2D Foam Research Articles

Effect of airflow rate and drainage on the properties of 2D smectic liquid crystal foams.

As a two-phase system, foams are widely applied in the industry and exist ubiquitously in our daily lives. For this reason, studying them and investigating the parameters that affect their properties is crucial for the development of new and improved foam-based products. In this paper, we create 2D foam using an ordered fluid, the smectic liquid crystal (LC), and discuss the experimental parameters that affect their fabrication, including temperature and confining conditions. Then, we examine the influence of the injected airflow rate and drainage on their structure, size, liquid fraction, and stability. Finally, we compare their behavior to that of low-viscosity liquid foams and discuss the difference between them. Our findings indicate that surface tension is the dominant parameter in LC foam systems. Despite the strong elasticity of LCs, surface tension plays a crucial role in determining the properties of elastic foams. These results provide valuable insights that can be applied to different industrial applications. For instance, they may find relevance in the fields of cosmetics, thermal insulation, oil recovery, and sensing, where the fabrication of foams with high-viscosity fluids is required.

2D foam film coating of antimicrobial lysozyme amyloid fibrils onto cellulose nanopapers.

Amyloid fibrils made from inexpensive hen egg white lysozyme (HEWL) are bio-based, bio-degradable and bio-compatible colloids with broad-spectrum antimicrobial activity, making them an attractive alternative to existing small-molecule antibiotics. Their surface activity leads to the formation of 2D foam films within a loop, similar to soap films when blowing bubbles. The stability of the foam was optimized by screening concentration and pH, which also revealed that the HEWL amyloid foams were actually stabilized by unconverted peptides unable to undergo amyloid self-assembly rather than the fibrils themselves. The 2D foam film was successfully deposited on different substrates to produce a homogenous coating layer with a thickness of roughly 30 nm. This was thick enough to shield the negative charge of dry cellulose nanopaper substrates, leading to a positively charged HEWL amyloid coating. The coating exhibited a broad-spectrum antimicrobial effect based on the interactions with the negatively charged cell walls and membranes of clinically relevant pathogens (Staphylococcus aureus, Escherichia coli and Candida albicans). The coating method presented here offers an alternative to existing techniques, such as dip and spray coating, in particular when optimized for continuous production. Based on the facile preparation and broad spectrum antimicrobial performance, we anticipate that these biohybrid materials could potentially be used in the biomedical sector as wound dressings.

Geometric dynamics of anchored filamentous networks subject to viscous flow

The Endoplasmic Reticulum (ER) is an organelle that can form a complex dynamic network of filaments embedded in the viscous flowing cytoplasm of plant cells, anchored to points in the cell membrane. We consider an idealized dynamical model of the ER network as constant tension filaments subject to viscous forces from cytoplasmic flow. We show that simple configurations lead to the creation of a filamentous network that is analogous to a 2D foam, but with different physical mechanisms. We consider a fixed set of anchor points and propose an adaptive algorithm to track the network in the presence of the flow. We find that minimal (Steiner) networks joining these anchor points can support filamentous network of varying geometries with and without an imposed flow. We demonstrate that, after the flow has ceased, the filamentous network can retain memory of previous flow direction and intensity.

Numerical analysis of compressive deformation for random closed-cell Al foam model

Most cellular solids presented random structure, while practically periodic models were often used in structure-property relations and numerical models. The finite element method was used to create a 2D random model that replicated the deformation characteristics of cellular models. The influences of porosity and strain rate on the deformation characteristic, energy dissipation mechanisms were investigated. The Poisson’s ratio evolution during compression was also studied. The simulated load-displacement curves were found to be consistent with experimental results, both containing elastic stage, plateau stage, hardening stage and densification stage. The yield load and plateau load were insensitive to the strain rate. In addition, it was also found that the generation and propagation of multiple random shear bands were responsible for the load-displacement characteristic. At the cell/membrane level, four failure modes and corresponding energy dissipation mechanisms were revealed. Moreover, the Poisson’s ratio decreased first and then increased with strain, which right manifested the compressibility of 2D foam in the initial stage and the densification in the end of compression. Meanwhile, the change of the Poisson’s ratio with porosity didn’t follow monotone function relation.

Stability of Two-Dimensional Liquid Foams under Externally Applied Electric Fields.

