Foam Dynamics Research Articles

Enhanced Flotation Separation of Iron and Silicon with Branched Block Polyethylene Oxide Polypropylene Oxide and Sodium Oleate: Mechanisms and Flotation Behavior

This study explores the strengthening mechanism of the surfactant branched block polyethylene oxide–polypropylene oxide (BB-PEO-PPO) in sodium oleate (NaOL) flotation systems. A comprehensive characterization of BB-PEO-PPO was performed using flotation experiments, contact angle measurements, surface tension analysis, zeta potential measurements, infrared spectroscopy, and foam dynamics assessments. Flotation results showed that the combination of BB-PEO-PPO and NaOL improved iron recovery by 2.71% and reduced the total iron (TFe) grade in tailings by 2.05%, demonstrating a significant enhancement in collecting efficiency. The addition of BB-PEO-PPO effectively reduced foam size and lowered the zeta potential on the surface of activated quartz. At a slurry temperature of 15 °C, BB-PEO-PPO increased the solubility of NaOL radicals, facilitating their chemical adsorption onto activated quartz and improving the hydrophobicity of quartz particles. Notably, the presence of BB-PEO-PPO extended the flotation foam discharge time (D50) by 50% without substantially increasing foam volume, thereby significantly enhancing foam stability.

The influence of viscosity buildup on the foaming dynamics of rigid polyurethane foams

AbstractThe viscoelastic properties development during the reactive foaming of four standard polyurethane formulations was monitored using a flooded parallel plate rheometer. The measurements in situ demonstrated how foams of low catalyst content took longer than 10 min to increase their viscosity from 1 to 103 Pa s, while foams with higher catalysts reached this modulus in less than 4 min. This polymerization speed deeply impacted the evolution of the cellular structure during foaming, which was demonstrated through in situ x‐ray imaging and computer simulation. Foams with high catalyst stabilized in their final cell size in 4–5 min, concurring with the stage of largest viscosity buildup. In contrast, the foams of low catalyst content underwent strong degeneration as a result of the slow gelification and stiffening of the matrix. Simulation results also revealed that stabilization of the cellular structure happens faster when the catalyst and blowing agent contents are increased.

Проблема изложения требований норм в области пожарной безопасности в России

Purpose. The success of fire extinguishment directly depends on discharging the necessary and sufficient amount of extinguishing agents onto the fire. Analysis of the characteristics of modern extinguishing agents and the research works in this area has shown that when extinguishing fires at power facilities the application of water is not always appropriate, and the specifics of using other means, such as, for example, compressed air foam, have not been fully studied. The article presents the findings of the research and mathematical modeling of fluid and gas dynamics of compressed air foam through delivery hoses when extinguishing fires at power facilities. Methods. The developed measuring system, programmes and experimental techniques have been applied in the research. Existing accurate models of mathematical evaluation of fluid and gas dynamics parameters of two-phase medium have been applied for numerical modelling. Findings. As a result of experimental study and mathematical modeling pressure loss indicators have been obtained along the hose line length when compressed air foam is supplied in a wide range of expansion from 2 to 20. The relative deviation of results has been no more than 7 %. Research application field. The obtained results and further research have practical significance in improving the efficiency of fire service units in performing firefighting tasks. Conclusions. The conducted research allowed obtaining data and their application in practical activity of firefighting units will make it possible to evaluate the capacity of firefighting units in preparing preliminary planning documents for critical facilities, including power facilities, and increase the efficiency of fire extinguishment.

Investigation into three-dimensional dry foam modelling using the boundary integral method

Understanding foam rheology relies on predictions of the foam structure and physical quantities associated with foam dynamics. In this work, we explore the modelling of dry foam dynamics using the boundary integral method, which can be used to predict the behaviour of dry foam in bulk or in confined geometries. The resultant equation for dry foam shows that the movement of foam films or lamellae is governed by the film curvature and the normal stress that the wall imposes on the fluid phase in bubbles and is characterized by three distinct motion modes: the background flow, the imposed flow due to the deformation of wall and the relaxation process of films. The singular integrals involved in the model are handled using a combined method of singularity subtraction and nonsingular contour integral. To demonstrate the validity of the method in potential applications, we consider two scenarios, for foam in bulk and in confined geometries, respectively. Dynamic foam motion is tracked using the model. The results show that the dry foam model has potentials applied in a variety of applications, such as foam flow in microfluidic devices and porous media.

