Satellite Droplets Research Articles

Liquid pinching dynamics in an inertial transitioning regime

The pinching of a liquid filament at low viscosity, whether in air or liquid, shows a rich and interesting behavior. The liquid thread thins according to a capillary-inertial regime power law at the beginning, before transitioning into other regimes when approaching the pinching moment. Here we study the pinching of a pendant drop revealing the effect of internal and external viscosity on thread thinning. We show an inertial transitioning regime in which slower thinning happens by slightly increasing not only the droplet viscosity but also the viscosity of the surrounding liquid. The viscosity is found to reduce the filament neck axial velocity leading to a slower thinning. We derive a simple universal scaling law that can predict the thinning inertial prefactor value as a function of the neck axial velocity showing excellent agreement with numerical data. Finally, the breakup of satellite droplets is characterized given the defined thinning regimes. Published by the American Physical Society 2024

Spontaneous Formation of π-Conjugated Polymeric Colloidal Molecules Through Stepwise Coacervation and Symmetric Compartmentalization.

Coacervation, the phase separation of liquid induced by polymeric solutes, sometimes results in the formation of oligomeric clusters of droplets. The morphology of the clusters is non-uniform because the clustering is a consequence of the random collisions of the drifting droplets. Herewereportdistinctively organized coacervation, yielding colloidal molecules with monodisperse size, morphological symmetry, and compositional heterogeneity.Weinvestigate the coacervation of a mixture of two types of synthetic polymers and find that one of the polymers coacervates first and serves as a core droplet, on which the other polymer coacervates subsequently to form satellite droplets. The satellite droplets arrange themselves symmetrically around the core and solidify without losing the morphology. The number of satellites and their symmetry are modulable depending on the chemical affinity and the diameter of the droplets. This finding highlights the capability of coacervation as a non-templated and non-covalent pathway to form aspherical colloidal materials with structural and functional complexity.

High-Speed Imaging of Giant Unilamellar Vesicle Formation in cDICE.

Giant unilamellar vesicles (GUVs) are widely used as in vitro model membranes in biophysics and as cell-sized containers in synthetic biology. Despite their ubiquitous use, there is no one-size-fits-all method for their production. Numerous methods have been developed to meet the demanding requirements of reproducibility, reliability, and high yield while simultaneously achieving robust encapsulation. Emulsion-based methods are often praised for their apparent simplicity and good yields; hence, methods like continuous droplet interface crossing encapsulation (cDICE), which make use of this principle, have gained popularity. However, the underlying physical principles governing the formation of GUVs in cDICE and related methods remain poorly understood. To this end, we have developed a high-speed microscopy setup that allows us to visualize GUV formation in real time. Our experiments reveal a complex droplet formation process occurring at the capillary orifice, generating >30 μm-sized droplets and only in some cases GUV-sized (∼15 μm) satellite droplets. According to existing theoretical models, the oil-water interface should allow for the crossing of all droplets, but based on our observations and scaling arguments on the fluid dynamics within the system, we find a size-selective crossing of GUV-sized droplets only. The origin of these droplets remains partly unclear; we hypothesize that some small GUVs might be formed from large droplets sitting at the second interface. Finally, we demonstrate that proteins in the inner solution affect GUV formation by increasing the viscosity and altering the lipid adsorption kinetics. These results will not only contribute to a better understanding of GUV formation processes in cDICE but ultimately also aid in the development of more reliable and efficient methods for GUV production.

Collision dynamics of binary equal-size droplets at high pressures: a focus on stretching separation and reflexive separation

ABSTRACT Stretching separation and reflexive separation are two collision regimes that give rise to satellite droplets, significantly impacting the droplet size distribution. However, the influence of high pressure on these regimes remains unclear. This paper investigates the collision dynamics of binary equal-size droplets under varying ambient pressures using the volume of fluid method and adaptive mesh refinement. The results show that vortices, generated during droplet motion changes or ligament ruptures, facilitate mass transport within the droplet–droplet deformation. Additionally, this paper summarizes four phases of droplet deformation in the separation regimes, which are delayed in stretching separation and advanced in reflexive separation with increasing ambient pressure. Elevated ambient pressure restricts droplet movement, resulting in tougher ligament fractures, smaller satellite droplets, and an expanded coalescence regime boundary. Unlike previous works, this paper incorporates gas kinetic and dissipation energies during droplet collisions at high pressures, revealing that at 7 MPa, the gas dissipation energy is comparable to the liquid dissipation energy and cannot be neglected. To account for these effects, a pressure-dependent formula is integrated into the composite collision model under the Lagrangian framework, offering enhanced predictions of droplet size within the stretching separation regime.

