Decreasing Heating Rate Research Articles

Finite element simulation investigation of warping deformation during baking temperature cycle of dissimilar materials sandwich adhesive bonded structures of car body

Adhesive bonding is crucial for joining lightweight, mixed-material car bodies but can cause distortion due to changes in adhesive properties during heat curing. In this paper, based on the characteristics of the roller-hemming structures, a sandwich adhesive bonded structure of aluminum-steel dissimilar materials was designed. A viscoelastic model for the hemming adhesive was developed, and a coupled thermal-chemical-structural model was implemented in ABAQUS. Baking experiments validated the model. Stress and strain variations were analyzed to understand warping mechanisms during the temperature cycle. Further analysis results showed that decreasing heating rate, holding temperature, or increasing cooling rate can reduce deformation.

Comparative Study of Heat Transfer Simulation and Effects of Different Scrap Steel Preheating Methods

The materials charged into a converter comprise molten iron and scrap steel. Adjusting the ratio by increasing scrap steel and decreasing molten iron is a steelmaking raw material strategy designed specifically for China’s unique circumstances, with the goal of lowering carbon emissions. To maintain the converter tapping temperature, scrap must be preheated to provide additional heat. Current scrap preheating predominantly utilizes horizontal tunnel furnaces, resulting in high energy consumption and low efficiency. To address these issues, a three-stage shaft furnace for scrap preheating was designed, and Fluent software was used to compare and study the preheating efficiency of the new three-stage furnace against the traditional horizontal furnace under various operational conditions. Initially, a three-dimensional transient multi-field coupling model was developed for two scrap preheating scenarios, examining the effects of both furnaces on scrap surface and core temperatures across varying preheating durations and gas velocities. Simulation results indicate that, under identical gas heat consumption conditions, scrap achieves markedly higher final temperatures in the shaft furnace compared to the horizontal furnace, with scrap surface and core temperatures increasing notably with extended preheating times and higher gas velocities, albeit with a gradual decrease in heating rate as the scrap temperature rises. At a gas velocity of 9 m/s and a preheating time of 600 s, the shaft furnace achieves the highest waste heat utilization rate for scrap, with scrap averaging 325 °C higher than in the horizontal furnace, absorbing an additional 202 MJ of heat per ton. In the horizontal preheating furnace, scrap steel exhibits a heat absorption efficiency of 35%, whereas in the vertical furnace, this efficiency increases notably to 63%. In the vertical furnace, the waste heat recovery rate of scrap steel reaches 57%.

Effect of the Heating/Cooling Rate of Nonisothermal Aging on Microstructure and Mechanical Properties of 2050 Al–Li Alloy

The effect of the heating/cooling rates of nonisothermal aging (NIA) on microstructure and mechanical properties of 2050 Al–Li alloy are investigated. The 2050 Al–Li alloy is first solid solutioned and predeformed and then heated from 130 to 220 °C at different rates of 20, 30 °C h−1, or 40 °C h−1 and then cooled to 150 °C. The results show that the mechanical properties of the alloy subjected to NIA treatment can be improved by adjusting the heating and cooling rate. When the heating and cooling rate is 30 °C h−1, the alloy achieves the best mechanical properties; the hardness, ultimate tensile strength (UTS), yield strength (YS), and elongation are 182.9 HV, 597, 571 MPa, and 9.6%, respectively. With the decrease of heating (or cooling) rate of NIA, the diameter and thickness of the T1 precipitate increase and the volume fraction decreases, resulting in the variation in mechanical properties. Therefore, herein, premier precipitation behavior and improved mechanical properties are both achieved by modifying the heating and cooling rate of NIA; the effect of the heating/cooling rate of NIA on the microstructure evolution of 2050 Al–Li alloy is revealed, and the underlying strengthening mechanism is investigated in detail.

