Foam Drainage Research Articles

Numerical solutions of the fractal foam drainage equation

The flow of liquid relative to the bubbles is called drainage. This paper presents a study of the numerical solution of a non-linear foam drainage equation with time-fractional derivative. We use the two-scale approach which is formulated by combining the fractional complex transform and the homotopy perturbation method (HPM). With the aid of the fractional complex transform, first, we transform the problem into its differential partner and then HPM is applied to obtain the He’s polynomials which are highly and powerful support for non-linear problems. Further, we put forward the theory of the two-scale approach which reveals the sketch between fractional complex transform and the solution of non-linear foam drainage equation. The significant results illustrate that this approach does not require any assumption while it reduces the heavy calculation without any restrictive variable. This approach also sheds a bright light on practical applications of fractal calculus.

Evaluation of Disappearance Time and Palatability of Foams in the Oral Cavities of Healthy Volunteers, and Preparation of Drug-Containing Foam Formulations for Use in the Treatment of Oral Mucositis.

Oral mucositis is one of the most common adverse effects of radiation and chemotherapy in treatments of cancers. Some clinical guidelines have focused on the prevention and treatment of oral mucositis, and thus, a mouthwash containing drugs is often recommended. In this study, we aimed to evaluate the disappearance time and palatability in the oral cavities of healthy volunteers in foams prepared from different concentrations of the three viscosity grades of methylcellulose (SM-4, -100, -400). In addition, we prepared foam formulations of drugs (benzydamine, dexamethasone, allopurinol and rebamipide) for use as a prevention and treatment of oral mucositis. There was a significant relationship between the foam drainage ratios at 5-15 min and the disappearance time in the oral cavities. The significant relationship of foam densities to the foam disappearance time and overall palatability in a clinical study were observed. Thus, the foam density is considered an important parameter and reflects these clinically important properties. The foam from SM-4 has the longest disappearance time and the best palatability followed by foams from the 4 and 1% SM-4. Drug contents in drug-containing foam formulations which were prepared with 1-4% SM-4 represented 101-112% of the loaded drug contents, and the relative standard deviations of drug contents were <2.2%, which suggests that these formulations had pharmaceutically acceptable properties. This is the first report in regard to foam formulations containing drugs for the prevention and treatment of oral mucositis, and these formulations could be potentially useful for the prevention and treatment of oral mucositis.

Recovery of nanoparticles from wastewater by foam fractionation: Regulating bubble size distribution for strengthening foam drainage

The application of nanoparticles (NPs) in many fields generated large amounts of wastewater which would result in resource loss and environmental pollution. In this work, foam fractionation was used to recycle NPs from their aqueous suspensions and a novel method was developed to strengthen foam drainage through regulating bubble size distribution. The results showed that the adjacent bubbles with different size were easy to coalesce and then the bubble size and surface excess were enhanced simultaneously. Thereby strengthening foam drainage and foam stability simultaneously. The enrichment ratio of NPs increased approximately 45% with almost no loss of recovery percentage by using this method. The recycle efficiency of NPs was also affected by their structures and shapes that the recycle of tubular NPs was more efficient than globular NPs. Under the suitable conditions, the enrichment ratio and recovery percentage of silica nanoparticles (SNPs) and carbon nanotubes (CNTs) were 7.1, 90.1% and 9.9, 94.5%, respectively.

Closed form soliton solutions to the space-time fractional foam drainage equation and coupled mKdV evolution equations

Abstract Fractional nonlinear evolution equations concerning conformable fractional derivative are effective models to interpret intricate physical phenomena in the real world. The space-time fractional foam drainage equation and the coupled mKdV equations with conformable fractional derivative are important model equations for shallow water waves, the waves of flow of liquid between bubbles, the capillary waves, the waves of foam density, the electro-hydro-dynamical model, the ion acoustic plasma waves etc. In this study, we extract the functional and further general exact wave solutions comprising the rational, trigonometric, exponential and hyperbolic functions to the above stated models taking the advantage of the auxiliary equation method with the assistance of the fractional complex transformation. The method is convenient, reliable and delivers fresh and useful solutions to fractional differential equations ascend in physical and engineering sciences. We depict figures of the obtained solutions in order to illustrate the inner structure associated to the phenomena.

