Interaction of rarefaction waves with wet foam

The interaction of rarefaction waves of different shapes with wet water foams is studied experimentally. It is found that the observed values of the pressure are greater, while the surface velocity is lower than the corresponding values predicted by the pseudogas model. The foam breakdown starts as the pressure decreases by 0.3 atm relative to the initial pressure. During downstream propagation of the rarefaction-wave leading edge the propagation velocity decreases.Using of water-based foams as effective screens for damping blast waves in different technological processes has caused considerable interest in studying wave propagation in such systems. The pressure wave dynamics in a foam have been investigated in much detail, both experimentally and theoretically [1–3]. However, the interaction of rarefaction waves with foam has practically never been studied, although it was mentioned in [4] that the unloading phase following the compression wave phase is one of the factors defining the damaging action of blast waves. Besides blast-wave damping, rarefaction wave propagation takes place if such waves are used to breakup foam in oil-producing wells [5].Below, the interaction of rarefaction waves of different shapes with wet water foams is studied. The vertical shock tube described in detail in [3] was used in these experiments.Brest. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 76–82, March–April, 1995.     

Ceramic foam substrates for automotive catalyst applications: fluid mechanic analysis

Several properties of ceramic foams render them promising substrates for various industrial processes. For automotive applications, the foam properties that need to be further studied include the substrate impact on the exhaust gas flow, in terms of pressure drop and flow uniformity. In this paper, pressure drop measurements are performed with different honeycomb and ceramic foam substrates, and pressure drop correlations are discussed. The flow uniformity upstream and downstream of the substrates is evaluated using particle image velocimetry. The results show that ceramic foam substrates induce higher pressure drop, while increasing the uniformity of the flow. In contrast to honeycomb monoliths, the flow uniformity downstream of ceramic foams does not decrease with increasing flow velocity. The higher flow uniformity of ceramic foams is not only caused by their higher pressure drop, but also by flow homogenization that occurs inside the ceramic foam structure, as a result of the momentum exchange perpendicular to the main flow direction.     

Lattice gas simulations of two-dimensional liquid foams

Liquid foam is a dense random packing of gas bubbles in a small amount of immiscible liquid containing surfactants. The liquid within the Plateau borders, although small in volume, causes considerable difficulties to investigations of the physical properties of foams, and the situation becomes even more complicated if the flow of the liquid through the foam is considered too. Here we propose a fresh approach to tackling these issues by introducing a discrete two-dimensional hybrid lattice gas model of liquid foams. While lattice gas models have been used to model two-phase liquids in the past, their application to the study of liquid foams is novel and proves promising. We represent bubble surfaces by a finite number of nodes, and model the surrounding liquid as a lattice gas (with a finite number of liquid particles). The gas in the bubbles is treated as an ideal gas at constant temperature. The model is tested by choosing an arbitrarily shaped bubble that evolves into a circular shape in agreement with Laplaces law. The model is then employed to simulate periodic ordered and disordered dry and wet foams. Since our model is specifically designed to handle wet foams up to a critical liquid fraction of 0.16 (void fraction of random packing of disks), we are able to compute the variation in coordination number (average number of neighbours of a bubble) over the whole range of liquid fractions, and we find it to be a linear function of the shear modulus.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, 11–13 September 2003.     

基于三维细观力学模型的开孔泡沫弹性性能预测

泡沫材料的宏观力学性能主要取决于基体材料的力学特性及其微细观结构特征,基于细观力学模型的分析方法是泡沫材料力学性能研究的重要途径。文中基于Matlab语言和Abaqus软件构建了描述中等孔隙率开孔弹性泡沫材料微结构特征的三维随机分布球形泡孔模型,并采用有限元方法对弹性泡沫压缩变形进行了模拟,并计算给出了不同孔隙率弹性泡沫材料弹性模量、剪切模量、体积模量以及泊松比的分布,建立了相应的唯象表达式。与理论模型及测试结果的比较表明,本文基于三维随机泡孔模型模拟结果构建的唯象表达式能够对弹性泡沫材料的弹性力学性能给出很好的预测。     

Geometrical modelling of foam structures using implicit functions

Mechanical, thermo-mechanical, and fluid dynamic simulations of open-cell foams require an accurate geometry model. Usually, models are derived from computer- tomography (CT) data which do not allow analysing systematically variation and optimisation of the geometry. On the other hand, entirely computer generated models are mostly assembled of primitive objects like cylinders. This disregards strut thickness variations and node rounding which are observed in real open-cell foams. This paper presents an approach to generate models of ceramic open-cell foams using simple objects with variable thickness generated by implicit functions. This approach can also account for cavities within struts and nodes, which are observed in many real foam structures. The specific rounding at the foam nodes can be modelled by applying the transformation of Blinn. The quality of the generated foam models is verified using CT data of real foams.     

