Power Law Equation Research Articles

Benchmark experimental study on cavitating flow around Clark-Y 11.7 % hydrofoil at various angles of attack under controlled levels of dissolved air

The present research aims to study cavitating flow around a CLARK-Y 11.7 % hydrofoil with variable angles of attack (α) while maintaining controlled levels of dissolved air in the operating fluid, which is water. A series of experiments were conducted using a water tunnel facility, where the cavitation characteristics were measured and observed using sensors and high-speed imaging techniques. The variables studied in the present work are cavitation number (1 ≤ σ ≤ 2.2) and angle of attack (α = 4°, 6°, 8°, 10°, and 12°), with dissolved air levels (DAL) in the range of 9.3 ppm to 13.1 ppm. The dimensionless cavity length decreases significantly with increasing values of σ/α, indicating an inverse relationship where higher cavitation numbers or lower angles of attack result in shorter cavities. The cavity length follows a power-law scaling relationship, with the empirical equation Lmax/C=4.78×σ/α−0.76.Increasing the angle of attack transitions the cavitation nature from stable (Mode I) to dynamic (Mode II) and highly oscillating (Mode III). Larger cavities result in lower Strouhal numbers, which indicates reduced vortex shedding activity. The relationship between the Strouhal number and the normalized cavitation number σ/α is characterized by the power-law equation St=0.041×σ/α0.3. The pressure coefficient at the leading-edge increases with the angle of attack at low cavitation numbers, while higher cavitation numbers lead to greater pressure coefficient differences between the leading and trailing edges.The present study offers an extensive dataset and empirical correlations that may serve as a benchmark framework, which facilitates the validation of computational and experimental models of cavitating flow under similar conditions.

Are Wild Prey Sufficient for the Top Predators in the Lowland Protected Areas of Nepal?

A balanced equilibrium between carnivores and their prey is crucial for maintaining ecosystem sustainability. In this study, we applied the predator-prey power law equation to assess the balance between the biomass densities of carnivores and their wild prey within Nepal's lowland protected areas during 2013, 2018, and 2022. The estimated value of the power law exponent k for predator-prey biomass was 0.71 (95% CI = 0.39-1.05), indicating an approximate threefold increase in predator biomass density for every fivefold increase in prey biomass density. Consequently, this creates a systematically bottom-heavy predator-prey biomass pyramid. This finding, consistent with the k = 3/4 trophic biomass scaling across ecosystems, suggests that predator biomass is proportionally sustained by prey biomass, indicating a balance between top predators and their wild prey in Nepal's lowland protected areas. We further demonstrated it is possible to retain the overall power law exponent while jointly measuring intraguild competition between two predators with canonical correlation analysis. This understanding opens avenues for future research directed toward unraveling the factors that drive these consistent growth patterns in ecological communities.

Modeling The Hydrogen Crossover Through Membrane With And Without Catalyst Layers

The hydrogen crossover flux is expressed as a function of the difference in the partial pressure of hydrogen and total pressure difference between the supply and permeate sides of a membrane. The hydrogen crossover rate was measured under several operating conditions by micro gas chromatography. The permeation flux was not influenced by the total pressure difference up to 50 kPa. A bare Nafion membrane and the membrane with catalyst layers were modeled as a stack of bulk and skin layers. Hydrogen permeability of both samples showed identical bulk layer expressed by a power-law equation of the moisture content and an Arrhenius equation of temperature with an activation energy of 22.8 kJ mol–1. The measurement of skin layer resistance wasn’t successful since the skin layer resistance was too low to be measured. A skin layer of Nafion with a catalyst layer wasn’t observed due to formation of fused layer.