Elimination of satellite droplets in droplet streams by superposing harmonic perturbations

In tin-droplet laser-produced plasma sources, uniform droplet streams with large droplet spacing are desired to minimize the interference of explosion on neighboring droplets. Such droplet streams can be generated in low wavenumber regimes. However, satellite droplets easily appear among main droplets in those regimes, resulting in plenty of undesirable debris. Herein, a novel odd harmonic superposition perturbation method is proposed to eliminate satellite droplets and enhance droplet spacing of uniform droplet streams. The superposition number (N) and the phase difference (θ) of odd harmonic perturbations are adjusted to facilitate the coalescence of satellite droplets with main droplets. First, the superposed odd-order harmonic components could induce additional disturbance growth in jet surfaces, and finally lead to the asymmetric necking on filaments formed between two adjacent main droplets, featured as various carrot-shaped configurations. This asymmetric necking will cause unbalanced surface tension forces at the two sides of filaments, resulting in a velocity difference between satellite and main droplets. Based on this principle, by setting N and k to 3 and 0.2, respectively, satellite droplets positioned above main droplets accelerate, while those below decelerate, achieving complete coalescence between main and satellite droplets. Furthermore, the phase difference is found to determine the jet breakup location and satellite droplet merging characteristics. As θ varies from 0° to 90°, the droplet size significantly decreases while the droplet spacing remains constant since the perturbation energy increases. The merge direction of satellite droplets reverses from upward to downward due to enhanced unbalanced surface tension forces and velocity differences. As θ continuously increases to 270°, the droplet size further decreases along with a slight decrease in droplet spacing. Finally, by setting N = 3 and θ = 0°, mono-disperse tin droplet streams with a mean diameter of 31.5 μm and a maximum droplet spacing-to-diameter ratio of 17.7 are successfully formed. This work presents a novel approach for eliminating satellite droplets to achieve uniform tin droplet streams with large droplet spacing without increasing the droplet diameter.

Long-time emergent dynamics of liquid films undergoing thermocapillary instability.

The study of viscous thin film flow has led to the development of highly nonlinear partial differential equationsthat model how the evolution of the film height is affected by different forces. We investigate a model of interaction between surface tension and the thermocapillary Marangoni effect, with a particular focus on the long-time limit. In this limit, the model predicts the creation of an infinite cascade of successively smaller satellite droplets near points where the film thickness vanishes. Motivated by recent progress on the analysis of discrete self-similarity in thin film equations, we compute solutions in a space- and time-rescaled coordinate system. Using this rescaled system we observe the dynamics much further in time than has previously been achieved. The observed behavior is close to, but distinct from, previous observations of discretely self-similar thin film flows, in that the rescaled system does not settle down to a periodic solution, but instead has aspects that continue to evolve monotonically in scaled time. This discovery suggests there are as-yet unexplored ways in which discrete self-similarity may be exhibited.

Modelling of the effects of driving signal parameters on the droplet formation dynamics in piezoelectric inkjet

Piezoelectric inkjet technology has been widely adopted in various industrial applications due to its versatility and compatibility with a wide range of ink chemistries. The driving signal, pivotal in activating the piezoelectric element to expel droplets, significantly influences droplet formation dynamics. Parameters such as droplet size, velocity, breakup time, and the occurrence of satellite droplets are all influenced by the driving signal and ultimately affect the overall quality of the printing process. This paper introduces a model for drop-on-demand (DOD) droplet formation dynamics from a single nozzle employing a bipolar driving signal. The model establishes a quantitative correlation between the waveform of the driving signal and key parameters including average jetting velocity at the nozzle exit, droplet jetting frequency, and droplet volume. Furthermore, an experimental setup is developed for the calibration and validation of the proposed model. Results demonstrate a close alignment between the model predictions and experimental observations, affirming its efficacy in forecasting droplet formation behaviors based on driving signal parameters.