Experimental study on self-heating strategy of lithium-ion battery at low temperatures based on bidirectional pulse current

Preheating is an effective solution to the severe degradation of lithium-ion battery (LIB) performance at low temperatures. In this study, a bidirectional pulse-current preheating strategy for LIBs at low temperatures without external power is proposed, which involves the incorporation of a direct current/direct current converter and a series of resistances, inductances, and switches. The effects of ambient temperature, initial state of charge, and preheating strategy on the voltage and current evolution, heating rate, and heating efficiency are experimentally analysed in a climatic chamber, in addition to the effects of various preheating strategies on battery degradation. A comparative analysis is conducted using the classical pulse self-heating strategy. The results indicate that the bidirectional pulse-current preheating strategy enables preheating under an ambient temperature of −15 °C at a rate of 6.38 °C/min and affords a thermal efficiency of 31.9%. By contrast, the pulse heating method affords a heating rate of 3.46 °C/min and a thermal efficiency of 24.2%. As the battery temperature decreases, both the charge/discharge switching period and heating rate decrease, whereas the thermal efficiency and energy consumption ratio improve. No significant degradation occurs after 30 heating cycles, and the bidirectional pulse-current preheating strategy is demonstrated through capacity testing, incremental capacity curves, and electrochemical impedance spectroscopy testing. This study proposes a new approach for preheating LIBs internally and provides experimental evidence for a bidirectional-pulse preheating strategy.

Thermal Analysis Kinetics Study of Pulverized Coal Combustion under Oxygen-Rich Atmosphere.

The thermal analysis kinetic behavior of pulverized coal combustion in different oxygen-rich atmospheres is studied with a thermogravimetric (TG) analyzer. The effects of heating rate on combustion characteristic are considered. The results showed that the combustion rate of pulverized coal increased and the burnout time decreased under the conditions of an oxygen-enriched atmosphere and high heating rate. As the heating rate increases, the TG and derivative TG curves of the coal samples generally move toward the high-temperature region, and the thermal hysteresis phenomenon occurs. The changes in oxygen concentration and heating rate mainly affect the combustion stage of coal samples. The decrease in heating rate or the increase in oxygen concentration will cause a decrease in ignition point temperature and burnout temperature. Under the condition of 40% O2, the oxygen concentration and heating rate have the greatest influence on the combustion characteristic parameters. In addition, the combustion reaction of pulverized coal in the warming process was analyzed by FWO and KAS methods, respectively. The results showed that the changes in oxygen concentration and heating rate affected the activation energy, and the activation energy of coal samples increased with the increase in oxygen concentration.

Analysis of Gas Turbine Performance based on Variation of Operating Load at PLTGU Panaran 1 Unit 1 PT.Mitra Energi Batam

Gas and steam power generation units often experience changes in load according to the requested electricity needs. Changes in generator workload will also affect the efficiency of the generator. The different efficiency in each workload will have an effect on the amount of heat rate production produced when compared. By calculating the efficiency at each load, it will be useful to find out the workload with the best performance. From the results of the enthalpy calculation process based on the temperature of each gas turbine process, in this study the gas turbine performance is calculated, and then it compares the turbine performance with variations in operating load. The turbine performance that will be calculated includes compressor power, turbine power, net power, thermal efficiency, compressor efficiency, combustion chamber efficiency, turbine efficiency, heat input, and heat rate. The results of the calculation of the highest average thermal efficiency at 27 MW load were 35.18%; the average compressor efficiency experienced the highest increase at 25 MW load of 83.24%, followed by an average increase in combustion chamber efficiency and an average decrease in turbine efficiency at each increase in load, as well as experiencing the lowest decrease in heat rate at 27 MW load conditions of 2,842 kJ/kWh

Effect of Operating Parameters on Agricultural Biomass Mixture Pyrolysis Process in a Batch Reactor