Liquid foams are highly complex systems consisting of gas bubbles trapped within a solution of surfactant. Electroosmotic effects may be employed to induce fluid flows within the foam structure and impact its stability. The impact of external electric fields on the stability of a horizontally oriented monolayer of foam (2D foam) composed of anionic, cationic, non-ionic, and zwitterionic surfactants was investigated, probing the effects of changing the gas–liquid and solid–liquid interfaces. Time-lapse recordings were analyzed to investigate the evolution of foam over time subject to varying electric field strengths. Numerical simulations of electroosmotic flow of the same system were performed using the finite element method. Foam stability was affected by the presence of an external electric field in all cases and depended on the surfactant type, strength of the electric field, and the solid material used to construct the foam cell. For the myristyltrimethylammonium bromide (MTAB) foam in a glass cell, the time to collapse 50% of the foam was increased from ∼25 min under no electric field to ∼85 min under an electric field strength of 2000 V/m. In comparison, all other surfactants trialed exhibited faster foam collapse under external electric fields. Numerical simulations provided insight as to how different zeta potentials at the gas–liquid and solid–liquid interfaces affect fluid flow in different elements of the foam structure under external electric fields, leading to a more stable or unstable foam.

Elastocapillary deformation of thin elastic ribbons in 2D foam columns.

The ability of liquid interfaces to shape slender elastic structures provides powerful strategies to control the architecture of mechanical self assemblies. However, elastocapillarity-driven intelligent design remains unexplored in more complex architected liquids – such as foams. Here we propose a model system which combines an assembly of bubbles and a slender elastic structure. Arrangements of soap bubbles in confined environments form well-defined periodic structures, dictated by Plateau's laws. We consider a 2D foam column formed in a container with square cross-section in which we introduce an elastomer ribbon, leading to architected structures whose geometry is guided by a competition between elasticity and capillarity. In this system, we quantify both experimentally and theoretically the equilibrium shapes, using X-ray micro-tomography and energy minimisation techniques. Beyond the understanding of the amplitude of the wavy elastic ribbon deformation, we provide a detailed analysis of the profile of the ribbon, and show that such a setup can be used to grant a shape to a UV-curable composite slender structure, as a foam-forming technique suitable to miniaturisation. In more general terms, this work provides a stepping stone towards an improved understanding of the interactions between liquid foams and slender structures.

Predicting and following T1 events in dry foams from geometric features

Machine learning techniques have been recently applied in predicting deformation in amorphous materials. In this study, we extract structural features around liquid film vertices from images of flowing 2D foam and apply a multilayer perceptron to predict local yielding. We evaluate their importance in the description of the T1 events and show that a high level of predictability may be achieved using well-chosen combinations of features as the prediction data. The most relevant features are extracted by performing the predictions separately for isolated sets of features, and these findings are verified using principal component analysis. Using this approach, we determine which properties of the images are most important with regard to the physics of the processes. Our findings indicate that film lengths and angles between the liquid films joining at the vertex are the most important features that predict the local yield events. These two features describe 83% of the yield events. As an application, we extract the statistics of event waiting times from the experiment.

Anti-inflammatory potential of simvastatin loaded nanoliposomes in 2D and 3D foam cell models

Atherosclerosis is a multifactorial disease triggered and sustained by risk factors such as high cholesterol, high blood pressure and unhealthy lifestyle. Inflammation plays a pivotal role in atherosclerosis pathogenesis. In this study, we developed a simvastatin (STAT) loaded nanoliposomal formulation (LIPOSTAT) which can deliver the drug into atherosclerotic plaque, when administered intravenously. This formulation is easily prepared, stable, and biocompatible with minimal burst release for effective drug delivery. 2D and 3D in vitro models were examined towards anti-inflammatory effects of STAT, both free and in combination with liposomes. LIPOSTAT induced greater cholesterol efflux in the 2D foam cells and significantly reduced inflammation in both 2D and 3D models. LIPOSTAT alleviated inflammation by reducing the secretion of early and late phase pro-inflammatory cytokines, monocyte adherence marker, and lipid accumulation cytokines. Additionally, the 3D foam cell spheroid model is a convenient and practical approach in testing various anti-atherosclerotic drugs without the need for human tissue.

Direct Single-Step Printing of Conductive Grids on Curved Surfaces Using Template-Guided Foaming.

Advanced transparent conductors have been studied intensively in the aspects of materials, structures, and printing methods. The material and structural advancements have been successfully accomplished with various conductive nanomaterials and spring-like structures for better electrical conductivity and high mechanical flexibility of the transparent conductors. However, the capability to print submicrometer conductive patterns directly and conformally on curved surfaces with low processing cost and high throughput remains a technological challenge to achieve, primarily because of the original two-dimensional (2D) nature of conventional lithography processes. In our study, we exploit a liquid-mediated patterning approach in the development of flexible templates, enabling printing of curvilinear silver grids in a single-step and strain-free manner at a submicrometer resolution within several minutes with minimum loss of noble metals. The template can guide arrays of receding liquid-air interfaces on curved substrates during liquid evaporation, thereby generating ordered 2D foam structures that can confine and assemble silver nanoparticles in grid patterns. The printed silver grids exhibit suitable optical, electrical, and Joule-heating performances, enabling their application in transparent heaters. Our technique has the potential to extend the existing 2D micro/nanofluidic liquid-mediated patterning approach to three-dimensional (3D) control of liquid-air interfaces for low-cost all-liquid-processed functional 3D optoelectronics in the future.

