsions monodispersed multicompartment microcapsules were obtained. The report offers insights on the relationship between the coalescence of internal droplets and their release.

Hydrodynamic analysis of one deformed double emulsion droplet under shear

The hydrodynamics of one double emulsion droplet under shear is investigated on the basis of a computational fluid dynamic simulation with the volume-of-fluid (VOF) method. The morphological features of the deformed double emulsion droplet at steady state are quantitatively characterized by the deformation and tilt angles, and the potential mechanisms are explored through analyzing pressure and flow information. The existence of the inner droplet engenders two effects (namely enhancing effect and restraining effect) on the outer droplet deformation D out, determined by which mechanism in a dominant position. With the increase in k, the character of the inner droplet on D out transforms from enhancing effect into restraining effect under smaller Ca out, while under larger Ca out the restraining effect is presented in the leading role that inner droplet with different k all inhibits the outer droplet deformation. As the interfacial tension ratio increases under constant Ca out, the higher-pressure region at the tip of the inner droplet turning to the “throat” region and the tilt angle θ in enlarging both restrain the deformation D out. In addition, with the increasing viscosity ratio λ 12, the outer droplet deformation D out increases whereas the inner droplet gets smaller deformation; the tilt angles θ in and θ out both increase and their tilt angle difference gradually increases.

Thermochromic Microcapsules Containing Chiral Mesogens Enclosed by Hydrogel Shell for Colorimetric Temperature Reporters

AbstractChiral mesogens spontaneously form a cholesteric phase and show structural colors through wavelength‐selective reflection. Although chiral mesogens are pragmatic materials to build cholesteric phase due to their low toxicity, low cost, and robustness, an elaborate encapsulation technique is not reported yet. In this work, cholesteryl esters are encapsulated with a calcium‐alginate hydrogel shell using oil‐in‐water‐in‐oil double‐emulsion droplets. With capillary microfluidic devices, monodisperse double‐emulsion droplets are prepared to have a mixture of cholesteryl ester and toluene in the innermost droplets and an aqueous solution of sodium alginate and calcium‐carrying complex in the outer droplets. As toluene diffuses out from the core, cholesteryl ester forms the cholesteric phase. At the same time, calcium ions are dissociated from the complex upon chemical cues, which causes ionic crosslinking of alginate. The microcapsules show the thermochromic property as the structural color of the cholesteric core blue‐shifts along with the temperature. Therefore, the microcapsules report local temperatures with colors or reflectance spectra. As the range and sensitivity of the colorimetric temperature measurement are controllable by adjusting the composition of cholesteryl esters, a wide range of temperature can be covered by employing a proper set of compositions while maintaining high sensitivity.

Magnetic field-induced control of a compound ferrofluid droplet deformation and breakup in shear flow using a hybrid lattice Boltzmann-finite difference method

The deformation and breakup dynamics of a compound ferrofluid droplet under shear flow and uniform magnetic field are numerically studied in this paper. Utilizing magnetic field provides the possibility to obtain better control over the compound droplet morphology and breakup in a simple shear flow. To solve the governing equations for interfaces motion and hydrodynamics, the conservative phase field lattice Boltzmann model is employed, and a finite difference approach is applied for calculating the magnetic field. To verify the accuracy of present simulations, the results are validated with those of four relevant benchmarks including liquid lens between two stratified fluids, three-phase morphology diagram, droplet under simple shear flow fluid flow, and ferrofluid droplet elongation under a uniform magnetic field. The magnetic field lines and magnetic force in the presence of ferrofluid are visualized. The effects of capillary and magnetic Bond numbers on the deformation and inclination angle of compound droplet under magnetic field at the angles of 45∘ and 135∘ are investigated when the inner or outer droplet is ferrofluid. The results show that by increasing capillary number, the shear force becomes greater and deforms the outer interface, whereas its effect on the inner interface is negligible and its small deformation is due to the squeezing force by the outer interface. As the magnetic Bond number increases, so does the magnetic force, and it leads to both of inner and outer interfaces elongation in the direction of the imposed magnetic field. Finally, the regime maps of compound droplet morphology and breakup in terms of capillary and magnetic Bond numbers are presented when the outer droplet is ferrofluid and the magnetic field is applied at the directions of 45∘ and 135∘, respectively. The border between breakup and non-breakup regions is illustrated, and according to the equilibrium shape of the compound droplet, donut-shaped, egg-shaped, eye-shaped, and peach-shaped regimes are observed in the non-breakup region.

