Mixing Law Research Articles

Experimental study evaluating the performance of thermal conductivity prediction models for air–water saturated weathered sandstone heritage

As a critical parameter, thermal conductivity directly determines the heat transfer and temperature variation within rocks, which can lead to mechanical damage and chemical corrosion. Consequently, understanding the thermal conductivity of stone heritage is vital for assessing their deterioration mechanisms and developing effective conservation strategies. This study obtained sandstone samples from the Yungang Grottoes and subjected them to freeze–thaw cycle experiments to generate weathered sandstone samples. Subsequently, the thermal conductivity of these samples was measured under both dry and water-saturated state using the transient plane source method. To analyze the relationship between air–water saturation, porosity, and thermal conductivity, a saturation influence coefficient was introduced. Thereafter, the effectiveness and applicability of 13 commonly used thermal conductivity mixing law prediction models were evaluated based on experimental data. The results suggested that the influence of water saturation on the thermal conductivity of rocks varies with porosity, and water saturation significantly enhances the thermal conductivity of weathered sandstone. Among the 13 common models, the Geometric mean model was found to be more accurate than other models, with superior performance in both dry (MAE, RMSE, MAPE are 0.148, 0.214, 5.59% respectively) and water-saturated (MAE, RMSE, MAPE are 0.244, 0.170, 8.4% respectively) state. The Albert model demonstrates a good fit in the dry state, whereas the Walsh model (with maximum effect), Ribaud model, and Huang model also exhibit good fitting efficacy in the water-saturated state. This study provides a solid foundation for better predicting the thermal conductivity of weathered stone heritage and developing effective preventive conservation strategies.

Accounting of imperfect interfaces in multilayer modeling

Multilayer systems are widely used in industry for their performances as compared with homogeneous materials. The layers are usually glued together but the bonding may be imperfect (air bubble, detachment). The interfaces are generally modeled as sliding or bonded. These two behaviors can be significantly different and the actual behavior is generally somewhere in between. The vibroacoustic behavior of the structure is thus modified by the imperfect interface. Several models have been implemented to describe the dynamic behavior of multilayer systems with imperfect interfaces. In this paper, we propose an analytical model of imperfect interfaces based on the Transfer Matrix Method (TMM). Two computations are performed in parallel (one with a perfectly bonded interface and the other with a sliding interface). Instead of mixing impedances or admittances matrices, a mixing law on the state variables is applied, resulting in an equivalent global matrix which can be coupled in any multi-layer. The model is compared in terms of the sound absorption or sound transmission loss with the existing ones and is applied on different classical multilayer systems with multi-layered solid plates and a multilayer composed of a porous layer with a heavy layer which is widely used in the automotive industry.

Heterogeneous mineralogical composition and fault behaviour: A systematic study in ternary fault rock compositions

The heterogeneous mineralogical compositions of fault gouges, formed during fault evolution, influence frictional properties and slip behaviour. While the influence of individual mineral phases on friction has been extensively studied, the impact of varying systematically mineral phases in gouge mixtures on macroscopic frictional behaviour remains unclear. Thus, we performed 34 frictional experiments on fault gouges composed of three representative mineral phases: muscovite (platy phyllosilicate), quartz (granular silicate) and calcite (granular carbonate), known for their markedly distinct frictional properties. Using a biaxial rock deformation apparatus (BRAVA), we performed tests on fault gouges with grain sizes <125 μm under normal stresses of 50–100 MPa, at room temperature and water-saturated conditions. Our data indicate that the mineralogical composition of fault gouges significantly affects frictional strength, healing, and stability with a non-trivial pattern. Increasing the muscovite content leads to a decrease in frictional strength, from 0.62 for pure calcite and 0.56 for pure quartz to 0.33 of pure muscovite, along with reduced frictional healing and a velocity-strengthening behaviour. This weakening is promoted by a transition from localized deformation along discrete shear planes in granular-rich fault gouges to distributed deformation within the entire gouge layer with increasing muscovite content. At fixed muscovite content, frictional properties depend on the dominant granular phase. Calcite-dominated mixtures exhibit more marked frictional weakening rather than quartz-dominated ones, suggesting a non-linear mixing law between friction coefficient and muscovite content. This different trend is likely due to favourable conditions for fluid-assisted pressure-solution of calcite and foliation development, unlike quartz. When only the granular phases are mixed, we observe complex behaviour with the indentation of quartz into calcite, resulting in higher values of healing rates than those of pure end-member mixtures.Our findings provide robust insights into microphysical processes strongly dependent on the complex mineralogical compositions usually observed along natural faults.