CO2 soluble surfactants for carbon storage in carbonate saline aquifers with achievable injectivity: Implications from the continuous CO2 injection study

Continuous CO2 injection (CCI) into saline aquifers suffers from low sweep efficiency. While utilizing foam can effectively address this issue, a relatively potent foam design may undesirably reduce the injectivity of CO2. In this study, the potential of CO2-soluble surfactants assisted carbon storage in carbonate saline aquifers was evaluated by core flooding tests and numerical simulations. It is found that foam can be generated at the displacement front during continuous CO2 injection with 0.39 g/L surfactant (CCI + S, fg = 100 %). The CO2 saturation can reach 60 % after 1.0 pore volume of CCI + S, approximately 50 % higher than that of CCI. The maximum pressure gradient is around 1.5 psi/ft at an injection rate of 1.0 ft/d in 162 mD Indiana Limestone for CCI + S. The effects of surfactant concentration, foam quality, and rock permeability were also investigated by core flooding. Moreover, the influence of surfactant partitioning and adsorption on CO2 transport behavior was systematically evaluated by numerical simulation in synthetic and geological models, using modeling parameters that are realistic for field applications. The advantage of injecting surfactant with CO2 is more evident in heterogeneous saline aquifers. Such novel injection strategy provides a promising approach for carbon sequestration in saline aquifers by controlling the mobility of CO2 at the displacement front and simultaneously maintaining acceptable injectivity in the field. The CCI + S process may also impose less risk to the caprock. Expanding the potential CO2 storage sites to heterogeneous saline aquifers could be a game-changer. Our understanding of foam dynamics in porous media could also be advanced.

The Effect of Multiple Cycles of Surfactant-Alternating-Gas Process on Foam Transient Flow and Propagation in a Homogeneous Sandstone

Summary Years of laboratory studies and field tests show that there is still uncertainty about the ability of foam to propagate deep into a reservoir. Many factors have been identified as potential causes of nonpropagation, the most concerning being the lack of sufficient pressure gradient required to propagate foam at locations far from the point of injection. Most researchers that investigated foam propagation did so by coinjecting surfactant and gas. Coinjection offers limited information about transient foam processes due to limitations in the experimental methods needed to measure foam dynamics during transient flow. Foam injection by surfactant-alternating-gas (SAG) has proven to be more effective and common in field application. Repeated drainage and imbibition cycle offer a more favorable condition for the quick generation of foam. Foam can also be propagated at a lower pressure gradient in SAG mode. The objective of this study is to experimentally investigate how transient foam dynamics (trapping, mobilization, and bubble texture) change with multiple cycles of SAG and also with distance from the point of injection. A pair of X-ray source and receiver, differential pressure transducers, and electrical resistance sensors were placed along a 27-cm long, homogeneous, and high-permeability (KL = 70 md) Berea sandstone core. Foam was then generated in situ by SAG injection and allowed to propagate through the core sample under a capillary displacement by brine (brine injection rate = 0.5 cm3/min, Nca = 3×10-7). By use of a novel analytical method on coreflood data obtained from axial pressure and saturation sensors, we obtained trapped foam saturation, in-situ foam flow rates, apparent viscosities, and inferred qualitative foam texture at different core sections. We then observed the following: (i) Maximum trapped foam is uniform across the core sections, with saturation ranging from 47% to 52%. At the vicinity of foam injection, foam apparent viscosity is dominantly caused by gas trapping. At locations farther away, foam apparent viscosity is dominated by both gas trapping and refinement of foam texture. (ii) Cyclic injection of foam further enhances the refinement of foam texture. (iii) Textural refinement increases foam apparent viscosity as it propagates away from the point of injection. (iv) As the foam strength increases, the average gas flow rate in the core sample decreases from 0.5 cm3/min to 0.06 cm3/min. (v) There is no stagnation of foam as remobilization of trapped gas occurs during each cycle at an average flow rate of 0.002 cm3/min.

Towards effective actions for the continuum limit of spin foams

Spin foams arise from a quantization of classical gravity expressed via the Plebanski action. Key open questions related to the continuum limit of spin foams are whether general relativity is reproduced and what type of corrections could emerge. As a central component for spin foam dynamics, recent results on the continuum limit of the Area Regge action suggest a close relation with actions for area metrics instead of a length metric. Inspired by these results, within the framework of modified Plebanski theory we construct a family of candidate actions for area metrics. These actions are expected to describe the continuum limit of spin foams and provide a starting point to explore phenomenological aspects of the large-scale dynamics of spin foams. More generally, they set the stage for exploring consequences of an enlargement of the configuration space for gravity from length to area metrics. The actions we construct lead to an effective action for the length metric, describing a non-local and ghost-free version of Einstein–Weyl gravity.