A micromechanical model for predicting the fracture toughness of functionally graded foams

In this paper, finite element method based micromechanical analysis is used to understand the fracture behavior of functionally graded foams. The finite element analysis uses a micro-mechanical model in conjunction with a macro-mechanical model in order to relate the stress intensity factor to the stresses in the struts of the foam. The stress intensity factor at the crack tip of the macro-mechanical model can be evaluated using either the J-contour integral or the stresses in the singularity-dominated zone. The fracture toughness is evaluated for various crack positions and length within the functionally graded foam. Then the relationship between the fracture toughness of the graded foam and the local density at the crack tip is studied. Convergence tests for both macro-mechanical and micro-mechanical model analysis were conducted in order to maintain adequate accuracy with reasonable computational time. Fracture toughness of homogenous foams and functionally graded foams for various cases are presented as a function of relative density. This study indicates that the fracture toughness of functionally graded foams mainly depends on the relative density at the crack-tip.     

Study of microstructure and flexural properties of microcellular acrylonitrile-butadiene-styrene nanocomposite foams: experimental results

In this paper, acrylonitrile-butadiene-styrene (ABS) nanocomposite foams are produced using carbon dioxide through the solid-state batch process. Microcellular closed-cell foams are produced with the relative density ranging from 0.38 to 0.97. The effects of the processing conditions on the density, morphology, and flexural properties of ABS and its nanocomposite foams are studied. It is found that nanoclay particles, as nucleating sites, play an important role in reducing the size of cells and increasing their number in the unit volume of foamed polymer, as well as increasing the flexural modulus of foam through reinforcing its matrix.     

DYNAMIC PROPERTIES OF AL-ALLOY FOAM BEAM DAMAGED BY COMPRESSIVE FATIGUE

The permanent residual strain in aluminum （Al） alloy foams induced by compressive fatigue gradually increases with the increasing number of loading cycles. Consequently, the progressive shortening of Al-alloy foam degrades the dynamic material performance by the failure and ratcheting of multi-cells in the foam. In this paper, the dynamic properties of Al-alloy foams damaged by compressive fatigue were studied. The beam specimens with various residual strains were made by cyclic compression-compression stress. The dynamic bending modulus and loss factor were evaluated by using a beam transfer function method. As a result, the dynamic bending stiffness of Al-alloy foam turned out to be decreased due to damage while the loss factor was improved because of the increasing energy dissipation of such factors as cracked cell walls formed during the shortening process of the foam. The loss factor shows a manifest dependence on the fatigue residual strain.     

Macro-mechanical modeling of blast-wave mitigation in foams. Part II: reliability of pressure measurements

A phenomenological study of the process occurring when a plane shock wave reflected off an aqueous foam column filling the test section of a vertical shock tube has been undertaken. The experiments were conducted with initial shock wave Mach numbers in the range $1.25\le {M}_\mathrm{s} \le 1.7$ and foam column heights in the range 100–450 mm. Miniature piezotrone circuit electronic pressure transducers were used to record the pressure histories upstream and alongside the foam column. The aim of these experiments was to find a simple way to eliminate a spatial averaging as an artifact of the pressure history recorded by the side-on transducer. For this purpose, we discuss first the common behaviors of the pressure traces in extended time scales. These observations evidently quantify the low frequency variations of the pressure field within the different flow domains of the shock tube. Thereafter, we focus on the fronts of the pressure signals, which, in turn, characterize the high-frequency response of the foam column to the shock wave impact. Since the front shape and the amplitude of the pressure signal most likely play a significant role in the foam destruction, phase changes and/or other physical factors, such as high capacity, viscosity, etc., the common practice of the data processing is revised and discussed in detail. Generally, side-on pressure measurements must be used with great caution when performed in wet aqueous foams, because the low sound speed is especially prone to this effect. Since the spatial averaged recorded pressure signals do not reproduce well the real behaviors of the pressure rise, the recorded shape of the shock wave front in the foam appears much thicker. It is also found that when a thin liquid film wet the sensing membrane, the transducer sensitivity was changed. As a result, the pressure recorded in the foam could exceed the real amplitude of the post-shock wave flow. A simple procedure, which allows correcting this imperfection, is discussed in detail.     

The elastic–plastic behaviour of foam under shock loading

An experimental investigation of the elastic–plastic nature of shock wave propagation in foams was undertaken. The study involved experimental blast wave and shock tube loading of three foams, two polyurethane open-cell foams and a low-density polyethylene closed-cell foam. Evidence of precursor waves was observed in all three foam samples under various compressive wave loadings. Experiments with an impermeable membrane are used to determine if the precursor wave in an open-cell foam is a result of gas filtration or an elastic response of the foam. The differences between quasi-static and shock compression of foams is discussed in terms of their compressive strain histories and the implications for the energy absorption capacity of foam in both loading scenarios. Through a comparison of shock tube and blast wave loading techniques, suggestions are made concerning the accurate measurements of the principal shock Hugoniot in foams.     