Electromechanics of stretchable hybrid response pressure sensors based on porous nanocomposites

Stretchable pressure sensors are a key enabler of human-mimetic e-skin technology, with promising applications in soft robotics, prosthetics, biomimetics, and biosensors. Stretchable hybrid response pressure sensor (SHRPS) is an emerging type of soft pressure sensor that employs hybrid piezoresistive and piezocapacitive responses. A unique feature of SHRPS based on barely conductive porous nanocomposite (PNC) is its exceptional pressure sensitivity which trivializes its sensitivity to lateral stretch or shear. In this work, we experimentally characterize the electromechanical responses of SHRPS under various loading conditions and provide theoretical explanations through an equivalent circuit model. The capacitance and resistance of the PNC are described by a parallel mixing law and Archie’s law, respectively. Our model can reasonably predict the responses of SHRPS. Our findings reveal that SHRPS exhibits minimal sensitivity to stretch and shear because the hybrid response mechanism is activated only under compression. The effects of PNC-electrode contact impedance and fringe effects are discussed.

Experimental measurement of the size distribution of microbubbles prepared by reciprocating syringe technique

Microbubbles have captured the attention of scholars due to their exceptional physical and chemical properties that exhibit practical applications. Transcranial Doppler ultrasound is a diagnostic tool used in clinical medicine to identify patent foramen ovale (PFO) heart disease caused by incomplete fusion of primary and secondary septum after birth, using microbubbles. The volume of gas and size of the bubbles determine the consequences of air entering the bloodstream. Therefore, it is imperative to investigate stable and efficient microbubble generation technology. The team designed and developed a new type of bubble generator and performed basic research on the flow and mixing rules in the gas-liquid two-phase system in the syringe. The shadow imaging method was used to explore the influence of the equipment operation parameters on the experimental system's microbubble flow process. After analyzing multiple sets of experimental data, it was found that the diameter of bubbles decreases as the frequency increases. After ten times of high-frequency reciprocating movement of the equipment, the microbubble size distribution is mainly between 10–100 μm, the mean diameter is between 23–26 μm, and the relative standard deviation is less than 4.5 %. Compared to manual methods, the device exhibits good accuracy and repeatability.

Dielectric properties and microstructure of BaTiO3-PTFE composites via cold sintering process

The cold sintering process is capable of densifying ceramics and metal powders with other phases into composite materials without inducing chemical reactions between the constituent phases or causing the decomposition of any phases. In this study, we considered the co-sintering of BaTiO3 powders with polytetrafluoroethylene (PTFE) in the grain boundaries. We examined the microstructure and dielectric properties of these composites with different volume fractions of PTFE. The composites were highly dispersive from microstructure and general mixing laws, due to using fine PTFE. Transmission electron microscopy studies demonstrated that the thickness of the PTFE in the grain boundaries was determined with different volume fractions of PTFE. The cold-sintered BaTiO3 composites had high volume resistivity (>1011 Ω·cm), enhancing the resistivity of the cold-sintered pure BaTiO3 using Ba(OH)2·8H2O transient phase. Reliability tests, such as breakdown strength, and Jt curves, were conducted, and the reliability was improved by using fine powders of PTFE with controlled mixing.