From spin foams to area metric dynamics to gravitons

Although spin foams arose as quantizations of the length metric degrees of freedom, the quantum configuration space is rather based on areas as more fundamental variables. This is also highlighted by the semi-classical limit of four-dimensional spin foam models, which is described by the Area Regge action. Despite its central importance to spin foams the dynamics encoded by the Area Regge action is only poorly understood, in particular in the continuum limit. We perform here a systematic investigation of the dynamics defined by the Area Regge action on a regular centrally subdivided hypercubical lattice. This choice of lattice avoids many problems of the non-subdivided hypercubical lattice, for which the Area Regge action is singular. The regularity of the lattice allows to extract the continuum limit and its corrections, order by order in the lattice constant. We show that, contrary to widespread expectations which arose from the so-called flatness problem of spin foams, the continuum limit of the Area Regge action does describe to leading order the same graviton dynamics as general relativity. The next-to-leading order correction to the effective action for the length metric is of second order in the lattice constant, and is given by a quadratic term in the Weyl curvature tensor. This correction can be understood to originate from an underlying dynamics of area metrics. This suggests that the continuum limit of spin foam dynamics does lead to massless gravitons, and that the leading order quantum corrections can be understood to emerge from a generalization of the configuration space from length to area metrics.

Cross over to collective rearrangements near the dry-wet transition in two-dimensional foams

Liquid foams respond plastically to external perturbations over some critical magnitude. This rearrangement process is directly related to the mechanical properties of the foams, playing a significant role in determining foam lifetime, deformability, elasticity, and fluidity. In this paper, we experimentally investigate the rearrangement dynamics of foams near a dry-wet transition. When a foam transforms from a dry state to a wet state, it is found that considering collective events, separated T1 events propagate in dry foams, while T1 events occur simultaneously in wet foams. This cross over to collective rearrangements is closely related to the change in local bubble arrangements and mobility. Furthermore, it is also found that a probability of collective rearrangement events occurring follows a Poisson distribution, suggesting that there is little correlation between discrete collective rearrangement events. These results constitute progress in understanding the dynamical properties of soft jammed systems, relevant for biological and material sciences as well as food science.

Early freezing dynamics of an aqueous foam.

Phase-change is an essential and unavoidable process to obtain solid foam. We study experimentally the solidification dynamics of a model aqueous foam in contact with a cold substrate. The substrate temperature, the foam bubble radius and the liquid fraction are changed. We show that the freezing dynamics always starts by following a self-similar square root of time diffusive dynamics. These early dynamics are then predicted as a function of the control parameters using a 1D diffusion model and by treating our foam as a homogeneous fluid with equivalent thermophysical properties. In particular, we build a new expression for the foam conductivity. Finally, experimental and theoretical results are compared and interpreted. This study paves the way towards the understanding of the complex foam freezing dynamics at longer times, when the freezing is then coupled to water migration in the foam.

Bubble-particle dynamics in multiphase flow of capillary foams in a porous micromodel.

Surfactant-free capillary foams (CFs) are known to be remarkably tolerant to oil, and possess unique stability and flow properties. These properties result from the presence of oil-and-particle-coated bubbles that are interconnected by a dense particle-oil capillary network. In this work, we present a study of the dynamics of capillary foams flowing through a porous micromodel. We determine that despite the presence of oil-particle networks, CFs can flow through a microporous environment and that above a threshold flowrate, >80% of foam pumped through the micromodel can be recovered. In addition, we highlight the absence of steady state in CF flow and identify the underlying phenomena including the increasing apparent viscosity, reconfigurable flow paths, and intermittent clogging of the micromodel from an oil-particle composite and bubbles trapped in pores. We also characterize bubble dynamics and show that CFs surprisingly exhibit the same bubble generation and destruction mechanisms as classical foams despite the absence of surfactants. Our observations suggest that the porous medium plays a key role in generating uniformly sized bubbles and that capillary foams in a microporous environment tend to reconfigure their flow paths in a manner that may provide opportunities for increased sweep efficiency in enhanced oil recovery.

Gas-Liquid Foam Dynamics: From Structural Elements to Continuum Descriptions

Gas-liquid foams are important in applications ranging from oil recovery and mineral flotation to food science and microfluidics. Beyond their practical use, they represent an intriguing prototype of a soft material with a complex, viscoelastic rheological response. Crucially, foams allow detailed access to fluid-dynamical processes on the mesoscale of bubbles underlying the large-scale material behavior. This review emphasizes the importance of the geometry and interaction of mesoscale structural elements for the description of the dynamics of entire foams. Using examples including bulk flow of foam under steady shear, interfacial instabilities, and foam fracture through bubble rupture, this article highlights the wide variety of available theoretical descriptions, ranging from network modeling approaches coupling structural element equations of motion to full continuum models with elastoviscoplastic constitutive relations. Foams offer the opportunity to develop rigorous links between such disparate descriptions, providing a blueprint for physical modeling of dynamical multiscale systems with complex structure.

