Two-step Homogenization Method Research Articles

Effects of Concentration of Soybean Protein Isolate and Maltose and Oil Phase Volume Fraction on Freeze-Thaw Stability of Pickering Emulsion.

There is growing interest in enhancing the freeze-thaw stability of a Pickering emulsion to obtain a better taste in the frozen food field. A Pickering emulsion was prepared using a two-step homogenization method with soybean protein and maltose as raw materials. The outcomes showed that the freeze-thaw stability of the Pickering emulsion increased when prepared with an increase in soybean protein isolate (SPI) and maltose concentration. After three freeze-thaw treatments at 35 mg/mL, the Turbiscan Stability Index (TSI) value of the emulsion was the lowest. At this concentration, the surface hydrophobicity (H0) of the composite particles was 33.6 and the interfacial tension was 44.34 mN/m. Furthermore, the rheological nature of the emulsions proved that the apparent viscosity and viscoelasticity of Pickering emulsions grew with a growing oil phase volume fraction and concentration. The maximum value was reached in the case of the oil phase volume fraction of 50% at a concentration of 35 mg/mL, the apparent viscosity was 18 Pa·s, the storage modulus of the emulsion was 575 Pa, and the loss modulus was 152 Pa. This research is significant for the production of freeze-thaw resistant products, and improvement of protein-stabilized emulsion products with high freeze-thaw stability.

Modelling of the effective thermal conductivity of composites reinforced with fibers and particles by two-step homogenization method

Fiber-particle-reinforced hybrid composites are widely applied in many fields. Knowing their effective thermal conductivity (ETC) is essential. This paper first calculates the ETC of different fillers reinforced composites by the Lattice Boltzmann method and proposes a correlation for the ETC of fiber-reinforced composites based on Lewis-Nielson's model with an average deviation of less than 2.7%. In what follows, a two-step model for the ETC of fiber-particle reinforced composite is proposed by combining the correlations for fiber-reinforced composites and particle-reinforced composites based on the two-step homogenization method. The results show that the two-step homogenization method could accurately predict the ETC of fiber-particle reinforced composites with randomly arranged fibers; however, a reasonable choice for the phase pair is crucial for this method. In addition, the accurate combinability of Lewis-Nielson's model for particle-reinforced composites with the parallel model and Perrins et al.'s model could accurately predict the ETC of fiber-particle-reinforced composites with aligned fibers with a maximum deviation of less than 3.9%. Finally, the two-step homogenization method is also validated for the particle-particle reinforced composites, and the phase pair selection hardly influences the results. However, this method fails to predict the ETC of fiber-fiber reinforced composites no matter how to choose the phase pair.

Incorporating lipid microparticles into carboxymethyl cellulose films as secondary carriers for stable loading and sustained releasing of carvacrol

Active compounds were always incorporated into biopolymer films in order to enrich and/or enhance their functions. However, the strong volatility of the active compounds and the weak interactions between the compounds and the polymer matrix always leads to an initial burst release and later unstable load of the volatile compounds. Thus, in order to develop a composite film with the function of sustained release of active substance, stearic acid (SA) was incorporated into carboxymethyl cellulose (CMC) films as a secondary carrier for the carvacrol loading and releasing. A two-step homogenization method including high-speed shear homogenizer (HSH) and high-press homogenizer (HPH) was employed to modify the film-forming emulsions. Lipid particle size and rheology behavior of the emulsions were determined, and the microstructure of their final films was characterized by scanning electron microscope (SEM) and X-ray diffraction (XRD). The release behavior of carvacrol from the films was also investigated as well. The results showed that the greatest intensity of homogenization (HSH at 22,000 rpm for 3 min plus HPH at 60 MPa for 10 cycles) resulted in the lowest lipid particle size in the film-forming emulsion and the most homogenous internal structure in final films. The release behavior of carvacrol indicated that the controllable size and distribution of lipid particles could be an effective method to ensure the sustained release of carvacrol from polysaccharide-based films, and furtherly regulate the release rate in a certain range.

Two-step Homogenization of Poroelastic Properties of a Limestone

This study aims at deriving the effective poroelastic properties of the oolitic limestones based on the Hashin composite sphere assemblage (CSA) micromechanical theory. The microstructure of oolitic limestones generally exhibits an assemblage of grains (oolites) surrounded by a matrix. Grain and matrix are linked via the interfacial transition zone (ITZ). Pores exist in these three material phases (oolite, ITZ and matrix). A two-step homogenization method is proposed. The first step consists of upscaling the properties of each porous phase (i.e. porous oolite, porous ITZ and porous matrix) in which each phase contains two sub-phases including pore and solid. The differential self-consistent scheme is used for the first step. At the second step, the three different porous constituents (oolite, ITZ and matrix) are assembled in a CSA model. A mathematical analogy between thermoelasticity and poroelasticity is used to obtain the effective poroelastic properties. A comparison between the proposed model and test data on the oolitic limestone from Bourgogne (France) helps to calibrate the model parameters and to highlight the role of ITZ phase.