Variation of average coordination number with liquid fraction for two-dimensional foams with finite contact angle

ABSTRACT We present Surface Evolver computer simulations for two-dimensional (2d) foams in which the contact angle at which liquid films and Plateau borders meet is non-zero. We determine the average coordination number Z of bubbles over a wide range of finite contact angles θ and liquid fractions ϕ. We find a linear scaling of Z for values of ϕ between about 0.07 and 0.15, corroborating previous data obtained for the case of zero contact angle. The results highlight the importance of attractive bubble interactions for 2d foams.

Scaling Laws in the Dynamics of Collapse of Single Bubbles and 2D Foams.

Avalanches of rupturing bubbles play an important role in the dynamics of collapse of macroscopic liquid foams. We hypothesized that the occurrence of cascades of rupturing bubbles in foams depends, at least in part, on the power released during the rupture of a bubble. In this paper, we present results on the dynamics of single bubble bursting obtained by analyzing the pressure wave (sound) emitted by the bubble when collapsing. We found that the released energy varies linearly with bubble size, the frequency of the emitted sound follows a power law with exponent 3/2 (compatible with the Helmholtz resonator model) and the duration of a rupturing event seems to be independent of bubble size. To correlate the dynamics of individual bubbles with the dynamics of foams, we studied the occurrence of avalanches on bubble rafts and found that the phenomenon appears to be a self-organized criticality (SOC) process. The distribution functions for the size of the avalanches are a power law with exponents between 2 and 3, depending on the surfactant concentration. The distribution of times between ruptures also follows a power law with exponents close to 1, independently of the surfactant concentration.

Effect of surfactant redistribution on the flow and stability of foam films.

The viscous froth model for two-dimensional (2D) dissipative foam rheology is combined with Marangoni-driven surfactant redistribution on a foam film. The model is used to study the flow of a 2D foam system consisting of one bubble partially filling a constricted channel and a single spanning film connecting it to the opposite channel wall. Gradients of surface tension arising from film deformation induce tangential flow that redistributes surfactant along the film. This redistribution, and the consequent changes in film tension, inhibit the structure from undergoing a foam-destroying topological change in which the spanning film leaves the bubble behind; foam stability is thereby increased. The system's behaviour is categorized by a Gibbs-Marangoni parameter, representing the ratio between the rate of motion in tangential and normal directions. Larger values of the Gibbs-Marangoni parameter induce greater variation in surface tension, increase the rate of surfactant redistribution and reduce the likelihood of topological changes. An intermediate regime is, however, identified in which the Gibbs-Marangoni parameter is large enough to create a significant gradient of surface tension but is not great enough to smooth out the flow-induced redistribution of surfactant entirely, resulting in non-monotonic variation in the bubble height, and hence in foam stability.

Multi-dimensional analysis of micro-/nano-polymeric foams by confocal laser scanning microscopy and foam simulations

Multi-dimensional foam structure analysis is critical to identify the properties of supercritical CO2 (scCO2) foamed materials, but most applied analysis only focus on two-dimensional (2D) foam morphology. A novel method of confocal laser scanning microscopy (CLSM), a powerful technique for material structure characterization, is then successfully applied for the first time to construct the multi-dimensional (including 2D and 3D) foam structure obtained in scCO2 foaming. In CLSM characterization, fluorescent dye is the key point to enhance polymeric foams’ fluorescence intensity so that the multi-dimensional foam structure is clearly observed. In the multi-dimensional analysis, it is noticed that the statistical cell size via 2D characterization is only 0.79 of that via 3D characterization. This specific conversion coefficient among multi-dimensional foam morphology is further verified in theoretical analysis via micro-/nano-cellular foam simulation. The universal specific conversion coefficient (2D/3D_cell size = 0.79 and 2D/3D_cell density = 1.2) then enables a 3D foam construction for polymeric foams made from scCO2 foaming with only 2D foam characterization data no matter the foam has a micro- or nano-cellular structure.

Implementation of Morse–Witten theory for a polydisperse wet 2D foam simulation

ABSTRACTThe Morse–Witten theory provides a formulation for the inter-bubble forces and corresponding deformations in a liquid foam, accurate in the limit of high liquid fraction. Here we show how the theory may be applied in practice, including allowing for polydispersity in the bubble sizes. The resulting equilibrated 2D structures are consistent with direct calculations, within the limitations of the theory. The path to developing a 3D model is outlined for future work.

Measurement of film permeability in 2D foams.