Enhanced control and efficiency in millimeter-scale composite droplets preparation

A microfluidic device utilising the flow focusing method was designed and fabricated for the high-throughput and controllable preparation of millimeter-scale water-in-oil (W1/O/W2) droplets. Two distinct flow focusing modes were employed in order to prepare the composite droplets. In the flow-focused axisymmetric jetting mode, the continuous phase propels the dispersed phase, forming a cone, which subsequently leads to a jet formation downstream of the small hole. When the outer phase is activated, perturbation growth interferes with downstream fragmentation, resulting in composite droplets with excellent monodispersity. In the dripping mode, the dispersed phase fails to form a jet downstream, and the interface disintegrates, resulting in droplet formation at the exit of the small orifice. In the jetting mode, the size and shell-to-core ratio of the generated droplets can be controlled by adjusting the volume of flow of the outer and inner phases, as well as the applied frequency. Furthermore, the applied perturbation allows for precise control of droplet size, which significantly reduces satellite droplet formation and enhances droplet monodispersity. In the dripping mode, the shell-to-core ratio is adjusted by manipulating the ratio of inner to outer flow rates, which is tailored to the specific requirements of the flow-focused dripping mode. The prepared compound droplets exhibit good monodispersity. Finally, the rotational solidification method can be employed to obtain spherical shells with a shell thickness of less than 20 μm. In conclusion, the flow focusing method is an effective, controllable, and stable method for synthesising millimetre-sized composite droplets.

Dewetting of a corner film wrapping a wall-mounted cylinder

In this study, we investigate the stability of a film that is attached to a corner between a cylinder and a substrate, using a combination of theoretical and numerical approaches. Notably, we place our focus on flat and thin films where the contact line is almost perpendicular to the cylinder wall whereas a small angle forms between the contact line and the substrate, and the film size is smaller than the cylinder radius. The film stability, which depends on the film size and the wall wettability, is first predicted by a standard linear stability analysis (LSA) within the long-wave theoretical framework. We find that the film size plays the most important role in controlling the film stability. Specifically, the thicker the film is, the less sensitive it becomes to the large-wavenumber perturbation. The wall wettability mainly impacts the growth rates of perturbations and slightly influences the marginal stability and postinstability patterns of wrapping films. We compare the LSA predictions with numerical results obtained from a disjoining pressure model (DPM) and volume-of-fluid (VOF) simulations, which provide more insights into the film breakup process. At the early stage there is a strong agreement between the LSA predictions and the DPM results. Notably, as the perturbation grows, thin film regions connecting two neighbouring satellite droplets form which may eventually lead to a stable or temporary secondary droplet, an aspect which the LSA is incapable of capturing. In addition, the VOF simulations suggest that beyond a critical film size, merging between two neighbouring drops becomes involved during the breakup stage. Therefore, the LSA predictions are able to provide only an upper limit on the final number of satellite droplets.

Lattice Boltzmann study of droplet dynamic behaviors impinging on textured surfaces under an external electric field

Textured surfaces contribute to enhancing the cooling effectiveness of electrostatic spray, while the droplet impacting dynamics on such substrates under the influence of electric field are crucial for cooling efficiency. This study utilized a multiphase lattice Boltzmann method combined with the leaky dielectric model to systematically examine the dynamics of droplet impingement on textured surfaces when exposed to electric field. The impact of Weber number, microstructural surface parameters, and electric field strength on droplet impact behavior was discussed in detail. Simulation outcomes reveal that, without the presence of an electric field, the impingement of droplets on textured surfaces results in three distinct deposition states: the Cassie state, partial penetration state, and Wenzel state, primarily contingent upon the surface solid fraction and the droplet impingement velocity. In the Cassie impact regime influenced by an applied electric field, the droplet spreading behaviors exhibit minimal sensitivity to the electric field, with surface tension and inertia primarily governing the spreading dynamics. Throughout the retraction stage, the droplet elongated the direction of the electric field as a result of electric field forces, and eventually, as the electric field strength grows, it bounces off the surface. In the Wenzel impact regime, as the strength of the electric field escalates, the droplet undergoes upward stretching and splits into satellite droplets during the retraction phase, attributed to the dynamic pressure and electrostatic pressure at the apex exceeding the capillary pressure and gravity. These findings could aid in advancing electrostatic spray cooling technology.

Upscaled Production of Satellite-Free Droplets: Step Emulsification with Deterministic Lateral Displacement.