Many phenomena affect devolatilization of biomass particles, including mass and heat transfer, chemical reactions and physical transformation. Mathematical models that are capable to describe pyrolysis phenomena can greatly assist the large-scale development and optimization of pyrolysis processes, but to be implemented into large-scale simulation the models need to be simplified at a certain degree. In the present study, an existing mathematical model is used to describe the pyrolysis of a single particle of biomass. It couples the heat transfer equations with the chemical kinetics equations. The common Euler explicit method is used for solving the heat transfer equation and the two-step pyrolysis kinetics equations. The model equation is solved for a sphere particle with a radius of 0.001 m and temperature ranging from 300 to 923 K. An original numerical model for the pyrolysis of agricultural biomass mixture is proposed and relevant equations solved using original program realized in MATLAB. Simplified particle model was validated with the experimental data in a non-isothermal pyrolysis reactor. The sample was heated in the temperature range of 300–923 K at average heating rates of 21, 30 and 54 K/min. The model results showed reasonable agreement with experiments. The difference (between the experimental and model results) is slightly more prominent with decreasing heating rate (21 and 30 K/min), but model results are in much better agreement with the experimental date for higher heating rate (54 K/min). It is demonstrated that a constitutive equation can be used to express devolatilization rate for higher heating rates.

Microwave Devulcanization of Ground Tire Rubber and Its Improved Utilization in Natural Rubber Compounds

We devulcanized ground tire rubber (GTR) with microwaves at different temperatures (140–200 °C) and heating rates (2–18 °C/min). We measured the soluble content and the cross-link density of the samples, and then evaluated them by Horikx’s analysis and determined the specific microwave energy during devulcanization and the selectivity parameter of the treatments. We also introduced the K·D number that can be calculated as the product of the selectivity parameter (K) and the relative decrease in the cross-link density (D). The results showed that GTR devulcanized at lower temperatures, selectivity was very high, and the degree of devulcanization was adequate. At higher temperatures (180–200 °C), the degree of devulcanization reached 85%, but the selectivity parameter was low, which indicates severe degradation at this temperature range. At lower temperatures (140–160 °C) and decreasing heating rate, i.e., increasing residence time, the degree of devulcanization showed an increase, but at higher temperatures, the heating rate had no significant effect on the degree of devulcanization. We introduced different devulcanized GTRs (dGTRs) to natural rubber-based mixtures and produced samples with two different mixing methods: conventional mixing and so-called two-step mixing. In the latter one, in the first mixing step, we added vulcanizing agents to the dGTR, and in the second mixing step, we added this mixture to the reference mixture. Two-step mixing helped recover mechanical properties, especially tear strength. Scanning electron microscopy–energy-dispersive spectroscopy and atomic force microscopy showed that microwave devulcanization and the vulcanizing agents mixed with dGTR acted in the cross-section of dGTR.

Effect of Heating on Hot Deformation and Microstructural Evolution of Ti-6Al-4V Titanium Alloy.

This paper presents a systematic study of heating effects on the hot deformation and microstructure of dual-phase titanium alloy Ti-6Al-4V (TC4) under hot forming conditions. Firstly, hot flow behaviors of TC4 were characterized by conducting tensile tests at different heating temperatures ranging from 850 °C to 950 °C and heating rates ranging from 1 to 100 °C/s. Microstructure analysis, including phase and grain size, was carried out under the different heating conditions using SEM and EBSD. The results showed that when the heating temperature was lower than 900 °C, a lower heating rate could promote a larger degree of phase transformation from α to β, thus reducing the flow stress and improving the ductility. When the temperature reached 950 °C, a large heating rate effectively inhibited the grain growth and enhanced the formability. Subsequently, according to the mechanism of phase transformation during heating, a phenomenological phase model was established to predict the evolution of the phase volume fraction at different heating parameters with an error of 5.17%. Finally, a specific resistance heating device incorporated with an air-cooling set-up was designed and manufactured to deform TC4 at different heating parameters to determine its post-form strength. Particularly, the yield strength at the temperature range from 800 °C to 900 °C and the heating rate range from 30 to 100 °C/s were obtained. The results showed that the yield strength generally increased with the increase of heating temperature and the decrease of heating rate, which was believed to be dominated by the phase transformation.