Modelling the effect of morphology on thermal aging of low-density closed-cell PU foams

Low-density closed-cell polyurethane (PU) foams are widely used in thermal insulation in diverse applications, therefore predicting their thermal aging has a distinct practical importance. Several approaches have been developed allowing forecasting the long-term changes of gas composition in foams, which manifest as the thermal aging. The accelerated aging test methods of foams need to be applied to each foam morphology of interest, while diffusion modelling-based methods, employing characterisation of the gas transport properties of PU polymer or monitoring the evolution of gas composition in foam cells, are relatively complicated. In this study, the experimentally determined evolution of PU foam conductivity is used for estimating the effective diffusivities of gases, based on which permeability of the PU polymer is subsequently evaluated by a structural model assuming Kelvin cell geometry of foam cells. The proposed approach enables prediction of aging dynamics of foams developed from the same PU polymer but possessing a markedly different morphology.

From Individual Liquid Films to Macroscopic Foam Dynamics: A Comparison between Polymers and a Nonionic Surfactant.

Foams can resist destabilizaton in ways that appear similar on a macroscopic scale, but the microscopic origins of the stability and the loss thereof can be quite diverse. Here, we compare both the macroscopic drainage and ultimate collapse of aqueous foams stabilized by either a partially hydrolyzed poly(vinyl alcohol) (PVA) or a nonionic low-molecular-weight surfactant (BrijO10) with the dynamics of individual thin films at the microscale. From this comparison, we gain significant insight regarding the effect of both surface stresses and intermolecular forces on macroscopic foam stability. Distinct regimes in the lifetime of the foams were observed. Drainage at early stages is controlled by the different stress-boundary conditions at the surfaces of the bubbles between the polymer and the surfactant. The stress-carrying capacity of PVA-stabilized interfaces is a result of the mutual contribution of Marangoni stresses and surface shear viscosity. In contrast, surface shear inviscidity and much weaker Marangoni stresses were observed for the nonionic surfactant surfaces, resulting in faster drainage times, both at the level of the single film and the macroscopic foam. At longer times, the PVA foams present a regime of homogeneous coalescence where isolated coalescence events are observed. This regime, which is observed only for PVA foams, occurs when the capillary pressure reaches the maximum disjoining pressure. A final regime is then observed for both systems where a fast coalescence front propagates from the top to the bottom of the foams. The critical liquid fractions and capillary pressures at which this regime is obtained are similar for both PVA and BrijO10 foams, which most likely indicates that collapse is related to a universal mechanism that seems unrelated to the stabilizer interfacial dynamics.

Energetically consistent inelasticity for optimization time integration

In this paper, we propose Energetically Consistent Inelasticity (ECI), a new formulation for modeling and discretizing finite strain elastoplasticity/viscoelasticity in a way that is compatible with optimization-based time integrators. We provide an in-depth analysis for allowing plasticity to be implicitly integrated through an augmented strain energy density function. We develop ECI on the associative von-Mises J2 plasticity, the non-associative Drucker-Prager plasticity, and the finite strain viscoelasticity. We demonstrate the resulting scheme on both the Finite Element Method (FEM) and the Material Point Method (MPM). Combined with a custom Newton-type optimization integration scheme, our method enables simulating stiff and large-deformation inelastic dynamics of metal, sand, snow, and foam with larger time steps, improved stability, higher efficiency, and better accuracy than existing approaches.

Friction Dynamics of Foams under Nonlinear Motion

Foams are viscoelastic soft materials with complex mechanical properties. Here, we evaluated the friction dynamics of foams between acrylic plates using a sinusoidal motion friction evaluation system and we found some interesting characteristics under accelerated conditions. On a typical solid surface, a symmetrical friction profile, in which static and kinetic frictions are observed, is obtained under reciprocating nonlinear motion. Meanwhile, significant lubricant effects and velocity-dependent friction profiles without static friction were observed in foams. The friction force in foams increased in proportion to the power of velocity, with a power index of <1. These characteristic and dynamic phenomena in foams were observed in this study. They had been caused by the formation of a thick lubricant film and various dissipative modes including surfactant diffusion, viscous dissipation, and wall slip of bubbles. Moreover, the addition of a thickener increased the friction force and the delay time of friction response and improved the foam durability against normal force and shear. These findings are useful for understanding dynamic phenomena in soft materials.