A model to describe the cyclic anisotropic mechanical behavior of short fiber-reinforced thermoplastics

Due to the injection molding process, short fiber-reinforced thermoplastic composites show a complex fiber orientation distribution and, as a consequence, an overall anisotropic mechanical behavior. The monotonic and cyclic mechanical behavior of PolyEtherEtherKetone thermoplastic reinforced with 30 wt.% of short carbon fibers was characterized through a series of tests generating various complex loading histories (loading–unloading with creep or recovery steps, cyclic loading with various stress amplitudes) performed at room temperature on samples with various homogeneous and heterogeneous fiber orientation distributions. A three-dimensional model relying on a thermodynamic framework was then developed to represent the anisotropic mechanical behavior of the material, including elastic, viscoelastic, and plastic phenomena. Relevant constitutive laws were defined to describe the phenomena within wide ranges of loading rates and levels, with a limited number of parameters. Elastic anisotropy and plastic anisotropy were naturally described by using a two-step homogenization method and a Hill-like equivalent stress taking into account the fiber orientation distribution. The model was implemented into a finite element code to be able to simulate the response of complex parts with a heterogeneous fiber orientation distribution subjected to a heterogeneous loading. Model parameters were identified by applying a robust and original approach relying on a limited number of relevant experiments. The prediction capability of the model was demonstrated by simulating several types of tests not used for the identification, covering a wide range of monotonic and cyclic, homogeneous and heterogeneous, loading conditions, for various simple and complex fiber orientation distributions. In particular, the model is shown to be able to predict the energy dissipated in the material when subjected to cyclic loading.

Two-step multiscale homogenization for mechanical behaviour of polymeric nanocomposites with nanoparticulate agglomerations

A multiscale analysis is performed to investigate the effect of nanoparticulate agglomeration on the mechanical properties of polymeric nanocomposites. The percolated interphase model is applied to consider the degradation of the elastic properties of the interphase zone caused by nanoparticulate clusters. Through parametric studies on various agglomeration states, we propose a new index called the ‘clustering density’, which indicates the degree of nanoparticulate agglomeration. As the clustering density increases, a significant degradation in the stiffness of the nanocomposites is observed from 10 to 30%. An efficient two-step homogenization method is proposed in the present study to effectively analyse large size representative volume elements (RVE) containing multi-clusters and free nanoparticles. The proposed computational scheme is based on multiscale homogenization and the clustering density concept. It is concluded that the two-step homogenization approach can provide accurate prediction of the mechanical properties of nanocomposites with heterogeneity from nanoparticle agglomeration with high computational efficiency.

Microstructure-based homogenization method for early-age creep of cement paste

In this study, a microstructure-based homogenization method is proposed for the creep behavior of cement paste at early age. With the aid of hydration model, the evolution of microstructure in hydrating cement paste is represented as a function of time. The inherent creep of C-S-H is characterized by the B3 creep model proposed by Bazant, whereas other chemical phases are assumed to behave elastically. A two-step homogenization method combining the analytical and numerical homogenization is proposed. Analytic homogenization method is applied for the effective mechanic properties of composites in the hydration model. Then the numerical homogenization is conducted based on the obtained microstructures. The numerical homogenization is implemented with the aid of FEM software Comsol Multiphysics. The reliability and precision of homogenization method are validated by experimental data in literature. The creep and creep recovery behavior of cement paste at early age is comprehensively studied. The main novelty of this study is the quantification of the contribution of each mechanisms to the creep and creep recovery behavior of cement paste at early age, which provides insights to better understand the creep mechanisms.

Influences of micro-pores and meso-pores on elastic and plastic properties of porous materials

Many engineering materials contain families of pores at different scales. In this study, a numerical homogenization analysis method is developed to describe the effective elastic and plastic properties of a class of porous materials with two populations of pores at two separated scales. The solid phase at the micro-scale is described by the Drucker-Prager criterion. An analytical plastic criterion is used for the effective plastic criterion of the porous matrix with the micro-porosity. The influence of the meso-porosity, which is embedded in the homogenized porous matrix, is investigated by developing a numerical method based on the Fast Fourier Transform (FFT). With this two-step homogenization method in hand, a series of numerical assessments are performed. The relative roles of both families of pores on the macroscopic elastic properties and plastic yield stresses for a given total porosity are particularly investigated and compared with existing analytical solutions. Moreover, the proposed numerical method is extended to describe the local strain fields of microstructure with compressible porous matrix under various loading paths.