Foam drainage enhancement in foam fractionation for dye removal: process optimization by Taguchi methodology and grey relational analysis

Abstract The isolation of dye (methylene blue) by employing a foam fractionation technique with the assistance of a surfactant (sodium dodecyl sulfate) has been dealt with in this paper. This study also incorporated the comparison between contrasted and experimental columns. Taguchi methodology and grey relational analysis techniques were used to ascertain optimal conditions at which the column should be operated to achieve maximum percentage removal and enrichment ratio, for both the columns. The analysis of variance study suggested dye concentration to be the most influencing parameter. The relationship between dye concentration in the bulk phase and the foam phase was also deduced.

Evaluation of Suitability of Carboxymethyl Cellulose in Performance Improvement of Sodium Lauryl Sulfate Foam and Compressive Strength of Foam Concrete

Abstract Currently, foam concrete is commonly used for various construction applications such as partitions, filling grades, road embankment infills, and sound and heat insulation. It is to be noted that the foam production parameters have significant influence on the cellular structure of foam concrete, which governs the material properties of concrete. Hence, in an attempt to improve the foam quality, the present work focuses on evaluation of the suitability of viscosity enhancing agent carboxymethyl cellulose (CMC) in performance improvement of foam produced with surfactant sodium lauryl sulfate (SLS) for use in foam concrete production. Firstly, the influence of the addition of CMC on behavior of foam produced with surfactant SLS was studied by evaluating essential characteristics such as foam density, foam stability, and viscosity of surfactant solution. As a next step, the microstructure of foam and its behavior in cement slurry and mortar at the optimized concentrations of SLS and CMC were studied. Experimental studies revealed that the addition of 0.2 % CMC to 2.5 % SLS surfactant solution resulted in a 134 % increase in viscosity of surfactant solution, which eventually resulted in tremendous improvement in foam quality in terms of 34 % reduction in foam drainage (at the 5th minute after foam generation) and 22 % reduction in larger size foam bubbles (D90). Furthermore, as the air void microstructure of foam concrete is dependent on the foam bubble sizes, the reduction in foam bubble sizes resulted in 20 % enhancement in compressive strength of foam concrete. The addition of CMC is also found to affect the workability of foam concrete mixes, which is evident from the reduction in flow spread and the increase in flow time. Also, as the foam has retarding properties, the increase in foam content is found to increase the demolding time requirement of foam concrete specimens.

Synergistic effect of octadecyl ammonium oxide and oleate amide propyl betaine and development of a foam drainage reagent for natural gas production

Betaine surfactants are used widely in oil field chemistry as well as other industrial applications, but their foaming ability is very poor so that it cannot be used in foaming. In this work, the effect of octadecyl ammonium oxide on the foam properties of oleate amide propyl betaine, a new compound foaming reagent, is studied based on foam performance. Then, a foam drainage reagent of 0.5 wt% oleate amide propyl betaine and 0.1 wt% octadecyl ammonium oxide is developed for natural gas production. Its salt resistance, methanol resistance, high temperature resistance, anti-condensate oil performance, and emulsification ability are systematically evaluated. Furthermore, the factors affecting foam performance are analyzed. The results show that the compound foaming reagent has good anti-salt, anti-methanol, and anti-condensate oil properties for meeting application requirements. The microstructures of foams derived from different reagents reveal the stability mechanism. All results reflect the fact that compounding can expand their application range in different environments to various extents, which benefits the design and use of compound surfactants.

Comparing and Contrasting Travelling Wave Behaviour for Groundwater Flow and Foam Drainage

Liquid drainage within foam is generally described by the foam drainage equation which admits travelling wave solutions. Meanwhile, Richards’ equation has been used to describe liquid flow in unsaturated soil. Travelling wave solutions for Richards equation are also available using soil material property functions which have been developed by Van Genuchten. In order to compare and contrast these solutions, the travelling waves are expressed as dimensionless height, {hat{xi }} , versus moisture content, varTheta . For low moisture content, {{hat{xi }}} exhibits an abrupt change away from the dry state in Richards equation compared to a much more gradual change in foam drainage. When moisture content nears saturation, {hat{xi }} reaches large values (i.e. {hat{xi }} gg 1 ) for both Richards equation and foam drainage, implying a gradual approach of varTheta towards the saturated state. The {hat{xi }} values in Richards equation tend, however, to be larger than those in the foam drainage equation, implying an even more gradual approach towards saturation. The reasons for the difference between foam drainage and Richards equation solutions are traced back to soil material properties and in particular a soil specific parameter “m” which is determined from the soil-water retention curve.