Breakup regimes of double emulsion droplets in a microfluidic Y-junction

The droplet breakup technology can effectively increase the generation throughput and adjust the droplets size, which has an important impact on the performance of the double emulsion droplets in medical, chemical, and other applications. This work presents an experimental study on the breakup regimes of double emulsion droplets after their on-chip generation. Five distinct breakup regimes are categorized according to the breakup times and the existence of the coupling effect during breakup process. Evolutions of the neck widths and thinning rates of both inner droplets and outer droplets are provided to discuss the dynamics of different regimes as well as different stages. In particular, the influences of the coupling effect on the interfacial evolution, collapsing mechanism, force analysis, and breakup critical condition are confirmed by comparisons with the results of single emulsion droplets.

Numerical analysis of deformation and breakup of a compound droplet in microchannels

Compound droplets with different sizes are increasingly used in industrial production and academic research. This study aims to improve understanding of the dynamical behaviors of the compound droplet moving in microchannels. The compound droplet consisting of one inner core is initially concentric and placed at the entrance of a circular channel with a cone at the downstream region. Following this primary channel is a secondary channel that is circular and straight. Manipulation of the droplet is assisted by a flow introduced via the gap between two channels. The numerical results show that when passing through these confined channels, the droplet experiences a finite deformation or breakup mode. In each mode, the deformation or breakup of the compound droplet is also different when changing the values of the parameters including the capillary number, the ratio of the droplet radii, the ratio of the interfacial tension, the size of the secondary channel, the gap size and the cone angle. The finitely deformed droplet can be either nearly ellipsoidal with a deformation index D of around unity (i.e., first deformation mode) or highly elongated with a high D (i.e., second deformation mode). Breakup of the compound droplet happens to the outer droplet, and the breakup point is located either in front of the inner droplet (i.e., first breakup mode) or behind it (i.e., second breakup mode). The simple droplets yielded in the first breakup mode has a higher total volume than those in the second breakup mode. It is found that the droplet experiences the first deformation mode to the first breakup mode, then the second deformation mode and finally the second breakup mode when Ca increases. The regime diagrams of these modes, based on these parameters, are also presented.

Numerical study of the indentation formation of a compound droplet in a constriction

A compound droplet deforming in a constricted tube widely appears in drug delivery and microfluidic devices. In such a constriction, an indentation can present at the trailing surface of the droplet. However, this aspect has not been fully investigated and understood so far. This study focuses on the effects of some dimensionless parameters on the negative curvature, i.e., indentation, at the trailing surface of a compound droplet moving through a constricted tube. The presence of the constriction at the middle of the tube length enhances the droplet indentation. Numerical results were obtained for the capillary number Ca (varied in range of 0.1–1.0), the inner-to-outer droplet radius ratio R21 (varied in range of 0.2–0.9), the droplet-to-tube radius ratio R10 (varied in range of 0.2–0.9), the inner-to-outer interfacial tension coefficient ratio σ21 (varied in range of 0.1–6.4), and the normalized depth of the constriction d/R (varied in range of 0.0–0.8). The results reveal that the most influencing factor is Ca, increasing its value leads to the increment of the maximum indentation at the trailing surface of the inner and outer droplets. The indentation is also increased with increasing the value of R10 and d/R. In contrast, increasing R21 results in a decrease in the indentation at the trailing surface of the outer droplet. When increasing σ21, the indentation at the trailing surface of the inner one is quickly suppressed, while the outer droplet is minorly affected. We also point out the patterns of the trailing surface of the inner and outer droplets and their transitions from one to the other patterns in the diagrams based on these parameters.