Step emulsification is a key technique for achieving scalable production of monodisperse emulsion droplets owing to its resilience to flow fluctuations. However, the persistent issue of satellite droplets, an inherent byproduct of main droplets, poses challenges for achieving truly uniform product sizes. In a previous study, we introduced a module with step-emulsifier nozzles upstream and deterministic lateral displacement (DLD) micropillar arrays downstream to generate satellite-free droplets at a low throughput. In this study, we demonstrate an upscaled parallelized setup with ten modules that were designed to produce satellite-free droplets. Each module integrated 100 step-emulsification nozzles in the upstream region with DLD micropillar arrays downstream. We conducted 3D flow simulations to ensure homogeneous distribution of the input fluids. Uniformly supplying an aqueous polyvinyl alcohol solution and an acrylate monomer as continuous and dispersed phases into the ten modules, the nozzles in each module exhibited a production rate of 539.5 ± 28.6 drop/s (n = 10). We successfully isolated the main droplets with a mean diameter of 66 μm and a coefficient of variation of 3.1% from satellite droplets with a mean diameter of 3 μm. The total throughput was 3.0 mL/h. The high yield and contamination-free features of our approach are promising for diverse industrial applications.

Satellite droplet formation and its inertial separation in integrated microchannels

The breakup of filament is often accompanied by the formation of satellite droplet, which affects the uniformity of droplets, and inertial microfluidic technology is usually used to separate droplets of different sizes. In this study, different filament breakup modes are observed, and the variation of satellite droplet size with operating conditions are analyzed. Based on the experimental results, predictive model for the satellite droplet size is proposed. To better control the separation of particles with different sizes, the focusing and separation process of main and satellite droplets in microdevices are investigated by numerical simulation. It is found that increasing the fluid flow rate, the width of microchannel and rear cavity, and reducing the satellite droplet size are all beneficial for the separation of droplets of different sizes. At last, models for predicting the focusing positions of main and satellite droplets in rear cavity are established, and an integrated microfluidic device is proposed.

Instability and breakup of rayleigh-plateau jets with capillary wave induced by electrowetting-on-dielectric

This paper discusses the lateral disturbances of vertical liquid flow enhancement using electrowetting-on-dielectric (EWOD) technique, which effectively reducing the breakup length of the liquid flow and minimizing the formation of satellite droplets. The EWOD technology is characterized by its minimal space occupation and low energy consumption. The successful implementation of the EWOD phenomenon relies on the formation of a three-phase contact line (TPCL) between the electrodes and the liquid, and the novel EWOD tube structure design provides an extended TPCL, enhancing the amplitude of capillary waves. Through experimental and theoretical analysis, this paper identifies key parameters affecting the liquid breakup process, such as the gap depth, angle of the EWOD tube, EWOD voltage amplitude, and frequency of the AC electrical signal. The research results indicate that the proposed EWOD tube responds rapidly and can consistently and stably manage liquid breakup and reduce the number of satellite droplets.

Rational Design of Liquid-Liquid Microdispersion Droplet Microreactors for the Controllable Synthesis of Highly Uniform and Monodispersed Dextran Microspheres.

Hydrogel microspheres are biocompatible materials widely used in biological and medical fields. Emulsification and stirring are the commonly used methods to prepare hydrogels. However, the size distribution is considerably wide, the monodispersity and the mechanical intensity are poor, and the stable operation conditions are comparatively narrow to meet some sophisticated applications. In this paper, a T-shaped stepwise microchannel combined with a simple side microchannel structure is developed to explore the liquid-liquid dispersion mechanism, interfacial evolution behavior, satellite droplet formation mechanism and separation, and the eventual successful synthesis of dextran hydrogel microspheres. The effect of the operation parameters on droplet and microsphere size is comprehensively studied. The flow pattern and the stable operation condition range are given, and mathematical prediction models are developed under three different flow regimes for droplet size prediction. Based on the stable operating conditions, a microdroplet-based method combined with UV light curing is developed to synthesize the dextran hydrogel microsphere. The highly uniform and monodispersed dextran microspheres with good mechanical intensity are synthesized in the developed microfluidic platform. The size of the microsphere could be tuned from 50 to 300 μm with a capillary number in the range of 0.006-0.742. This work not only provides a facile method for functional polymeric microsphere preparation but also offers important design guidelines for the development of a robust microreactor.