Thermodynamic characteristics of CO2 adsorption on β-cyclodextrin based porous materials: Equilibrium capacity function with four variables

This work focuses on establishing a kind of extended adsorption model equation including four variables relevant to preparation conditions (activation temperature and heating rate) except adsorption situations (adsorption temperature and adsorption pressure). And the equation is used for thermodynamic analysis of CO2 adsorption on a promising cyclodextrin based porous material. Novelty, those isotherms of CO2 adsorption on the porous materials prepared at different activation temperatures and heating rates are experimentally obtained to investigate the effects of activation temperature and heating rate on CO2 adsorption. Then the parameters of the model equation are quantified based on 589 data points from the isotherms by the least squares regression method combined with the steepest descent mode. Research results indicate that high performance for CO2 uptake appears on the porous material prepared at high activation temperature and low heating rate. Differently with the previous studies, the adsorption site energy distribution is found to exhibit an asymmetrical peak and the peak site energy increases with an increase of activation temperature but the decrease of heating rate. Moreover, a series of interesting phenomena of those thermodynamic state parameters via adsorption temperature and pressure are verified based on both extended Slip model and D-R model, which have not been reported before.

Oxidation kinetics of overstoichiometric TiB2 thin films grown by DC magnetron sputtering

We systematically study the oxidation properties of sputter-deposited TiB2.5 coatings up to 700 °C. Oxide-scale thickness dox increases linearly with time ta for 300, 400, 500, and 700 °C, while an oxidation-protective behavior occurs with dox=250∙ta0.2 at 600 °C. Oxide-layer’s structure changes from amorphous to rutile/anatase-TiO2 at temperatures ≥ 500 °C. Abnormally low oxidation rate at 600 °C is attributed to a highly dense columnar TiO2-sublayer growing near oxide/film interface with a top-amorphous thin layer, suppressing oxygen diffusion. A model is proposed to explain the oxide-scale evolution at 600 °C. Decreasing heating rate to 1.0 °C/min plays a noticeable role in the TiB2.5 oxidation.

Evolved Gases and Unified Kinetic Model for Low-temperature Thermal Decomposition of Rice Straw Hydrolysis Residue for Possible Value Addition

Low-temperature thermal decomposition (LTTD) of Rice straw hydrolysis residue (RSHR) was studied using thermogravimetric analysis and Fourier Transform Infrared spectroscopy (TGA-FTIR) at different heating rates. During thermogravimetry, the maximum rate of mass loss of 135% per min was observed at 339 °C ( Tmax ) for heating rate of 50 °C per min. Tmax decreased to 323, 315, and 299 °C with decrease in heating rate to 40, 30, and 20 °C min−1, respectively. LTTD of RSHR yields volatile oxygenated organics – acids, esters, aldehydes, ketones, alcohols and phenols – as revealed by the FTIR spectra of evolved gases. At increased decomposition temperature, carbonyl moieties were less conjugated. The main gaseous products of LTTD were carbon dioxide, carbon monoxide, and methane. Kinetics of LTTD of RSHR was analysed using thermogravimetry results. Activation energy of LTTD followed a Lorentzian distribution with respect to residual mass fraction (RMF). Dependence of LTTD rate on RMF was found to adhere to the truncated Sestak and Berggren model.

Biomass hard carbon of high initial coulombic efficiency for sodium-ion batteries: Preparation and application

Biomass hard carbon anodes have attracted wide attention due to the advantage of low cost and renewability, but the low initial coulombic efficiency (ICE) limits their practical application in sodium-ion batteries (SIBs). In this work, a carbonization method with low heating rate was conducted to prepare biomass hard carbon materials from camphor wood residues and explore the key factors that influence the ICE. As the heating rate decreases, the as-prepared biomass hard carbon with a relatively low amount of defects displays a high ICE of 82.8% by decreasing the initial irreversible capacity loss. Specifically, when the heating rate decreases to 0.25 ℃ min−1, the obtained hard carbon exhibits the optimal electrochemical performance with the initial charge capacity of 324.6 mAh g−1 and excellent cycle stability (90.0% capacity retention after 200 cycles at 50 mA g−1). Besides, matched with Na3V2(PO4)/C cathode, the full cell exhibits a high energy density of 245.3 Wh kg−1 and stable cycling performance. This comprehensive study provides a feasible method and opens new opportunities for biomass hard carbon, and extends the strategy to design the high-performance anode materials for SIBs.