Viscosity-driven stabilization of CO2-in-brine foams using mixtures of cocamidopropyl hydroxysultaine and sodium dodecyl sulfate

Foam stability is one of the key factors determining the success of any foam-field application, and for that, it is imperative to identify surfactant formulations able to reduce the extensive foam drainage and coarsening occurring in harsh environments, such as in high salinity brines. In this work, mixtures of cocamidopropyl hydroxysultaine (CAHS) and sodium dodecyl sulfate (SDS) at 1 wt% were evaluated as foaming agents to obtain CO2-in-brine foams with improved stability, compared to the single surfactant foams. The results showed that the mixture with excess of the zwitterionic surfactant (2:1, CAHS:SDS) produced a CO2-foam with a half-life four times higher than that of the foam formed using single components, at the same surfactant concentration. These foams exhibited a drastic reduction in both drainage and coarsening mechanisms, which was attributed to the significant increase (four orders of magnitude) in bulk phase viscosity due to the formation of large surfactant aggregates in the brine, as confirmed by dynamic light scattering (DLS) and rheological measurements. The analysis of the gas fraction in the foams formulated with the surfactant mixtures revealed that they were also able to comprise large amounts of CO2 (83–88% per volume of aqueous phase), as a result of retarding the diffusion of CO2 through the viscous aqueous phase of the foam. The results obtained in this work demonstrated that the synergy exhibited by CAHS and SDS in brine had a direct impact not only in the viscosity-driven stabilization of the CO2-foams, but also for the capture and retention of large amounts of CO2 inside the foam, which can have a direct impact in the sweeping efficiency, in the case of EOR, and in the CO2 storage, in the case of carbon capture and storage (CCS) technologies.

Foam Quality of Foams Formed on Capillaries and Porous Media Systems

Foams are of great importance as a result of their expansive presence in everyday life—they are used in the food, cosmetic, and process industries, and in detergency, oil recovery, and firefighting. There is a little understanding of foam formation using soft porous media in terms of the quality of foam and foam formation. Interaction of foams with porous media has recently been investigated in a study by Arjmandi-Tash et al., where three different regimes of foam drainage in contact with porous media were observed. In this study, the amount of foam generated using porous media with surfactant solutions is investigated. The aim is to understand the quality of foam produced using porous media. The effect of capillary sizes and arrangement of porous in porous media has on the quality of foam is investigated. This is then followed by the use of soft porous media for foam formation to understand how the foam is generated on the surface of the porous media and the effect that different conditions (such as concentration) have on the quality of the foam. The quality of foam is a blanket term for bubble size, liquid volume fraction, and stability of the foam. The liquid volume fraction is calculated using a homemade dynamic foam analyser, which is used to obtain the distribution of liquid volume fraction along with the foam height. Soft porous media does not influence substantially the rate of decay of foam produced, however, it decreases the average diameter of the bubbles, whilst increasing the range of bubble sizes due to the wide range of pore sizes present in the soft porous media. The foam analyser showed the expected behaviour that, as the foam decays and becomes drier, the liquid volume fraction of the foam falls, and therefore the conductivity of foam also decreases, indicating the usefulness of the home-made device for future investigations.