A composite sphere assemblage model for porous oolitic rocks: Application to thermal conductivity

The present work is devoted to the determination of linear effective thermal conductivity of porous rocks characterized by an assemblage of grains (oolites) coated by a matrix. Two distinct classes of pores, i.e. micropores or intra oolitic pores (oolite porosity) and mesopores or inter oolitic pores (inter oolite porosity), are taken into account. The overall porosity is supposed to be connected and decomposed into oolite porosity and matrix porosity. Within the framework of Hashin composite sphere assemblage (CSA) models, a two-step homogenization method is developed. At the first homogenization step, pores are assembled into two layers by using self-consistent scheme (SCS). At the second step, the two porous layers constituting the oolites and the matrix are assembled by using generalized self-consistent scheme (GSCS) and referred to as three-phase model. Numerical results are presented for data representative of a porous oolitic limestone. It is shown that the influence of porosity on the overall thermal conductivity of such materials may be significant.

Effects of relevant parameters on the bandgaps of acoustic metamaterials with multi-resonators

Locally resonant acoustic metamaterials with multi-resonators are generally regarded as a fine trend for managing the bandgaps, the different effects of relevant structural parameters on the bandgaps, which will be numerically investigated in this paper. A two-step homogenization method is extended to achieve the effective mass of multi-resonators metamaterial in the lattice system. As comparison, the dispersive wave propagation in lattice system and continuum model is studied. Then, the different effects of relevant parameters on the center frequencies and bandwidth of bandgaps are perfectly revealed, and the steady-state responses in the continuum models with purposed relevant parameters are additionally clarified. The related results can well confirm that the bandgaps exist around the undamped natural frequencies of internal resonators, and also their bandwidth can be efficiently controlled with the ensured center frequencies. Moreover, the design of purposed multi-resonators acoustic metamaterial in vibration control is presented and discussed by an example.

Maneuvering thermal conductivity of magnetic nanofluids by tunable magnetic fields

We report an experimental investigation of magnetic field dependent thermal conductivity of a transformer oil base magnetic fluid as a function of volume fractions. In the absence of magnetic field, thermal conductivity increases linearly with an increase in volume fraction, and magnitude of thermal conductivity thus obtained is lower than that predicted by Maxwell's theory. This reveals the presence of clusters/oligomers in the system. On application of magnetic field, it exhibits a non-monotonous increase in thermal conductivity. The results are interpreted using the concept of a two-step homogenization method (which is based on differential effective medium theory). The results show a transformation of particle cluster configuration from long chain like prolate shape to the aggregated drop-like structure with increasing concentration as well as a magnetic field. The aggregated drop-like structure for concentrated system is supported by optical microscopic images. This shape change of clusters reduces thermal conductivity enhancement. Moreover, this structure formation is observed as a dynamic phenomenon, and at 226 mT field, the length of the structure extends with time, becomes maximum, and then reduces. This change results in the increase or decrease of thermal conductivity.

Effective mechanical properties of lattice material fabricated by material extrusion additive manufacturing

In this paper, a two-step homogenization method is proposed and implemented for evaluating effective mechanical properties of lattice structured material fabricated by the material extrusion additive manufacturing process. In order to consider the characteristics of the additive manufacturing process in estimation procedures, the levels of scale for homogenization are divided into three stages – the levels of layer deposition, structural element, and lattice structure. The method consists of two transformations among stages. In the first step, the transformation between layer deposition and structural element levels is proposed to find the geometrical and material effective properties of structural elements in the lattice structure. In the second step, the method to estimate effective mechanical properties of lattice material is presented, which uses a unit cell and is based on the discretized homogenization method for periodic structure. The method is implemented for cubic lattice structure and compared to experimental results for validation purposes.

Theory for anisotropic thermal conductivity of magnetic nanofluids

Effective thermal conductivity tensor for magnetic nanofluids containing magnetizable nanoparticles suspended in a base liquid is theoretically investigated with a two-step homogenization method. First, we adopt differential effective medium theory to determine the equivalent thermal conductivity of magnetizable nanoparticle chains. Second, we generalize self-consistent anisotropic effective medium theory to study the effective thermal conductivity tensors of magnetic nanofluids. Numerical results show that the aspect ratio of chain-like aggregated clusters plays an important role in enhancement of anisotropic thermal conductivity. In addition, our theoretical results on the elements of thermal conductivity parallel to the fields K e z and perpendicular to the fields K e x are in good agreement with experimental data. Furthermore, we predict the nonmonotonic dependence of effective thermal conductivity on magnetic field strength, in accordance with experimental reports.