Modeling The Hydrogen Crossover Through Membrane With And Without Catalyst Layers

The hydrogen crossover flux is expressed as a function of the difference in the partial pressure of hydrogen and total pressure difference between the supply and permeate sides of a membrane. The hydrogen crossover rate was measured under several operating conditions by micro gas chromatography. The permeation flux was not influenced by the total pressure difference up to 50 kPa. A bare Nafion membrane and the membrane with catalyst layers were modeled as a stack of bulk and skin layers. Hydrogen permeability of both samples showed identical bulk layer expressed by a power-law equation of the moisture content and an Arrhenius equation of temperature with an activation energy of 22.8 kJ mol–1. The measurement of skin layer resistance wasn’t successful since the skin layer resistance was too low to be measured. A skin layer of Nafion with a catalyst layer wasn’t observed due to formation of fused layer.

Using the Montgomery-Koyama-Smith equation to calculate the stomatal area per unit lamina area for 12 Magnoliaceae species.

The Montgomery-Koyama-Smith (MKS) equation predicts that total leaf area per shoot is proportional to the product of the sum of individual leaf widths and maximum individual leaf length, which has been validated for some herbaceous and woody plants. The equation is also predicted to be valid in describing the relationship between the total stomatal area per micrograph (AT) and the product of the sum of individual stomatal widths (denoted as LKS) and maximum individual stomatal length (denoted by WKS) in any particular micrograph. To test the validity of the MKS equation, 69,931 stomata (from 720 stomatal micrographs from 12 Magnoliaceae species) were examined. The area of each stoma was calculated using empirical measurements of stomatal length and width multiplied by a constant. Six equations describing the relationships among AT, LKS, and WKS were compared. The root-mean-square (RMSE) and the Akaike information criterion (AIC) were used to measure the goodness of fit, and the trade-off between the goodness of fit and the structural complexity of each model, respectively. Analyses supported the validity of the MKS equation and the power-law equation AT ∝ (LKS∙WKS)α, where a is a scaling exponent. The estimated values of α at the species level and for the pooled data were all statistically smaller than unity, which did not support the hypothesis that AT ∝ LTS∙WTS. The power-law equation had smaller RMSE and AIC values than the MKS equation for the data from the 12 individual species and the pooled data. These results indicate that AT tends to allometrically scale with LKS∙WKS, and that increases in AT do not keep pace with increases in LTS∙WTS. In addition, using the product of LKS and WKS is better than using only one of the two variables.

Crystallographic orientation dependence in creep deformation of micron-thick silicon films for 3-D microstructures

In this study, the steady-state creep deformation properties of 5 μm-thick single crystal silicon (Si) films at elevated temperatures were investigated using punch creep-forming tests for the design of three-dimensional (3-D) microstructured MEMS. The relationship between the creep strain rate and stress of the Si films with {100}, {110}, and {111} planes at temperatures of 1223–1323 K was derived using finite element analysis following punch creep-forming tests, and a power-law creep constitutive equation for Si films was determined. The steady-state creep properties of the Si film samples varied clearly with crystallographic orientations. Among the three crystallographic orientations, the creep strain rate of the micron-thick Si films was the fastest for the {011} plane, followed by the {111} and {001} planes, in the applied stress range of 110 MPa to 220 MPa. This is consistent with the increasing order of magnitude of the thermal activation energy. The crystallographic orientation dependence of the steady-state creep properties of Si films is discussed based on the mobility of dislocation gliding per unit lattice and scanning electron microscope observations. The sample-size dependence of the creep strain rate of Si with the {001} plane was clearly observed between the micron- and millimeter-thick samples, which was attributed to the difference in the frequency factor of the power-law creep. However, the thermal-activation energy remained constant. This study successfully revealed the steady-state creep properties of Si films and provided useful engineering data for the design of 3-D Si-MEMS fabrication by the plastic processing of Si films.