The coarsening of quasi-2D wet foams is well described theoretically by the model of Schimming and Durian, that takes into account the diffusion through the Plateau borders and the vertices in a rigorous manner. In this article, we describe an experimental study of coarsening in which the foam film permeability is measured in such quasi-2D wet foams. We first performed a full characterization of the structure of the studied foams. Then we measured the coarsening rates. It appears that, in these foams, the film thicknesses are still too small for the Plateau borders and the vertices to contribute, but the surface Plateau borders lead to a smaller coarsening rate compared to dry foams. This rate increases with capillary pressure and follows well the prediction of the model. We demonstrate the importance of working in controlled pressure conditions during permeability measurements. Indeed, permeability depends on film thickness itself depending on capillary pressure.

Foam as a self-assembling amorphous photonic band gap material

We show that slightly polydisperse disordered 2D foams can be used as a self-assembled template for isotropic photonic band gap (PBG) materials for transverse electric (TE) polarization. Calculations based on in-house experimental and simulated foam structures demonstrate that, at sufficient refractive index contrast, a dry foam organization with threefold nodes and long slender Plateau borders is especially advantageous to open a large PBG. A transition from dry to wet foam structure rapidly closes the PBG mainly by formation of bigger fourfold nodes, filling the PBG with defect modes. By tuning the foam area fraction, we find an optimal quantity of dielectric material, which maximizes the PBG in experimental systems. The obtained results have a potential to be extended to 3D foams to produce a next generation of self-assembled disordered PBG materials, enabling fabrication of cheap and scalable photonic devices.

The Potential of Fluocinolone Acetonide to Mitigate Inflammation and Lipid Accumulation in 2D and 3D Foam Cell Cultures.

Inflammation plays an important role in all stages of atherosclerosis development. Therefore, the use of anti-inflammatory drugs could reduce the risk of major adverse cardiovascular events due to atherosclerosis. Herein, we explored the capacity of fluocinolone acetonide (FA), a glucocorticoid (GC), in modulating foam cell formation and response. Human THP-1 derived foam cells were produced using 100 μg/mL oxidized low-density lipoproteins (OxLDL) and fetal bovine serum (1 and 10%). 2D cultures of these cells were treated with FA (0.1, 1, 10, and 50 μg/mL) in comparison with dexamethasone (Dex). Results showed that treatment with 0.1 and 1 μg/mL FA and Dex improved foam cell survival. FA and Dex also inhibited inflammatory cytokine (CD14, M-CSF, MIP-3α, and TNF-α) secretion. Notably, at the concentration of 1 μg/mL, both FA and Dex reduced cholesteryl ester accumulation. Compared to Dex, FA was significantly better in reducing lipid accumulation at the therapeutic concentrations of 1 and 10 μg/mL. In a novel 3D foam cell spheroid model, FA was shown to be more effective than Dex in diminishing lipid accumulation, at the concentration of 0.1 μg/mL. Taken together, FA was demonstrated to be effective in preventing both lipid accumulation and inflammation in foam cells.

The effect of cell boundary on 2D foam

We have studied the effect of cell boundary on 2D foam, with particular attention to perfect arrays of identical bubbles, and those containing only a single defect with time. We have also examined the effect of the wetness of the foam, observing the stability of two-dimensional foam comprising bubble rafts constrained to a fixed area of liquid surface. Perfectly six-fold coordinated foam appear to be unstable against loss of cohesion, but the lifetime to breakage of the perfect foam increases systematically with changing the cell boundaries. Foams containing a single defect are stable against such breakage due to the elastic stress fields around it.

Statistics and topological changes in 2D foam from the dry to the wet limit

The software PLAT, for the simulation of two-dimensional foams, has never been fully exploited, particularly in the wet limit, where it has difficulty converging. Present computer resources have enabled us to circumvent this problem. Using a data-set of 600,000 simulations, we are able to compute the polydisperse foam excess energy all the way from the dry to the wet limit. We also present data and a simple empirical function for the number distribution of n-sided bubbles for all values of the average contact number Z. Furthermore we show that, starting from a dry foam, incremental increases in liquid fraction bring with them a steadily increasing fraction f of bubbles involved in rearrangements. The size distribution of these rearrangements is found to be exponential, , where the mean, , increases in the wet limit.

2D foams above the jamming transition: Deformation matters

Jammed soft matter systems are often modelled as dense packings of overlapping soft spheres, thus ignoring particle deformation. For 2D (and 3D) soft disks packings, close to the critical packing fraction ϕc, this results in an increase of the average contact number Z with a square root in ϕ−ϕc. Using the program PLAT, we find that in the case of idealised two-dimensional foams, close to the wet limit, Z increases linearly with ϕ−ϕc, where ϕ is the gas fraction. This result is consistent with the different distributions of separations for soft disks and foams at the critical packing fraction. Thus, 2D foams close to the wet limit are not well described as random packings of soft disks, since bubbles in a foam are deformable and adjust their shape. This is not captured by overlapping circular disks.