Bimodal grain sized barium titanate dielectrics enabled under the cold sintering process

In barium titanate (BaTiO3) the relative permittivity varies as a function of grain size due to the influence of various sizes and scaling effects. The cold sintering process (CSP) has been applied to sinter nanocrystalline BaTiO3 (<200 nm), however in conventionally sintered BaTiO3 a maximum relative permittivity is achieved at average grain sizes around 0.8 μm. In this work the feasibility of cold sintering 1 μm BaTiO3 inclusions in ratios of fine-grained BaTiO3 matrixes from 50 to 200 nm is investigated. Occurrences of both conformal sintering of inclusions into the matrix and constrained sintering with residual porosity are observed. Subsequently, electrical resistivities increased from 1 × 108 Ω cm to approximately 1 × 1012 Ω cm by a post CSP heat treatment of 500 °C. Relative permittivity of annealed samples increases systematically following a logarithmic mixing law as a function of matrix grain size and increasing the ratio of inclusions to matrix.

Water-polymer interactions and mechanisms of water-driven glass transition decrease in non-isocyanate polyhydroxyurethanes with varying hydration sites

Non-isocyanate polyurethanes (NIPUs) with varying content of secondary amino groups along their chain were studied with respect to water absorption and plasticization. Secondary amino groups promote water uptake. Water sorption isotherms in the water activity range 0–0.97 are discussed in terms of various sorption models. Secondary amino groups act as additional hydration sites, increasing monolayer capacity. The red shift of the IR band assigned to the carbonyl of the urethane and the simultaneous blue shift of the urethane N–H bending band show cleavage of the polymer-polymer hydrogen bonds upon water uptake, due to strong interactions between water molecules and hydroxyurethanes constituting the primary hydration sites. A decrease in glass transition temperature (Tg) is observed with increasing water content. The effect is discussed in terms of plasticization and slaving mechanisms, while a peculiar decrease of Tg at very low hydrations is attributed to a mechanism not following common mixing laws.

Microstructure, mechanical properties, and fracture behavior of multi-core through steel wire reinforced brass composite rod produced by a solid-liquid continuous casting and composite technique

A multi-core through steel wire reinforced brass composite rod was fabricated using a solid-liquid continuous casting and composite technique. Microstructure evolution, interface, mechanical properties, and deformation behavior of the composite rod during the room temperature tensile process were studied. The results showed that the steel wires in the composite rod were distributed in a regular hexagonal shape, forming a brass/steel interface with good metallurgical bonding. After annealing at 700 °C for 1h, the tensile strength of the composite rod was 376 MPa, and the elongation to failure was 46.3 %, whose tensile strength was 21 % higher than that of the brass cladding single steel wire composite rod with the same steel percentage. During uniform tensile deformation, each steel wire in the composite rod experienced a consistent and uniform tensile stress. When the tensile deformation became unstable, the central steel wire experienced the highest level of tensile stress, initially leading to the occurrence of necking and fracture. As the tensile strain increased, the brass grains underwent twisting and rotation. In addition, the steel grains were elongated along the tension direction, and the number of low-angle boundaries increased. The straight brass/steel interface was transformed into a wavy pattern with a good bonding interface, indicating that the composite rod exhibited excellent synergetic deformation capability. The mixing laws based on hybrid effects have good applicability to multi-core through steel wire reinforced brass composite rod, with a strength error of less than 7 %.

Computational characterisation of the heat flow meter method applied to moist bio-based insulating building materials

This paper investigates the role of moisture content on the measurement of the thermal conductivity of wood-based low-density fibreboards (LDFs) used for building insulation. To that purpose, a computational code of coupled transfers was used to simulate the widely used Heat Flow Meter (HFM) method. To widen the range of study, the thermal conductivity is obtained with a mixing law model to account for the properties and fractions of the constitutive phases. This mix law model was fitted from thermal conductivity values reported for commercial LDFs. The prediction of the heat flow density during the HFM test was compared with the measurements for dry and wet LDF. Through a series of case studies, the simulations showed that, in the case of moist products, the thermal conductivity determined by the HFM method was overestimated by up to 20%. This overestimate depends on the density distribution, thickness, moisture content, and measurement parameters such as time and the equilibrium criterion. Recommendations are made to limit this error.