Towards Simpler Modelling Expressions for the Mechanical Characterization of Soft Materials

Aims: The aim of this paper is to develop a new, simple equation for deep spherical indentations. Background: The Hertzian theory is the most widely applied mathematical tool when testing soft materials because it provides an elementary equation that can be used to fit force-indentation data and determine the mechanical properties of the sample (i.e., its Young’s modulus). However, the Hertz equation is only valid for parabolic or spherical indenters at low indentation depths. For large indentation depths, Sneddon’s extension of the Hertzian theory offers accurate force-indentation equations, while alternative approaches have also been developed. Despite ongoing mathematical efforts to derive new accurate equations for deep spherical indentations, the Hertz equation is still commonly used in most cases due to its simplicity in data processing. Objective: The main objective of this paper is to simplify the data processing for deep spherical indentations, primarily by providing an accurate equation that can be easily fitted to force-indentation data, similar to the Hertzian equation Methods: A simple power-law equation is derived by considering the equal work done by the indenter using the actual equation. Results: The mentioned power-law equation was tested on simulated force-indentation data created using both spherical and sphero-conical indenters. Furthermore, it was applied to experimental force-indentation data obtained from agarose gels, demonstrating remarkable accuracy. Conclusion: A new elementary power-law equation for accurately determining Young’s modulus in deep spherical indentation has been derived.

Fractal permeability model for power-law fluids in embedded tree-like branching networks based on the fractional-derivative theory

The investigation of permeability in tree-like branching networks has attracted widespread attention. However, most studies about fractal models for predicting permeability in tree-like branching networks include empirical constants. This paper investigates the flow characteristics of power-law fluids in the dual porosity model of porous media in embedded tree-like branching networks. Considering the inherent properties of power-law fluids, non-Newtonian behavior effects, and fractal properties of porous media, a power-law fluids rheological equation is introduced based on the fractional-derivative theory and fractal theory. Then, an analytical formula for predicting the effective permeability of power-law fluids in dual porous media is derived. This analytical formula indicates the influences of fractal dimensions and structural parameters on permeability. With increasing length ratio, bifurcation series, and bifurcation angle, as well as decreasing power-law exponent and diameter ratio, the effective permeability decreases to varying degrees. The derived analytical model does not include empirical constants and is consistent with the non-Newtonian properties of power-law fluids, indicating that the model is an effective method for describing the flow process of complex non-Newtonian fluids in porous media in natural systems and engineering. Therefore, this study is of great significance to derive analytical solutions for the permeability of power-law fluids in embedded tree-like bifurcation networks.

Multi-scaling allometry in human development, mammalian morphology, and tree growth

Various animal and plant species exhibit allometric relationships among their respective traits, wherein one trait undergoes expansion as a power-law function of another due to constraints acting on growth processes. For instance, the acknowledged consensus posits that tree height scales with the two-thirds power of stem diameter. In the context of human development, it is posited that body weight scales with the second power of height. This prevalent allometric relationship derives its nomenclature from fitting two variables linearly within a logarithmic framework, thus giving rise to the term “power-law relationship.” Here, we challenge the conventional assumption that a singular power-law equation adequately encapsulates the allometric relationship between any two traits. We strategically leverage quantile regression analysis to demonstrate that the scaling exponent characterizing this power-law relationship is contingent upon the centile within these traits’ distributions. This observation fundamentally underscores the proposition that individuals occupying disparate segments of the distribution may employ distinct growth strategies, as indicated by distinct power-law exponents. We introduce the innovative concept of “multi-scale allometry” to encapsulate this newfound insight. Through a comprehensive reevaluation of (i) the height-weight relationship within a cohort comprising 7, 863, 520 Japanese children aged 5–17 years for which the age, sex, height, and weight were recorded as part of a national study, (ii) the stem-diameter-height and crown-radius-height relationships within an expansive sample of 498, 838 georeferenced and taxonomically standardized records of individual trees spanning diverse geographical locations, and (iii) the brain-size-body-size relationship within an extensive dataset encompassing 1, 552 mammalian species, we resolutely substantiate the viability of multi-scale allometric analysis. This empirical substantiation advocates a paradigm shift from uni-scaling to multi-scaling allometric modeling, thereby affording greater prominence to the inherent growth processes that underlie the morphological diversity evident throughout the living world.