Electrohydrodynamic-induced interactions between droplets

Dispersion of droplets in an emulsion is commonly seen in several chemical, pharmaceutical and petroleum industries. Electric field has been shown to affect the stability of these dispersions. We study the dynamics of a pair of leaky dielectric droplets in a leaky dielectric liquid in the presence of an externally applied electric field. A pair of droplets may coalesce or repel each other in the presence of an electric field. Interactions between a pair of drops have been shown to be governed by the ratio $\varepsilon _r/\sigma _r$ , where $\varepsilon _r$ and $\sigma _r$ are the ratios of drop to ambient fluid electric permittivities and conductivities, respectively. When inertia is neglected, the droplets approach each other if $\varepsilon _r/\sigma _r > 1$ , whereas droplets repel when $\varepsilon _r/\sigma _r < 1$ . However, inclusion of inertia permits interesting transient behaviour, where the droplets may attract due to the electrostatic dipole–dipole attraction even for $\varepsilon _r/\sigma _r < 1$ . The approach velocity then is governed by the electrostatic forces and varies as $1/h^4$ , where $h$ is the separation distance between the droplets, in contrast to being hydrodynamically driven as predicted in the Stokes flow limit by Baygents et al. (J. Fluid Mech., vol. 368, 1998, pp. 359–375). For compound droplets, interactions between droplets are essentially governed by the electrical properties of the outer droplet and the ambient fluid. However, transient dynamics may also result in the breakup of a compound droplet and lead to formation of single droplets.

Numerical study of double emulsion droplet generation in a dual-coaxial microfluidic device using response surface methodology

This paper presents a parametric study using a three-phase axisymmetric numerical simulation on a dual co-axial microfluidic device for creating compound droplets. The Volume of Fluid-Continuum Surface Force model (VOF-CSF) was developed to perform a parametric analysis of the double emulsion formation in a dual co-axial microfluidic device. The model was used to investigate the effects of phase velocities, viscosities, and interfacial tensions on the size and generation rate of the double emulsions, with the assistance of the Design of Experiments (DOE) and Response Surface Methodology (RSM). The DOE considerably decreased the number of simulations. A sensitive analysis revealed that the outer phase parameters have the most noteworthy influence on double emulsion characteristics. Dimensionless numbers, including Weber number of the inner phase (Wein), the capillary number of the middle phase (Camid), and the capillary number of the outer phase (Caout), were also implemented to examine the effects of essential forces on the double emulsion size. The simulation results verified that the size of both the inner and the outer droplets could be easily adapted within a broad range by adjusting non-dimensional parameters. The simulation results can be utilized to generate a broad range of liquid-liquid encapsulated structures.

Low‐Field High‐Resolution PFG‐NMR to Predict the Size Distribution of Inner Droplets in Double Emulsions

AbstractIn double emulsions, the inner and outer droplet size distribution (DSD) determines the quality of the double emulsion and is therefore essential to be measured. Low‐field high‐resolution pulsed‐field gradient nuclear magnetic resonance is used to measure the inner DSD in water‐in‐oil‐in‐water double emulsions. The Gaussian phase distribution approach is employed with a mixture of two normal distributions to predict bimodal inner droplets. This approach allows the prediction of the swelling of inner droplet during storage of double emulsions, and thus to validate a phenomenological population balance model estimating inner droplet swelling. Only a fraction of the inner droplets are found to swell during storage, due to differences in the Laplace pressure, thus leading to the formation of a bimodal size distribution of the inner droplets.Practical Applications: This methodology is useful to predict the evolution of double emulsions during storage, in a wide range of applications, such as food and pharmaceutical products.

Protein isolate from Stauntonia brachyanthera seed: Chemical characterization, functional properties, and emulsifying performance after heat treatment

The seed of Stauntonia brachyanthera is usually regarded as waste after fructus processing. Here, the potential utilization value of the protein isolate (SSPI) from seeds was evaluated by investigating its physicochemical and functional properties. SSPI was a complex protein containing 7 distinct subunits that had high contents of most essential amino acids. The maximum foaming capacity of SSPI was 406.7 ± 41% at pH 9.0, and the water holding/oil adsorption capacities were 4.66 g/g and 9.06 g/g, respectively. SSPI aggregates with a particle size of 154.1 ± 5.2 nm was prepared after heat treatment, which was performed as a Pickering-like stabilizer for the structuring of water-in-oil-in-water emulsions. The outer droplet size of emulsions decreased as the aggregate concentration increased. Emulsion gels could be observed with the increasing aggregate concentration and oil fraction. Further study found that the stabilities of inner water-in-oil droplets and creaming were progressively increased by increasing the aggregate concentration during storage.

Interfacial behavior of surfactant-covered double emulsion in extensional flow.