Study on the separation and mixing laws of wide-grained dense medium in vibration separation fluidized bed

Vibro-fluidized dry coal beneficiation involves the unavoidable mixing of −1 mm coal dust into a fluidized bed, which compromises the stability and homogeneity of the bed density and reduces the effectiveness of fine-grained coal separation. To understand the features of coal powder separation and mixing (-1 mm) in a vibrating fluidized bed, as well as to achieve a uniform and stable bed density, a wide-grained dense medium consisting of −1 mm coal dust and 0.3–0.15 mm magnetite powder was homogeneously mixed in this work. The degree of density separation in the entire bed and the local mixing properties of the wide-grained dense medium were examined. It was discovered that when low vibrational energy was introduced at the same air velocity, particle separation was enhanced compared to the usual fluidized bed. Small bubbles were found to ensnare fine coal dust and migrate upwards, increasing the density separation. The introduction of high vibrational energy led to particle disorder within the bed and an increase in the level of particle mixing. The beneficial effects of the vibration on the bed diminished when the air velocity was gradually increased under the specified vibration conditions. This caused large bubbles to develop more frequently, which increased particle mixing. The 1–0.5 mm fine-grained coal exhibited the best mixing state; it was less affected by variations in air velocity and vibration levels, whereas the −0.5 mm coal dust was more affected by each variable. Furthermore, the particle system achieved a wide range of air velocity regulations without a significant segregation state change under the vibration conditions of f= 25 Hz and A=1 mm and f= 25 Hz and A=2 mm.

Using FGM concept in fiber-matrix coupling laws to predict the damage in carbon-Epoxy graded composite application in notched plate under thermo-mechanical loading

Reinforcement in composite and notched structures has long been the objective of many researchers. One of the commonly used solutions is hybrid composite. Other recently reemerged solutions are graded materials. These respond, according to their modes of solicitation, to the targeted resistance objectives. However, composites with UD (unidirectional) fiber quality limit the choice of structural grading solely based on their thickness. Using the finite element method and the ABAQUS calculation code, this work presents the embodiment through numerical prediction of an idea based on the concept of material grading by FGM function. The objective of this approach is to introduce the volumetric fraction of the FGM concept into the Fiber-Matrix mixing laws in UD composite. Thickness-graded composites are subjected to a volumetric fraction function raised to the power of a parameter called volumetric fraction index (n). These structures, according to the proposed concepts, are analyzed under thermomechanical loading. The proposed grading of these composites is based on the presence of fibers in the matrix, where the fiber is denser on one side, called the simple concept C-S. The other two symmetrical concepts, named C-2 and C-3, present denser fibers in the middle and on both sides of the plate, respectively. These proposed concepts aim to observe how damage is caused by different responses and levels. The results under the different analyzed parameters are evaluated and compared to the results of the two other non-graded composites, thus showing the limits of those that are graded in terms of properties. According to the thermomechanical loading, the proposed graded composite has demonstrated a resistance overcapacity by the grading index (n) or their locations by concept C1- and C-2 of fibers have played a role in optimizing this capacity. The results also show that damage is caused by deformation overcapacity.

Nonlinear combined harmonic resonances of composite cylindrical shells operating in hygro-thermo-electro-magneto-mechanical fields

By considering the effects of the hygro-thermo-electro-magnetic environments, von Karman nonlinear terms, and multi-harmonic excitations, a coupled nonlinear vibration modeling of composite cylindrical shells comprising a carbon nanotube-reinforced composite (CNTRC) core and two piezoelectric/magnetic composite (PEMC) skins is developed, and the nonlinear dynamic behaviors of such cylindrical shells under primary, super/sub-harmonic, and combined resonance states are investigated. In the theoretical modeling process, the effective mechanical properties of the CNTRC core are first determined using the mixing and Schapery laws, and the hygro-thermo-electro-magneto-mechanical constitutive relations of the PEMC skins are then formulated. Within the framework of Reissner-Mindlin shell theory, the Lagrangian of the system containing Green-Lagrange and von Karman nonlinear terms is derived, and solution techniques based on the multiscale method are provided to obtain nonlinear frequencies, dynamic responses, and phases of CNTRC-PEMC cylindrical shells under multi-physics fields. Consequently, comparison studies are conducted to validate the correctness of the proposed model from different aspects. Based on this, various resonance and chaos behaviors of such structures subjected to multiple load components are revealed and compared, and the influences of environmental factors and structure composition on the amplitude-frequency curves, time-history responses, and phase planes are explored, with several recommendations and findings being drawn.