Characteristics of Oil and Gas Produced by In Situ Heating of Shale: A Case Study of the Chang 7 Member, Ordos Basin, China

Shale in the Chang 7 member of the Triassic Yanchang Formation of Ordos Basin is just suitable to shale oil development by in situ heating for its low maturity. In this study, continuous in situ heating simulations at three different heating rates were undertaken to investigate oil and gas characteristics of the Chang 7 shale. Results indicated that the shale has an oil production potential of up to 43–44 kg/t shale when heated to 450 °C. The heating rate had a minor effect on oil yield. The produced oil was light oil with a C8–C10 main peak. Saturated and aromatic hydrocarbons took up a total proportion of 87–90%. The saturated hydrocarbon contents in produced oil decreased with the increasing temperature accompanying aromatic increasing. Total gas yields for the three heating rates after heating to 450 °C were not significantly different, with total yields of 15.68–16.68 m3/t shale. However, yields of different gas components varied with the heating rate. The yield of hydrocarbon gas at a fixed temperature increased with the decreasing heating rate. Our experimental results also indicated that slow heating was favorable to reduce harmful gas formation by an in situ heating method during Chang 7 shale oil development.

Energy absorption performances of silicon carbide particles during microwave heating process

In this study, energy absorption performances of SiC particles during microwave heating process were analyzed, and effects of SiC loading (20, 25, 30, 35, and 40 g), microwave power (300, 350, 400, 450, and 500 W) and reactor volume (50, 100, 150, 200, and 250 mL) were investigated. The results show that when the SiC is heated to 200 °C and loading increases from 20 g to 40 g, average heating rate decreases and then increases in the range of 0.36 ∼ 0.86 °C/s whereas energy absorption efficiency increases and then decreases in the range of 1.49% ∼ 15.57%. When microwave power increases from 300 W to 500 W, average heating rate increases from 0.89 °C/s to 7.08 °C/s whereas energy absorption efficiency increases and then decreases in the range of 4.71% ∼ 37.38%. When reactor volume increases from 50 mL to 250 mL, average heating rate decreases from 3.37 °C/s to 0.65 °C/s whereas energy absorption efficiency increases and then decreases in the range of 5.70% ∼ 35.38%. The maximum energy absorption efficiency of 37.38% was observed at the SiC loading of 30 g, microwave power of 350 W, and reactor volume of 50 mL.

The melting properties of D-α-glucose, D-β-fructose, D-sucrose, D-α-galactose, and D-α-xylose and their solubility in water: A revision

Saccharides are still commonly isolated from biological feedstock by crystallization from aqueous solutions. Precise thermodynamic data on solubility are essential to optimize the downstream crystallization process. Solubility modeling, in turn, requires knowledge of melting properties. In the first part of this work, following our previous work on amino acids and peptides, D-α-glucose, D-β-fructose, D-sucrose, D-α-galactose, and D-α-xylose were investigated with Fast Scanning Calorimetry (FSC) in a wide scanning rate range (2000 K·s−1 to 10000 K·s−1). Using the experimental melting properties of saccharides from FSC allowed successfully modeling aqueous solubility for D-sucrose and D-α-galactose with the equation of state PC-SAFT. This provides cross-validation of the measurement methods to determine accurate experimental melting properties with FSC. Unexpectedly, the experimental FSC melting temperatures, extrapolated to zero scanning rates for thermal lag correction, were higher than results determined with DSC and available literature data. To clarify this inconsistency, FSC measurements towards low scanning rates from 10000 K·s−1 to 1 K·s−1 (D-α-glucose, D-β-fructose, D-sucrose) overlapping with the scanning rates of DSC and literature data were combined. At scanning rates below 1000 K·s−1, the melting properties followed a consistent non-linear trend, observed in both the FSC and the literature data. In order to understand the non-linear decrease of apparent melting temperatures with decreasing heating rate, the endothermic peaks were investigated in terms of isoconversional kinetics. The activation energies in the non-linear dependency region are in the range of 300<{E}_{A}< 600 {text{kJ}}bullet {text{mo}}{text{l}}^{-1}. These values are higher than the enthalpy of sublimation for D-α-glucose, indicating that the non-linear behavior does not have a physical nature but attributes to chemical processes corresponding to the decomposition of molecular compounds within the crystal lattice before melting. The melting properties reported in the literature, commonly determined with conventional methods such as DSC, lead to inaccurate results due to the decomposition of these biomolecules at low heating rates. In addition, the FSC results at lower scanning rates coincide with results from DSC and literature in the overlapping scanning rate range, further validating the accuracy of FSC measurements to determine reliable melting properties of thermally labile biomolecules. The experimental FSC melting properties determined at higher scanning rates are considered as the correct equilibrium melting properties, which are not influenced by any chemical processes. The combination of FSC and PC-SAFT opens the door to model solubility of solid compounds that commonly decompose before melting.