Convective instability in sheared foam

Abstract

Effect of homogenisation in foam and emulsion mix beverage colloidal system: A case in Teh Tarik

Teh Tarik is a frothed milk tea consisting of Ceylon Tea, condensed milk, sugar, where it is traditionally prepared by pulling motion to get aerated. High-shear homogenisation through rotor-stator homogeniser was explored in this study as an alternative method to produce Teh Tarik at a larger scale and at the same time enhancing the stability of the Teh Tarik emulsion and foam. Varying speeds (11,000 rpm, 18,000 rpm and 25,000 rpm) of homogenisation resulted in size reduction of milk fat globules to various degrees. This reduction in particle size by at least 0.4 μm consequently increased the stability of the milk tea emulsion, which is the most significant (α = 0.05) at the speed of 18,000 rpm. At the same time, increasing speed of homogenisation from 11,000 rpm to 18,000 rpm and 25,000 rpm also reduces dynamic surface tension through the increased protein adsorption rate at the water-air interphase and ultimately reducing foam drainage. Subsequently, the improved physical stability of emulsion and foam could be made use to develop satiety- and satiation-enhanced beverage as a modus operandi to reduce calorie intake among Malaysians.

Analysis of the foam-forming of non-woven lightweight fibrous materials using X-ray tomography

Foam-forming has in the past predominantly been used to create two-dimensional sheet-like fibrous materials. Allowing the foam to drain freely and decay under gravity, rather than applying a vacuum to remove it rapidly, we can produce lightweight three-dimensional fibrous structures from cellulose fibres, of potential use for thermal and acoustic insulation. muCT scanning of the fibrous materials enable us to determine both void size distributions and also distributions of fibre orientations. Through image analysis and uniaxial compression testing, we find that the orientation of the fibres, rather than the size of the voids, determine the compressive strength of the material. The fibrous samples display a layering of the fibres perpendicular to the direction of drainage of the precursor liquid foam. This leads to an anisotropy of the compressive behaviour of the samples. Varying the initial liquid fraction of the foam allows for tuning of the compressive strength. We show an increase in over seven times can be achieved for samples of the same density (13 kg.m-3).Graphic abstract

Foam drying of aquafaba: Optimization with mixture design

The aim of the present investigation was to optimize the variables of the aquafaba foam drying process using response surface methodology. Foaming conditions, amount of foaming agents (carboxymethylcellulose (CMC), Na-alginate, polydextrose, and whey powder) optimized by the mixture design of response surface methodology (RSM) minimizing foam density and drainage volume. The effect of different drying air temperatures (50, 60, and 70°C) was then evaluated on the physico-chemical properties of foam-mat dried aquafaba powder. Different drying temperatures were significantly affected the color parameters (L* and a*) of powders (p < .05). An increase in the temperature also resulted in a decrease of 1.63-, 1.40-, and 1.42-fold in moisture, water activity, and wettability, respectively, and a 1.22-fold increase in hygroscopicity. Finally, solubility and water absorption index of powders effected no significantly with different drying temperature (p > .05). Practical applications Aquafaba have high protein content and health-promoting ingredients such as polyphenols and generally discarded as food waste. Aquafaba have high water content and limited shelf life, so the drying process is provided some advantages such as small volume and storage space, easy transportation, and long shelf life. Foam- mat drying process was successfully application for sensitive products due to rapid drying at lower temperature, retention of high nutrition, easy reconstitution characteristics, and cost-effective. The aquafaba powder can be used in bakery products, snacks, beverages, and ice creams in the food industry.

The Effect of Salt on Stability of Aqueous Foams

The properties of foams are often affected by environmental variables such as salt contamination. The objective of this study is to investigate the impact of salt on the drainage behavior of aqueous foams. To accomplish this objective, drainage experiments were conducted on aqueous foams. Test variables were foam quality (40–65%), and salt content (0% to 18%), and type. To investigate drainage, the foam was generated in a flow loop and trapped in a vertical test section. Then, the pressure profile in the foam column was measured using ten pressure sensors. Foam drainage is determined as a function of time using measured pressure profiles. The results show that the drainage of NaCl-containing foams decreased with foam quality, whereas the CaCl2-containing foams did not exhibit a clear trend with foam quality. The effect of salt content on foam rheology was minimal.

Calculating Model of Frictional Pressure Drop for Gas Well During Foam Drainage

In the process of enhanced of development of gas wells, the liquid loading may cause obstacles for the affective production of the gas wells. Gas-foam drainage technology has the advantage of low cost and simple operation. The design of the drainage technology requires providing a reliable formula to evaluate the friction coefficient of foam in the tube. In this paper, we have applied a theoretical analysis and indoor experiments to study the liquid volume lifted by the gas-foam flow and the pressure gradient in the well pipe in the process of foaming drainage, and established the calculating formula for the foaming friction in the well pipe, considering the different injection speed of the foaming agent. The validation for comprehensive analysis of the foaming technology in production gas wells.