Discrete element simulation of the grain mixing law in brown rice germination device

Discrete element simulation of the grain mixing law in brown rice germination device

Deciphering the quantitative relationships between age-induced hierarchical microstructure characteristics and tensile properties of Ti20C alloy

Hierarchical microstructure (HM) shows excellent comprehensive properties, but the relationship between mechanical properties and HM characteristics is not clear. In this work, seven HMs of Ti20C were tailored by aging treatments, containing equiaxed α (αep), lamellar α of micron and submicron scale (αlp-i, αlp-ii) and transformed βt (with nano-scale precipitated phases ω/αs in β). Different combinations of strength and plasticity were achieved. It was found that, the different phase interfaces hindered dislocation transferring, and ω/αs phase restricted dislocation movements in βt, which resulted in strength improvement. Moreover, HM was quantitatively characterized, then the relationship between HM characteristics and yield strength (Rp0.2), elongation after fracture (A) was precisely deciphered by referring to Hall-Petch formula and mixing law. It was found that the influence of βt, αlp-ii, αep and αlp-i on Rp0.2 decreased orderly. The decrease in the thickness of αlp-ii and increase in the volume fraction (VF) of βt, αlp-ii, were the most effective methods to improve Rp0.2. For A, the VF of βt was negatively correlated with it, but the equivalent circle diameter (ECD) of αep and the thickness of αlp-i, αlp-ii were positively correlated with it. Specifically, αep and αlp-ii had a higher contribution to plasticity than αlp-i, and the increase in the ECD (or thickness) and VF of αep and αlp-ii was most beneficial to improve plasticity.

Fractal thermal conductivity of unsaturated soils considering pore heterogeneity

Accurately predicting the thermal conductivity of unsaturated soils is crucial for assessing and simulating the long-term environmental impact of subterranean engineering structures. This study presents a fractal thermal conductivity model for unsaturated soils that considers the influence of heterogeneous pore topology, water content and volumetric deformation. Based on the results from the scanning electron microscopy (SEM) and mercury intrusion-extrusion cyclic porosimetry (MIECP) tests on Shanghai clay and Kaolin, we introduce the pore-throat structure to describe the soil heterogeneity and deal with the coupling of solid-pore thermal properties through the mixing law at the pore scale. Together with the self-similar fractal law, the thermal conductivity model is upscaled from the pore scale to the representative element volume (REV) scale. During the process, heterogeneity factors are introduced to describe differences between local and bulk properties, such as porosity and saturation. Thermal property tests of Shanghai clay and Kaolin with varying porosities are then conducted to validate the proposed thermal conductivity model. Additionally, nineteen published datasets on thermal conductivity are also utilized to confirm the adaptability and robustness of the model. The results show that the proposed model predicts well the thermal conductivity of unsaturated soils. Moreover, when compared to existing models, the proposed model offers superior performance in describing the thermal properties of unsaturated soils.

Thermal conductivity of sediments from well-logs and its application to determine heat flow density in the Pannonian Basin, Hungary