We analyze the interface-interface interactions of a surfactant-covered double emulsion using the lattice Boltzmann method and study the interaction of the inner and outer interfaces and the local surfactant distribution under a uniaxial extensional flow. First, the capillary effects are analyzed. Upon surfactant application, the outer droplet deformation increases and the inner droplet deformation decreases. The concentrated surfactants on the outer interface increase deformation, and the inner droplet is affected by the inner flow. At a fixed Péclet number (Pe), the surfactant concentration at the outer interface increases with an increase in capillary number (Ca); however, such a tendency is difficult to identify at the inner interface. Next, the Pe effects are analyzed. With an increase in Pe, the deformation of the inner droplet decreases significantly. The local distribution of the surfactant considerably affects the double emulsion stabilization, which is analyzed in terms of internal flow. The interfacial tension gradient induced by the surfactant generates vortices internally, which is verified by applying the surfactant to each interface independently. The radius ratio affects droplet deformation and surfactant transport. The compression of the inner flow region increases the viscous force and decreases the interface velocity. Therefore, with an increase in radius ratio, the deformation increases, and the surfactant transport becomes slow.

Insights into the impact and solidification of metal droplets in ground-based investigation of droplet deposition 3D printing under microgravity

Droplet deposition 3D printing is an additive manufacturing technique offering a great potential for metal parts fabrication in space, of which some preliminary testing is usually performed on ground in the early research. The previous work (Huang et al., 2020) mimicked the anti-gravity deposition of molten metal droplet through manipulating it into perpendicularly depositing on a vertical substrate. However, the ground-based simulation of droplet deposition 3D printing under microgravity remains an elusive goal, since the spreading and receding processes are still affected by gravity. To address this issue, the prevailing physical mechanisms of gravity effect on droplet impact and solidification are urgent to be defined. Here, we present the studies on the impact dynamics and transient solidification of the molten metal droplet deposited on vertical substrates through numerical modeling and experiments. It is observed that the spreading and retraction of the droplet are asymmetric, besides its solidification shape tilts to gravitational direction. The formation mechanisms of these undesired behaviors are further demonstrated. The results show that the asymmetrical spreading, retraction and solidification shape of the droplet originate from the interaction of gravity and solidification. Moreover, the tilt of the solidified droplet has a correlation with the critical process parameters, i.e. impact velocity, temperatures of droplet and substrate. With a larger impact inertia and a lower solidification rate, the undesired solidification shape can be effectively eliminated. This work provides a foundation for the further investigation of the ground-based physical simulation of outer space droplet deposition 3D printing.

Deformation and breakup of a compound droplet in three-dimensional oscillatory shear flow

A compound droplet subject to three-dimensional oscillatory shear flow is studied using a three-phase lattice Boltzmann model. Firstly, focusing on low values of capillary number (Ca) where the compound droplet eventually reaches steady-state oscillatory condition, we study the effect of oscillatory period, viscosities of inner and outer fluids of the compound droplet, wall confinement and Ca on the droplet behavior. As the oscillatory period increases, the maximum deformation parameters gradually approach the steady-state values in the corresponding simple shear flow for both inner and outer droplets, and the compound droplet is more synchronous with applied shear. We demonstrate for the first time that due to high pressure near two tips inside the outer droplet the inner droplet may rotate counterintuitively in a direction opposite to the outer one. The compound droplet undergoes larger deformation when either droplet is less viscous, which also decreases the synchronization between inner and outer droplets. Increasing confinement ratio not only promotes the deformations of both constituent droplets, but also makes them more synchronous with applied shear. It is also found that the maximum deformation parameters of both droplets increase linearly with Ca up to Ca=0.35 but deviate from the linearity at higher Ca, where multipeaked oscillations are observed for the deformation of the inner droplet, which can be due to the extensional flow resulting from the rapid contraction of the outer droplet. We then analyze the breakup behavior of compound droplet in the oscillatory shear flow for varying confinement ratios, and compare the findings with those in simple shear flow. The critical capillary number for droplet breakup exhibits a non-monotonic behavior with the confinement ratio in both shear flows, but its value is always higher in oscillatory shear flow than in simple shear flow. As the confinement ratio increases, in the case of oscillatory shear flow, the droplet undergoes a transition from inner ternary breakup to inner binary breakup, distinct from the one observed in the case of simple shear flow. Finally, increasing oscillatory period is found to not only decrease the critical capillary number but also change the mode of droplet breakup.