泡沫材料对冲击波的衰减特性

对冲击波与开式、闭式泡沫作用及其在空气中的传播特性开展实验研究,探讨不同结构的泡沫材料对冲击波衰减的力学特征。通过定量分析泡沫材料对冲击波的超压峰值、正冲量的损失,分析冲击波入射、反射、透射的正冲量。实验结果表明, 泡沫材料对冲击波的衰减体现在对冲击波的反射衰减等方面,其中开式泡沫对冲击波的衰减效果比闭式泡沫稍好,且它们衰减冲击波的具体力学过程也不尽相同。     

Experimental studies on the yield behavior of ductile and brittle aluminum foams

Specimen size effects are a major cause of the unreliability of foam models in finite element codes. Here, the modified Arcan apparatus is used to investigate the biaxial yielding of ductile and brittle Al foams. This apparatus subjects a central section of a “butterfly-shaped” specimen to a uniform state of plane stress. The stresses have local maxima at the central section, thus ensuring that yielding occurs there. A yield envelope, which directly relates to the crushing process, can then be determined. Size effects are introduced when using conventional methods such as tri-axial or plate-shear tests. In such tests, averages of stress and strain are measured. These measures do not represent the actual yield event, because foam's internal structure is inhomogeneous and so is the deformation field. Strain localization and failure can occur at any weak layer of cells in the bulk. In this study, we have performed a series of biaxial tests on isotropic Alporas and anisotropic Hydro closed-cell Al foams of approximately equal densities. Alporas failed locally by a ductile phenomenon of progressive crushing of cells. It also possessed uniaxial strength asymmetry. Hydro specimens parallel and perpendicular to ‘foam rise’ were investigated. The Hydro foam developed a local, characteristic brittle crack at loads in the vicinity of the yield point. Phenomenological yield surfaces, which incorporate these features are obtained for the foams, and show dependence on both the deviatoric and hydrostatic stresses. We also provide expressions for the shear and hydrostatic strengths in terms of the uniaxial strengths. Finally, the size-independence of the yield surface is verified using the uniaxial compression of tapered specimens.     

液态泡沫渗流的机理研究进展

液态泡沫是具有高度自组织结构的非平衡系统. 泡沫中的微量液体在重力与毛细管力作用下, 在由薄膜、柏拉图通道以及交汇点形成的通道网络内的流动称为泡沫渗流(foamdrainage), 它直接影响泡沫结构的稳定性. 本文从泡沫物理学角度对液态泡沫的结构首先做了简单介绍, 并对泡沫材料与多孔介质之间的区别和联系做了简单介绍. 文章分析了由泡沫渗流、气泡粗化和液膜破裂而引起的泡沫结构演化规律, 着重介绍了目前泡沫渗流研究中对柏拉图通道边界条件的处理方法、相应的渗流模型及其在一维泡沫渗流中的应用, 并对泡沫渗流实验检测手段及微重力条件下的泡沫渗流实验和理论研究做了综述.      

玻璃纤维增强聚氨酯泡沫塑料的压缩力学性能研究

本文研究了两种不同密度的玻璃纤维增强聚氨酯泡沫塑料在准静态压缩下的力学性能。给出了与相应密度的普通泡沫塑料力学性能的比较，实验结果表明：两种增强泡沫塑料在压缩载荷作用下，具有不同于普通泡沫塑料的应力－应变特性，压缩模量和强度一般均有不同程度的提高，而且对相同纤维含量的增强泡沫塑料来说，密度较高的材料增强效果较好。     

The Blocking Ability and Flowing Characteristics of Steady Foams in Porous Media

Foam flow experiments were carried out to study the influence factors such as surfactant concentration, foam quality, injection rate of liquid and gas, permeability of porous media, temperature, and oil saturation on blocking ability and flowing characteristics of steady foams in porous media. Foam blocking mechanisms and flowing characteristics were summarized according to the experimental results and foam migration behavior. The results showed that the pressure distribution of flowing foams was linearly descending in porous media at steady state. The results further showed that the foam size and quality in pores along the sand pack were almost uniform, that is, foam generation and destruction gradually reached dynamic equilibrium at steady state. In porous media, the blocking ability of steady foams increased with the concentration of the foaming agent and the increase in the permeability of porous media, but the blocking ability decreased with the increase in the temperature, the shearing rate, and the oil saturation of the porous media. Foam resistance factor reached maximal value at the foam quality of 85% in porous media.     