The thermal conductivity of rocks can be deduced from available data of exploration wells such as core samples, cuttings, lithological descriptions and geophysical well logs. We present a methodology for determining the thermal conductivity of the Neogene and Quaternary clastic sediments in the Pannonian Basin using geophysical well logs and thermal conductivity data measured in laboratory. The lithological composition consisting of shale, sand and water was identified and the volumetric fractions of these components were derived from wireline logging data that included natural gamma ray, resistivity, bulk density and neutron porosity logs. The bulk thermal conductivity was computed by applying an appropriate mixing law using the thermal conductivity values of the lithological components. The thermal conductivities of the lithological components were determined by the best fit of the calculated bulk thermal conductivity values to the laboratory data. Different mixing models are recommended to calculate thermal conductivity of shales and sandstones. The thermal conductivity of shales was calculated with the weighted harmonic mean of the constituents, where the volumetric fractions and the porosity were the weights. The thermal conductivity of sandstones can be equally well estimated by the weighted geometric mean and the three component lower Hashin-Shtrikman bound. The geometric mean was used in calculations due its simplicity. Shale to sand ratio was utilized to separate shaly and sandstone samples. Heat flow density determination was carried out using the Bullard-plot technique with thermal conductivities calculated by our method. Heat flow density calculated by our method is in the range of heat flow density values previously conducted but with substantially lower uncertainties. The significance of the method is that it allows the harmonization of the heat flow density in the countries lying in the Pannonian Basin, because the Neogene and Quaternary sedimentary cycle resulting in the filling of the basin was uniform throughout the basin.

Prediction model for properties of hot-rolled steel strip: An ICME approach

The Integrated Computational Materials Engineering (ICME) approach is implemented to develop an integrated model for the processing of steel at a hot strip mill. The effect of temperature, deformation, and subsequent cooling rate on microstructure and its associated properties of the steel are mapped using analytical, numerical as well as machine learning approaches, all applied in tandem. The modeling approaches include a rigid visco-plastic approach for the flow formulation, finite volume method to calculate temperature distribution profile, artificial neural network (ANN) modeling for predicting CCT diagram, and Mecking–Kock model along with stress mixing law for the structure–property correlation. The composite model for mapping the final microstructure and microstructure-dependent properties of the steel, which depends on the composition, and various parameters of the hot strip mill is validated through a comparison of predicted values with the published results. The work shows that the hybridization of constitutive equations with the data-driven approach in ICME can successfully model a complex system like the hot strip mill.

Nonlinear CZM-based predictive analysis of damage in single-lap composite joints: An exploration of the FGM concept in Fiber–Matrix coupling

This study introduces an innovative numerical approach, validated through experiments, to incorporate functional graded materials (FGMs) volume fractions into mixing laws for fiber–matrix unidirectional composites. Nonlinear techniques address adhesive ductility, with the cohesive zone modelling (CZM) model integrated into finite element analysis using the ABAQUS code. The CZM model encompasses shear and detachment modes, characterized by adhesive stress increase in a trapezoidal shape. Proposed strategies introduce layer-specific fiber presence; concepts like C-1 exhibit denser fibers toward the middle, while C-2 and C-3 position them nearer to the plate edge. Stiffness from attached plates significantly governs overall responses, particularly under mixed loading conditions. The results have shown that the proposed grading concept C-2 provides an over-resistance capacity compared to other concepts. Additionally, using a special mesh in the composite grading, the results indicate that the adhesive formulation used in this analysis and the approach followed are primarily based on experimental results, demonstrating good agreement with the numerical model employed.

Analysis of dielectric resonator antenna using natural fiber reinforced polymer composites

This work aims to demonstrate the viability of replacing natural fiber reinforced polymer composites for hard ceramics in millimeter-wave dielectric resonator antennas (DRA). The dielectric characteristics of three novel natural fiber reinforced polymer composites were determined using the Lichtenecker logarithmic mixing law. Using two commercial antenna design software packages, CST Studio and ANSYS HFSS, the resulting dielectric characteristics were utilized to study a probe-fed rectangular DRA. Natural fiber-reinforced polymer-based DRAs offer a wider bandwidth than ceramic-based DRAs. Close coupling is obtained by the three natural fiber-reinforced polymer-based antennas and the ceramic DRA. In all cases, the impedance bandwidths observed are the consequence of quasi-TM111 mode radiation. HFSS studies indicate that the resonance frequency of the natural fiber reinforced polymer based DRAs is roughly 75 percent higher than that of the ceramic DRA. CST results indicate that the resonance frequency of the natural fiber polymer-based DRA is approximately 88 percent higher than that of the ceramic DRA. Natural fiber reinforced Polymer-based DRAs have three times the −10 dB impedance bandwidth of ceramic-based DRAs.