A comprehensive kinetic modeling study on NH3/H2, NH3/CO and NH3/CH4 blended fuels

Ammonia (NH3), as an ideal zero-carbon fuel, plays a positive role in mitigating global warming. By cofiring NH3 with highly reactive small molecule fuels such as hydrogen (H2), carbon monoxide (CO) and methane (CH4), the reactivity of NH3 combustion can be significantly enhanced. In this work, a detailed kinetic mechanism for NH3/CH4/H2/CO containing 146 species and 1099 reactions was developed and extensively validated with selected experimental data from the literature on laminar burning velocity (LBV), ignition delay time (IDT), and species concentrations measured in burner-stabilized flames (BSF), plug flow reactors (PFR) and jet-stirred reactors (JSR), covering temperatures of 273–2000 K, pressures of 0.053–40 atm and equivalence ratios of 0.1–2. In addition, the detailed mechanism was simplified to include 53 species and 353 reactions using three simplification methods. Kinetic modeling analysis showed that the chemical and transport effects of H2, CO and CH4 are the main factors enhancing NH3 combustion, which rising with the increasing initial temperature and decreasing ammonia blending ratio. Among the four reactants, H2 is consumed first, followed by CH4 and NH3, with CO reacting last. By modifying the Metghalchi-Kech power law equation, it was found that a clear linear relationship exists between LBV and the sum of the maximum mole fractions of O, H, OH, and NH2 radicals.

Research on the Effect of Static Pressure on the Rheological Properties of Waxy Crude Oil

In this paper, with the application of a MARS 60 high-pressure rheometer, experimental tests are conducted on Shengli crude oil to test its gel point, viscosity and thixotropy under different static pressures. Consequently, the effect of static pressure on the rheological parameters of waxy crude oil is revealed. It is proven that with the increase in the static pressure, the gel point of Shengli crude oil increases linearly, and the viscosity also gradually increases. The power law equation is employed to describe the relationship between the apparent viscosity and shear rate of Shengli crude oil under different static pressures. With the increase in the static pressure, the consistency coefficient (K) increases linearly, and the rheological index (n) decreases linearly. The relationship between the viscosity of Shengli crude oil and the static pressure and shear rate can be obtained. The Cross thixotropic model is used to describe the thixotropic curve of Shengli crude oil under different static pressures. With the increase in the static pressure, the thixotropic coefficient of consistency (ΔK) and the structure fracture constant (b) increase linearly. This is because a high pressure results in high structure strength and strong non-Newton rheological behavior in gelled crude oil and also causes remarkable structure fracture in crude oil. The results in this paper can provide an important theoretical basis for crude oil production and transportation.

FRESH-based 3D bioprinting of complex biological geometries using chitosan bioink

Traditional three-dimensional (3D) bioprinting has always been associated with the challenge of print fidelity of complex geometries due to the gel-like nature of the bioinks. Embedded 3D bioprinting has emerged as a potential solution to print complex geometries using proteins and polysaccharides-based bioinks. This study demonstrated the Freeform Reversible Embedding of Suspended Hydrogels (FRESH) 3D bioprinting method of chitosan bioink to 3D bioprint complex geometries. 4.5% chitosan was dissolved in an alkali solvent to prepare the bioink. Rheological evaluation of the bioink described its shear-thinning nature. The power law equation was fitted to the shear rate-viscosity plot. The flow index value was found to be less than 1, categorizing the material as pseudo-plastic. The chitosan bioink was extruded into another medium, a thermo-responsive 4.5% gelatin hydrogel. This hydrogel supports the growing print structures while printing. After this, the 3D bioprinted structure was crosslinked with hot water to stabilize the structure. Using this method, we have 3D bioprinted complex biological structures like the human tri-leaflet heart valve, a section of a human right coronary arterial tree, a scale-down outer structure of the human kidney, and a human ear. Additionally, we have shown the mechanical tunability and suturability of the 3D bioprinted structures. This study demonstrates the capability of the chitosan bioink and FRESH method for 3D bioprinting of complex biological models for biomedical applications.