Formation dynamics of the satellite droplet in the breakup of a symmetrical liquid bridge

Inkjet printing technology has played an irreplaceable role in life science, precision manufacturing, and other frontier fields in recent years. However, the further development of this technology is limited by the fact that its printing resolution is difficult to raise to a higher level. The emerging satellite droplet printing technology offers a new approach for inkjet printing to break through the bottleneck of printing resolution limitations. In this paper, a symmetrical satellite droplet printing strategy is proposed. The effects of the geometric parameters of the satellite droplet generating device, the physical properties of the ink, and the operating parameters on the liquid bridge breakup process and the size of the satellite droplet are systematically studied. The phase field method and adaptive mesh refinement strategy are applied to solve the two-dimensional symmetrical model. The results indicate that the length of the liquid bridge, the radius of the bridge, the viscosity of the ink, and the drainage velocity are all positively correlated with the satellite droplet size, while the surface tension coefficient has a negative correlation with the satellite droplet size. Furthermore, the three-phase contact line at the orifice end will slip toward the center if the initial radius of the liquid bridge is quite large. Based on these investigations and discussions, a corresponding effective working space for satellite droplet printing is obtained, which lays the foundation for the popularization and further development of satellite droplet printing technology.

Analysis of drop-on-demand printing characteristics and stability driven by inertial forces

As the core technology in the field of microdroplet related applications, researchers have been striving to develop new driving methods and improve the stability of inkjet printing technology to meet the diverse needs of various materials and applications. In this study, a novel, simple, and cost-effective droplet printing method based on inertial force driving is proposed, and its printing characteristics and stability are investigated through experimental and numerical simulation studies. A numerical model was developed to explore the effects of operating parameters and fluid properties on the printing process. The results showed that for a given fluid, it is easier to form satellite droplets when driven from a smaller nozzle with higher voltage and pulse width. The hydrophilic nature of the nozzle can suppress the formation of satellite droplets, but it is prone to retain liquid, thereby affecting the next printing effect. Under certain operating conditions, fluids with lower density, higher viscosity, and higher surface tension are difficult to be driven but can suppress the formation of satellite droplets and promote printing stability. Finally, a parameter space composed of dimensionless numbers Op representing operating parameters and Z representing fluid properties (reciprocal of the Oh number) was established to investigate the comprehensive influence on the printing. The correctness of this parameter space in guiding the selection of parameters for stable droplet printing was validated through experiments.

Transition from dripping mode to jetting mode under passive control with a drainage device

Traditional Chinese medicine is a pivotal industry in China, and the technology for manufacturing high-quality pills is of great interest to numerous sectors. Among various methodologies, the liquid drip method has gained significant attention from the pharmaceutical industry due to its advantages such as high drug content uniformity, low cost, ease of operation, high production efficiency, and extensive adjustment range. However, the occurrence of undesirable satellite droplets during the drip production process remains a persistent issue. These satellite droplets are challenging to collect and their prolonged presence can disrupt the normal functioning of the system. Previous studies have identified two primary modes of droplet formation: dripping mode and jetting mode. Given that droplet formation in dripping mode is more stable and satellite droplets can be effectively suppressed, studying the transition between dripping and jetting modes and improving the uniformity of the generated droplets become crucial. Achieving this transition can be accomplished through both active and passive methods. In view of the limitations of the active methods in actual productions, we explored a passive method of adding a drainage device, which can effectively inhibit satellite droplets.In this experimental and numerical simulation investigation, we successfully induced the dripping-to-jetting transition by incorporating a drainage device into the dropper. Additionally, we examined how modifications to the dropper's structure influenced droplet formation. Results indicated that increasing the length and diameter of the drainage device resulted in higher critical Weber numbers required for the dripping-to-jetting transition. Contrarily, the effect of the Kapitza number on the critical Weber numbers exhibited an opposite trend. The critical Kapitza number without complex droplets was also discussed.