Assessing uncertainties and identifiability of foam displacement models employing different objective functions for parameter estimation

Foam injection in porous media is often used to control the gas fingering in multi-phase flow. Mathematical models of foam dynamics involve non-Newtonian formulations. To numerically simulate these complex phenomena, experimental data is gathered and used to estimate the parameter values of models via optimization techniques. The present work improves this procedure by introducing a new objective function based on the mobility reduction factor and does not require further experimental observations other than those usually obtained in core-flooding experiments. A series of numerical experiments were carried out to show the features and robustness of the proposed approach. In particular, the identifiability analysis results show that key parameters of the models are practically non-identifiable when using traditional objective functions that rely only on apparent viscosity. When the proposed objective function is used for parameter estimation, the identifiability issues are solved. In addition, the uncertainty quantification analysis revealed that lower uncertainty is achieved when using the new objective function when compared to the one that uses only apparent viscosity. In summary, we show that the new objective function generates better-calibrated models with high fidelity and low uncertainties and alleviates parameter non-identifiability issues. Therefore, the results suggest the new objective function is better suited for calibrating foam displacement models for enhanced oil recovery.

The role of continuous phase rheology on the stabilization of edible foams: A review

Foams play an essential role in food. They contribute to the texture, aroma, and mouthfeel of a product; potentially reduce calories; and visually inspire the consumer. Understanding factors that control foam structure and bubble lifetimes is, therefore, of considerable interest. This review focuses on the effect of the continuous phase rheology for bubbly systems with an emphasis on edible foams. We review common biopolymers used to alter the rheology of the continuous phase of food foams and discuss potential mechanisms responsible for the production and stabilization of such systems. Variations to the matrix (i.e., foamulsions and oil-based foams) and the addition of gelling particles are also considered. This review emphasizes the necessity for fine control over the mechanical properties of the continuous phase to achieve the desired sensorial attributes and foam stability in food products. However, the dynamics of viscoelastic food foams are poorly understood due to their complex nature. We, therefore, discuss rheological studies on model foams and provide future directions for research that is in keeping with current trends and challenges in the food industry and culinary arts.

Modeling of dynamic phenomena in aqueous foams (review)

Analytical review of investigations aimed at studying the aqueous foam behavior under the shock-wave impact is given. The main approaches and theoretical approximations used in the development of aqueous foams models are analyzed. The two-phase gas-drop model of aqueous foam is considered, based on the laws of conservation of mass, momentum, and energy in accordance with one-pressure, two-velocity, two-temperature approximations. The model describes foam dynamics under a high - intensity impact, which destroys the foam structure into microdroplets, and takes into account interfacial heat transfer, interfacial drag and virtual mass forces and the phenomenon of foam syneresis (deposition). The numerical implementation of the model was carried out using new solvers in the OpenFOAM software. The analysis of the numerical solution of the spherical explosion in aqueous foam is given for the conditions of the literature experimental data. The syneresis influence on the intensity and velocity of shock wave propagation is shown. The two-phase model of aqueous foam is considered, which takes into account its elastic- viscous-plastic properties for conditions of weak impact that does not destroy foam structure. The model takes into account the elastic properties of aqueous foam at small deformations and describes it as a non-Newtonian fluid when the foam changes its state from the elastic to viscoplastic. The weak shock wave propagation dynamics in the layer of aqueous foam with the formation of a two-wave structure, consisting of the main wave and the elastic precursor ahead of it, is analyzed. The process of local aqueous foam compaction zone formation, followed by a gaseous region, behind the shock wave front is shown. The reliability of the obtained results of numerical studies is confirmed by their agreement with the literature experimental data.

Dynamic X-ray micotomography of microfibrous cellulose liquid foams using deep learning

Using X-ray microcomputed tomography (micro-CT) as a 3D microstructural analysis tool elucidates the time evolution of foam Plateau borders and nodes, providing unprecedented vision of foam dynamics. Deep learning facilitates the capability by allowing for quantifiable images to be collected at the time scale of five minutes. The stability mechanism of microfibrous cellulose is assessed demonstrating that trapping of fibers in the foam structure results in a critical concentration that marks an arrested foam. The mechanism of arrest is explained by 3D structural information extracted from micro-CT and confocal laser scanning microscopy images demonstrating the entanglement of cellulose fibers. A detailed analysis of the micro-CT data is provided to substantiate the quantitative nature of the digital images and assess advanced deep learning approaches. It is demonstrated that deep learning allows for the dynamic imaging of liquid foams whereas traditional data processing approaches cannot capture accurate geometrical information of foam structure.