Durability and kinetic effects of CO2-rich oxidizing streams on LSCF-based solid oxide fuel cells

In the SOS–CO2 cycle, a novel hybrid cycle for blue power production, the solid oxide fuel cell's (SOFC) cathode is supplied with a CO2-rich oxidizing stream (e.g., 21 % O2 79 % CO2 vol.). The durability of state-of-the-art anode-supported SOFCs (25 cm2, SolydEra) with LSCF-GDC/LSC (La0.6Sr0.4Co0.2Fe0.8O3-δ-Gd0.1Ce0.9O3+δ/La0.6Sr0.4CoO3+δ) cathodes was tested at atmospheric pressure for 1090 h with 7 % humidified H2 and reformate, at 700 °C and 0.85 V. The SOFC performance was investigated with periodic I/V curves and electrochemical impedance spectroscopy (EIS) measurements. The results highlighted a 24 % power density loss when air was replaced with the O2/CO2 mixture (672 mW/cm2 in air vs. 508 mW/cm2 in O2/CO2 with humidified H2). A stable power output was observed, and complete reversibility was found when the air supply was restored. A distribution of relaxation times (DRT) analysis of the EIS spectra allowed to extract an anodic rate equation for the hydrogen oxidation reaction (HOR) and evaluate the frequency region affected by cathodic CO2. The kinetic effect of CO2 was also studied via EIS on symmetric button cells at varying O2 and CO2 amounts, and a power-law rate equation was derived. The results verify the feasibility of the SOS–CO2 cycle feed conditions at 700 °C and atmospheric pressure.

Electrical properties and conduction mechanisms of Ba0.75Sr0.25Ti1-xZrxO3 ceramics synthesized by sol-gel route

A series of Ba0.75Sr0.25Ti1-xZrxO3 (x = 0, 0.01, 0.03, 0.05, and 0.1) ceramics were synthesized via a facile sol-gel route. The confirmation of a tetragonal structure was achieved through Rietveld refinement of the powder X-ray diffraction (XRD), and the finding was subsequently corroborated by Raman spectroscopy. The Scanning electron microscopy (SEM) confirmed the roughly cubical-shaped grains and average grain size is 0.31 μm for x = 0 and 0.70 μm for x = 0.05. The electrical properties such as dielectric constant, dielectric loss and ac/dc conductivity were investigated as a function of temperature and frequency. The Jonscher's universal power law (JPL) and Arrhenius equation have been used for the analysis of conductivity. The electrical conductivity variation at intermediate frequencies was explained using JPL. The Super-linear power law (SPL) explains the electrical response at higher frequencies. The temperature-dependent frequency exponents ‘s1’ and ‘s2’ were employed to predict the quantum mechanical tunneling (QMT), non-overlapping small polarons hopping (NSPT), and correlated barrier hopping (CBH) conduction mechanisms.

Monthly hydraulic geometry relationship quantification with environmental LAI by utilizing sentinel data: A case in Jingjiang reach of the Yangtze River

This study presents a novel approach for quantifying the dynamics of monthly hydraulic geometry relationships in the Jingjiang reach of the Yangtze River by integrating leaf area index (LAI) data as an indicator of riparian vegetation. A comprehensive system of ordinary differential equations (ODEs) couples traditional power-law hydraulic geometry equations with LAI, capturing the influence of erosion control on channel morphology. The periodic delayed response theory and automatic differentiation techniques are employed to enhance the modeling framework’s capabilities. Calibration and verification demonstrate the models’ effectiveness in capturing overall trends in discharge, width, and depth dynamics, outperforming traditional constant-parameter approaches. However, model predictive abilities are limited under extreme climate conditions due to training on normal climate data. Key assumptions, including the periodic delayed response theory’s neglect of peak discharges, simplified representation of artificial cut-offs, and reliance on remotely sensed data with limited local validation, introduce uncertainties. The proposed modeling framework shows potential for broader application to other river systems with appropriate adjustments. Future research could incorporate additional environmental factors, integrate models across scales, couple with advanced simulation techniques, and expand stability assessments beyond the riverbed index. By addressing related challenges, this integrated approach lays a foundation for enhancing understanding of river morphodynamics and channel stability.