A composite sphere assemblage model for porous oolitic rocks

The present work is devoted to the determination of linear effective poroelastic properties of porous rocks characterized by an assemblage of grains ( oolites) coated by a matrix. In the framework of Hashin composite sphere assemblage (CSA [1]) models, a two-step homogenization method is developed. Three porous materials are considered and assembled into a CSA: oolite ( o) coated by an interfacial transition zone ITZ ( i) and a matrix ( m). The overall porosity is supposed connected and decomposed into oolite porosity, interphase porosity and matrix porosity. The three constitutive porous materials ( o, i, m) are homogenized at the first step and a sensitive study is performed on the homogenization scheme by comparing self consistent SC, differential self consistent DSC, generalized self consistent GSC, iterative self consistent ISC and Mori Tanaka schemes. At the second step, the simple three-phase model [2] is firstly recalled and general relations for effective linear poroelastic coefficients are presented in the four-phase model case [3]. Mathematical analogy between linear thermoelasticity and linear poroelasticity is used to establish theoretical results in the context of CSA.

Faraday magneto-optical rotation in compositionally graded films

We present a two-step homogenization method for studying the Faraday magneto-optical effect in graded metal-dielectric composite films of width W, in which the volume fraction of metal particles in a slice varies along the direction perpendicular to the film surface. First, we adopt the effective-medium theory to formulate the equivalent (local) dielectric permittivity tensor for a z slice. Second, the graded composite films are homogenized with an effective (overall) dielectric permittivity tensor including the diagonal and off-diagonal elements. Faraday rotation is studied as a function of the graded profile p(z) with the same total volume fraction. For a power-law form p(z)=a(z/W)m with different m, it is found that with increasing m, the magnitude of Faraday rotation becomes weak near the surface plasmon resonant band, accompanied with the redshift of the resonant center. Interestingly, it is possible to achieve strongly enhanced Faraday rotation in the high-frequency region, and to change the direction of rotation in the low-frequency one. Moreover, the magnitude can be further enhanced for needle-like particles. In the dilute limit, we show that Faraday rotation is indeed independent of m within Maxwell-Garnett theory.

Homogenization of Negative-Index Composite Metamaterials: A Two-Step Approach

We present a two-step homogenization method for composite metamaterials. First, each layer of wires or resonators is homogenized as a slab with negative permittivity or permeability, respectively. Second, the single negative stack which results is homogenized to form the effective medium. Comparing the predictions of the first and second step can serve as a gauge of the homogeneity of the composite. We thus take a gradual approach to homogenization, asking not whether, but to what extent a composite metamaterial approaches the sought after effective medium. Our two-step approach can also capture phenomena which otherwise may be wrongly attributed to effective medium behavior. We illustrate by qualitatively reproducing and reinterpreting a set of experimental data from the literature.

Effective thermal conductivity of partially saturated porous rocks

The present work is concerned with the determination of the effective thermal conductivity of porous rocks or rock-like composites composed by multiple solid constituents, in partially saturated conditions. Based on microstructure observations, a two-step homogenization scheme is developed: the first step for the solid constituents only, and the second step for the (already homogenized) solid matrix and pores. Several homogenization schemes (dilute, Mori–Tanaka, the effective field method and Ponte Castañeda–Willis technique) are presented and compared in this context. Such methods are allowing: (i) to incorporate in the modellization the physical parameters (mineralogy, morphology) influencing the effective properties of the considered material, and the saturation degree of the porous phase; (ii) to account for interaction effects between matrix and inhomogeneities; (iii) to consider different spatial distributions of inclusions (spherical, ellipsoïdal). An orientation distribution function (ODF) permits simultaneously to incorporate in the modelling the transverse isotropy of pore systems. Appearing as homogeneous at the macroscopic scale, it is showed that the effective conductivity depends on the physical properties of all subsidiary phases (microscopic inhomogeneities). By considering the solution of a single ellipsoïdal inhomogeneity in the homogenization problem it is possible to observe the significant influence of the geometry, shape and spatial distribution of inhomogeneities on the effective thermal conductivity and its dependence with the saturation degree of liquid phase. The predictive capacities of the two-step homogenization method are evaluated by comparison with experimental results obtained for an argillite.