多孔介质中稳定泡沫的流动计算及实验研究

将多孔介质简化为一簇变截面毛管束,根据多孔介质的颗粒直径、颗粒排列方式、孔喉尺度比及束缚水饱和度,计算出变截面毛细管的喉道半径和孔隙半径. 在考虑多孔介质喉道和孔隙中单个气泡的受力和变形基础上,利用动量守恒定理,推导出单个孔隙单元内液相的压力分布和孔隙单元两端的压差计算公式,最终得到多孔介质的压力分布计算公式. 利用长U型填砂管对稳定泡沫的流动特性进行了实验研究. 研究结果表明:稳定泡沫流动时多孔介质中的压力分布呈线性下降,影响泡沫在多孔介质中流动特性的因素包括:多孔介质的孔喉结构、泡沫流体的流量和干度、气液界面张力、气泡尺寸,其中孔喉结构和泡沫干度是影响泡沫封堵能力的主要因素.关键词: 稳定泡沫;多孔介质;变截面毛管;流动;表观粘度;压力分布;实验研究      

Compressive response of open-cell foams. Part I: Morphology and elastic properties

This study is concerned with the understanding and modeling of the compressive response of open cell foams. The response starts with a nearly linear elastic regime which terminates into a limit load followed by an extensive load plateau. The plateau, which is responsible for the excellent energy absorption capacity of foams, is followed by a second stiff branch. Results from polyester urethane open cell foams with relative densities of about 0.025 are used to illustrate this behavior using experiments coupled with several levels of modeling. The experiments include characterization of the microstructure and the properties of the base material and measurement of the compressive response of the foams of various cell sizes.A sequence of models for predicting the complete response of such foam is developed. The foam is idealized to be periodic using the space-filling Kelvin cell assigned the major geometric characteristics found in the foams tested. The cells are elongated in the rise direction, the ligaments are assumed to be straight, to have Plateau border cross-sections and nonuniform cross-sectional area distribution. The ligaments are modeled as shear-deformable extensional beams and the base material is assumed to be linearly elastic. Prediction of the initial elastic moduli are addressed in Part I. Closed form expressions for the material constants are presented as well as results using a FE model of the characteristic cell. Comparison between measurements and predictions is very favorable. The paper finishes with results from a limited parametric study of the elastic moduli. The results demonstrate that inclusion of the geometric complexities mentioned above is essential for successful prediction of the moduli of such foams. The nonlinear parts of the response including the foam crushing behavior are addressed in Part II.     

Self-lubricated transport of aqueous foams in horizontal conduits

The flow characteristics of aqueous foams were studied in a thin flow channel and a round pipe instrumented for pressure gradient and flow rate measurements. The quality of the foam was varied by controlling the volumetric flow rate of liquid and gas, and different flow types were identified and charted. Uniform foams move as a rigid body lubricated by water generated by breaking foam at the wall. A lubrication model leading to a formula for the thickness of the lubricating layer is presented. The formula predicts a layer thickness of 6–8 μm in the channel and 10–12 μm in the pipe. The thickness depends weakly on foam quality. An overall correlation for the friction factor as a function of Reynolds number which applies to both channel and pipe is derived. This correlation is consistent with a model in which a rigid core of foam is lubricated by laminar flow of a water layer in the range of measured thickness.     

Nonlinear deformation of elastomeric foams

The nonlinear deformation of a porous foam-type elastomeric material is studied, both theoretically and experimentally. The elastomer is modeled by the neo-Hookean material. The one-dimensional compressive behavior of the foam is analysed by using certain kinematic assumptions. The stress required to compress the foam is predicted by the model in terms of the porosity of the foam and the single constant in the neo-Hookean stress-strain form. A particular silicone foam is used as a test of the theory. The neo-Hookean constant is evaluated from a test of the homogeneous elastomer. Hence the behavior of the corresponding foam is predicted theoretically and compared with experimental results. The general results are applicable to closed-cells foams of intermediate density.     

A plasticity model for cellular materials with open-celled structure

Based on a rigid-plastic material model that obeys the von Mises yield criterion, the plastic behavior of foams with an open-celled structure is studied in this paper using a single unit cell. An approximate continuum plasticity model is developed within the framework of the upper bound theorem of plasticity to describe the yield behavior of foams. The microscopic velocity fields are derived for the unit cell, which satisfy the incompressibility and the kinematic boundary conditions, and expressed in macroscopic rate of deformation. From the microscopic velocity fields, a macroscopic yield function is developed for foams under multi-axial stresses and includes the effects of the hydrostatic stress due to the void presence and growth. The dependency of the derived yield surfaces of foams on their relative densities is studied. The plastic behavior of foams is also studied numerically using the finite element method. The newly developed plasticity model is compared with the finite element analysis results and other available foam models and then correlated with the finite element results.