Physicochemical, rheological, sensory, and proximal properties of yogurt flavored with Aloe vera gel

Aloe vera leaves have a transparent mucilaginous, showing an important polysaccharides content and potential bioactive phytochemicals. This study evaluated the physicochemical, rheological, sensorial, and proximal properties of yogurt elaborated using Streptococcus thermophilus and Lactobacillus bulgaricus and flavored with Aloe vera gel. Previous studies have shown that the variation of some ingredients, such as the percentage of fat or inoculum, can modify the sensory and rheological characteristics of fermented dairy beverages. Different treatments were prepared using a 2n factorial design varying the percentage of fat (2 and 3%), inoculum (2 and 3%), and Aloe vera gel (5 and 10%).All the samples presented pseudoplastic behavior, and the power law equation showed a better fit in all the samples. The higher percentage of inoculum decreased the fermentation time and increased the apparent viscosity. An increase in fat concentration amplified yogurt’s pH, °Brix, and pseudoplastic behavior. Meanwhile, the gel increased the percentage of syneresis and decreased the apparent viscosity.The formulation with 3% fat, 3% inoculum, and 5% Aloe vera gel obtained higher values in these sensory parameters of smell, flavor, appearance, and acceptability. The production of supplemented probiotic yogurt- up to 5% Aloe vera gel is feasible from an industrial and consumer point of view since it shows acceptable sensory, nutritional, and microbiological characteristics.

Rainfall threshold for prediction of shallow landslides in the Garhwal Himalaya, India

Rainfall is a significant triggering factor for landslides, after tectonics and structurally vulnerable lithology— particularly in Himalayan Range. Globally, extensive efforts have been undertaken to determine the specific rainfall threshold conditions that lead to the initiation of a slide on a regional scale. Rainfall-induced landslides disrupt life and cause extensive damage to properties in the Himalayan region. This study has a two-fold objective; to determine the relationship between the occurrence of landslides and a significant triggering factor, namely rainfall, based on intensity-duration (I-D) and antecedent rainfall methods, and also to determine the best fit distribution for rainfall data based on goodness of fit tests within the four western-most districts of the Garhwal Himalaya, in Dehradun, Rudraprayag, Tehri Garhwal, and Uttarkashi. The rainfall patterns of these four districts conform to the log-logistic (3P) distribution, and the rainfall threshold has been fitted over a power-law equation with the lower boundary demarcated by a quantile regression that is presented as a threshold with an established relationship of y(I)=1.38D−0.126 (I=rainfall intensity, D=duration). The results suggest that a rainfall intensity of 0.45-0.50 mm per hour over short durations (48 h) has the potential to trigger landslides in this region. Antecedent rainfall of around 80 mm in the 15 days prior to a landslide event significantly raises the landslide risk. Further, lithologies like mud and sandstones are highly susceptible to landslides and can be triggered by rainfall of 10–20 mm occurring, consecutively, over a 5-day period.

Physicochemical, rheological, sensory, and proximal properties of yogurt flavored with Aloe vera gel