Numerical study on the effect of actuation parameters on the formation characteristics of metal droplets in magnetohydrodynamic drop-on-demand (DOD) jetting

Numerical simulations have investigated the effects of electromagnetic drive waveform amplitude and pulse width on the state of metal droplet generation during drop-on-demand printing of molten metal aluminum by electromagnetic drive. It indicates that positive and negative pulses of magnetohydrodynamic(MHD) actuation applied to the molten metal in the crucible can form a so-called “push-pull” effect, which is the main mechanism affecting droplet generation and breakup. The positive pressure pulse causes the liquid metal to be extruded outward, and the negative pressure pulse promotes the fluid retraction at the nozzle to promoting the thinning of the liquid bridge and the generation of liquid droplets. With the increase in the amplitude of the applied current, the ejected molten aluminum from the crucible experiences three states: no droplet, single droplet, and droplet with satellite droplets. In the single drop state, the droplet formation time is shortened as the current peak increases and the droplet volume increases with the increase of pulse width. The energy conversion and force changes during droplet formation and falling are analyzed. When the peak kinetic energy of the ejected molten metal exceeds its surface energy, the jet breaks up and generates a single droplet. For the actuation with constant amplitude and duration for positive pulses, extending the duration of negative pulses weakens the "pull" effect, leading to a transition from the generation of a single droplet to multiple droplets. The numerical simulation results provide information on the current amplitude, pulse width, and Weber number range necessary for stable single droplet generation.

Hypergolic Ignition by Off-Center Binary Collision of Monoethanolamine-NaBH4 and Hydrogen Peroxide Droplets

Hypergolic ignition of H2O2 and MEA-NaBH4 by off-center collision of their droplets was experimentally studied, focusing on the characteristics and mechanism of droplet mixing, droplet heating and evaporation, and gas-phase ignition. The whole collision ignition process was divided into five stages, which were compared, respectively, with that of head-on collision. Under the condition of a slightly off-center collision (for cases where B < 0.35), H2O2 droplets penetrate MEA-NaBH4 droplets after the collision and coalesce with it, but the internal H2O2 drop inside the MEA-NaBH4 droplet does not form a stable sphere. Instead, it rotates and expands inside the mixed droplet. With B increasing to 0.59, the droplets no longer coalesce after collision but separate away, forming satellite droplets. In such cases, multi-ignition mode is observed. When B increases to a certain extent, specifically, 0.85, a grazing collision is observed such that no mass transfer exists during the interaction of droplets, which leads to ignition failure. A theoretical model quantifying droplet swelling rate was established to calculate the volume change of the droplet. It was found that the swelling can be attributed to the flash boiling of superheated internal H2O2 fluid. Meanwhile, the ignition delay time was found to linearly decrease with B at various Wes until the extent where the chemical reaction takes over control, leading to an almost constant time delay defined as RDT. Additionally, the regime of ignition modes corresponding to different droplet mixing features is summarized in the We-B parametric space.

Component Effects in Binary Droplet Impact Behaviors on the Heated Plate: Comparison Study of Ethanol/Propanol and Ethanol/Water Droplets and Observation of Novel Bubble Shrinkage Phenomenon

This work aims to investigate the effect of liquid physical properties on the behavior of binary droplets impact on the heated smooth aluminum alloy plate with a high-speed imaging system. Two groups of mixed solutions with similar boiling point differences are selected as the working liquid, in which the low-boiling-point components are both ethanol and the high-boiling point components are propanol and water, respectively. Compared to the ethanol/propanol binary droplets, the experimental results show that the ethanol/water binary droplets have diverse impact phenomena and significantly broad transition boiling regimes, as well as the reduced droplet residence time and increased Leidenfrost temperature point. With the decreasing ethanol content in ethanol/water binary droplets, these effects become more prominent. For secondary atomization, the ethanol/water binary droplet undergoes parent droplet breakup into fragment droplets with larger diameters (Ds > 0.3 mm). Both binary droplets produce satellite droplets with small diameters (Ds < 0.3 mm) by puffing and ejection. In terms of the ethanol/propanol binary droplet impact, the probability of puffing is higher and the satellite droplet diameters are small. In the ethanol/water binary droplet impact, the probability of ejection is higher and the satellite droplet diameter distribution is wider. When an ethanol/water binary droplet of 25 vol.% ethanol content impacts the heated wall at Ts = 120 °C, a novel large bubble shrinkage phenomenon occurs at the late stage of droplet evaporation. This phenomenon is proposed to be relevant to the increasing surface tension and saturation temperature with decreasing ethanol content, as well as the decreasing ambient temperature above the top surface of the bubble.