Comparative study of two techniques on some nonlinear problems based ussing conformable derivative

AbstractIn this paper, three eminent types of time-fractional nonlinear partial differential equations are considered, which are the fractional foam drainage equation, fractional Gardner equation, and fractional Fornberg–Whitham equation in the sense of conformable fractional derivative. The approximate solutions of these considered problems are constructed and discussed using the conformable fractional variational iteration method and conformable fractional reduced differential transform method. The conformable derivative is one of the admirable choices to handle nonlinear physical problems of different fields of interest. Comparisons of approximate solution obtained by two techniques, to each other and with the exact solutions are also presented and affirm that the considered methods are efficient and reliable techniques to study other nonlinear fractional equations and models in the sense of conformable derivative. To explain the effects of several parameters and variables on the movement, the approximate results are shown in tables and two-and three-dimensional surface graphs.

Aggregation behavior and foam properties of the mixture of hydrocarbon and fluorocarbon surfactants with addition of nanoparticles

Aqueous foam is widely used in many industrial fields. Study on foam properties is the key to reducing additive amount of foaming agents and stabilizers as well as the economic cost, and improving utilization efficiency of foam products. The molecular aggregation behavior, foaming ability, foam drainage, and foam coarsening of the mixtures of hydrophilic silica nanoparticle (NP), anionic hydrocarbon surfactant (SDS), and amphoteric fluorocarbon surfactant (FS-50) were studied systematically. Results indicated that the addition of NP slightly affected the molecular aggregation behavior of the mixed solutions of SDS/FS-50. The surface activity, dynamic viscosity, and foaming ability of the foam dispersions increased slightly with increasing NP concentration. The conductivity of the dispersions decreased slightly with increasing NP concentration. Foam stability was significantly affected by NP concentration. When the NP concentration is lower than 1%, the addition of NPs accelerated foam drainage and coarsening. When the NP concentration is higher than 1%, the addition of NPs decelerated foam drainage and foam coarsening and thus reduced foam stability. The foam stability of SDS/FS-50 solutions was further enhanced with increasing NP concentration. This study provides a basis for the application of foams stabilized by NPs in fire extinguishing agents.

Critical bubble diameters and Plateau border dimensions for drainage in aqueous xanthan foams

Xanthan gum is used to stabilize aqueous foams in a wide number of commercial and industrial processes and is one of the numerous hydrosoluble polymers used to slow foam drainage. The slowing effects of viscosity on drainage flow have been well studied but the situations leading to a drainage delay are poorly described in the literature. The aim of this study was to shed light on the mechanisms governing drainage delay and drainage initiation. Drainage delay seems to be the result of liquid retention caused by the confinement of xanthan molecules in the Plateau borders, which increases local yield stress. Drainage begins when the bubbles and Plateau borders grow above a certain threshold size that allows liquid to flow through the foam.

Rheological characterization and prediction model of compressed air Class A foam

When the compressed air Class A foam used in firefighting covers the surface of the object, free drainage and changes of structural occur. The evolution of the foam and the law of drainage and rheological properties were investigated. It was observed by experiments that the evolution of the foam structure was consistent with the drainage process in terms of the time nodes division at room temperature. The foam evolved from a spherical structure to an ellipsoidal structure at about 900 s, began to evolve toward a polygonal structure at 3000 s, and eventually became a polygonal structure at 3600 s. At the same time, the foam drainage mass rate can be divided into three stages: increasing stage (300–900 s), dropping stage (900–3000 s), and stabilizing stage (3000–3600 s). The similarity of the time nodes determines the interaction between the two phenomena. At room temperature, when the liquid volume fraction is between 0.03 and 0.14, a linear relationship between the foam yield stress and the liquid volume fraction could be established. Furthermore, the Herschel–Bulkley model was modified by introducing a structural damage factor λ(t) to describe the change in foam rheological properties over time.