Aloe vera leaves have a transparent mucilaginous, showing an important polysaccharides content and potential bioactive phytochemicals. This study evaluated the physicochemical, rheological, sensorial, and proximal properties of yogurt elaborated using Streptococcus thermophilus and Lactobacillus bulgaricus and flavored with Aloe vera gel. Previous studies have shown that the variation of some ingredients, such as the percentage of fat or inoculum, can modify the sensory and rheological characteristics of fermented dairy beverages. Different treatments were prepared using a 2n factorial design varying the percentage of fat (2 and 3%), inoculum (2 and 3%), and Aloe vera gel (5 and 10%).All the samples presented pseudoplastic behavior, and the power law equation showed a better fit in all the samples. The higher percentage of inoculum decreased the fermentation time and increased the apparent viscosity. An increase in fat concentration amplified yogurt’s pH, °Brix, and pseudoplastic behavior. Meanwhile, the gel increased the percentage of syneresis and decreased the apparent viscosity.The formulation with 3% fat, 3% inoculum, and 5% Aloe vera gel obtained higher values in these sensory parameters of smell, flavor, appearance, and acceptability. The production of supplemented probiotic yogurt- up to 5% Aloe vera gel is feasible from an industrial and consumer point of view since it shows acceptable sensory, nutritional, and microbiological characteristics.

Температурные изменения в мясных изделиях при жарке в пароконвекционных печах

Combination steam ovens, or combi steamers, have entered all spheres of food production, including the meat industry. Their rational use requires a scientific and practical foundation. This research featured the changes in mean volume temperature and temperature gradient that occur in meat products (one-dimensional bodies with different nutrient compositions) during heat treatment in dry air and a steam-air mix.
 The research involved two samples of meat products with different moisture and fat contents. The chicken fillet sample had a moisture content of 74.5% and a fat content of 1.9% while the pork shoulder sample had a moisture content of 55.1% and a fat content of 29.4%. Shaped as a one-dimensional cylinder and a plate, the samples were subjected to heating at the temperature range of 160–240°C in a Unox-203G steam-convection oven (Italy). Dry air and a steam-air mix with a humidity of 80–85% served as a heating medium. The temperature was measured using thermocouples attached to a Sosna-004 meter.
 The research revealed some patterns in the mean volume temperature and temperature gradient. The temperature gradient involved three stages during processing in a steam-air mix and four stages when treated with dry air. The change in the mean volume temperature for the steam-air mix could be described by a power law equation; the dry air treatment was described using a linear equation. When heated in dry air, the rate of change in the temperature gradient was constant at first but started to decrease at a certain stage. The change rate in the mean volume temperature remained low for 5 min and started to increase onwards, maintaining its value until the end of the process. When heated in a steam-air mix, the change rate in the temperature gradient dropped to its minimum in 4–5 min and started to grow. The mean volume temperature demonstrated a high change rate during the first 5 min and went down. The chicken fillet with its low fat content warmed up faster by 13–26% when processed in a steam-air mix and by 9–23% when treated in dry air. The plate-shaped products needed longer heat treatment. The composition and form had no significant effect on the nature of the change in the temperature gradient and mean volume temperature.
 The obtained dependencies made it possible to select the optimal temperature and humidity conditions for convective frying of meat products.

Micromechanical characterization of zirconia and silicon nitride ceramics using indentation and scratch methods

Micromechanical characterization of brittle ceramics remains challenging due to the difficulty in sample preparation required by conventional tests. The micromechanical properties (e.g., elastic modulus EIT, indentation hardness HIT, and fracture toughness KIC) of ZrO2 and Si3N4 were investigated by indentation and scratch tests with different indenters (e.g., Vickers, Knoop, and Berkovich indenters) under various loads. The ratio of the true hardness by the Vickers indenter over that by the Knoop indenter is approximately a constant of 1.13 and independent of material. Elastic recovery of residual imprint by the Knoop indenter was also used to assess elastic modulus of ZrO2 and Si3N4, and modified equations were proposed. The length of Vickers indenter-induced cracking was found to be proportional to the applied load under large loads, and a modified formula for calculating fracture toughness was proposed for ZrO2 and Si3N4, which have relatively large fracture toughness of about 9 MPa⋅m1/2. The critical void volume fraction f* in the nanoindentation energy-based methods was found to linearly decrease with the exponent mf of the power-law equation used for curve fitting of the degradation of HIT or EIT with hmax. The determination of fracture toughness by scratch methodology was found to be affected by mechanical properties of material, indenter geometry, and data range.