Facile synthesis of novel porous nickel/carbon fibers obtained from cigarette butts for high-frequency microwave absorption

Recently magnetic metals/ carbon composites with porous structures have attracted much investigation for lightweight microwave absorbing materials (MAMs). In this study, a facile synthesis method of carbonizing Ni(NO3)2·6H2O impregnated cigarette butts was designed to manufacture novel porous nickel/carbon (Ni/C) structures. The surface morphology, microstructure, surface area, and magnetic properties of synthesized composites can be adjusted by Ni(NO3)2.6 H2O concentration and heating rate in the hydrothermal process. The surface and bulk structure exhibited that nickel nanoparticles are formed on the porous carbon. The formation of the nickel nanoparticles onto composites improved magnetic characteristics, not only increasing the saturation (16–71 emu/g) but also decreasing coercivity (30–117 Oe). With decreasing heating rate and nickel concentration, the surface area increases to 215.7 m2/g and mesoporous structure, resulting in the multiple reflections and absorption of the incident microwave. The Ni/C composite with 0.5 mol/L nickel concentration and 2 °C/min heating rate with 2.5 mm matching thickness possesses the extraordinary MAMs with minimum reflection loss (RL) of −75.5 dB at 11.5 GHz, 11.0 GHz of effective bandwidth, and 1661.0 GHz.dB/mm of relative RL at very low Ni/C content of 20 wt%. This study displayed a controllable facile protocol for the fabrication of porous Ni/C composites through recycling abundant cigarette butts with lightweight and tunable MAMs.

Effects of adding polystyrene blocks in rectangular containers on radio frequency heating rate and uniformity of watermelon seeds

Non-uniform heating is a main problem for applying radio frequency (RF) treatments to eliminate the seed-borne pathogens in seeds before commercial import/export. In this study, thermal and dielectric properties of watermelon seed coats and embryos with different moisture contents were measured for computer simulation. The simulation model of RF heated watermelon seeds with or without adding a polystyrene block was developed and validated based on experimental results using the commercial COMSOL software. The effect of adding different sizes of polystyrene block on RF heating rate and uniformity of watermelon seeds was also studied by the validated simulation model. The results showed that the difference in heating rate between first and second layers and average temperature of seeds increased from 0.63 to 18.78 °C/min and 40.74 to 58.60 °C with increasing thickness and height of polystyrene block increased from 5 to 30 mm and 4 to 28 mm. The volumetric RF heating uniformity index in seeds decreased with decreasing heating rate difference. Meanwhile, the height of 7.7 mm combined with thickness of 25 mm of the polystyrene block could provide the best RF heating uniformity for watermelon seeds. These findings from the established new methods to improve the heating uniformity could be used to develop an effective RF treatment protocol for controlling the seed-borne pathogens of watermelon seeds without reducing their quality.

Thermal shock response behaviour of carbon fibre reinforced silicon carbide matrix composites prepared by chemical vapour infiltration at different heating rates

The present work investigated the effects of thermal cycles in air on the tensile properties of a two-dimensional carbon fibre reinforced silicon carbide composite (2D C/SiC) prepared by chemical vapour infiltration at different heating rates. The composite was exposed to different cycles of thermal shock between 20 °C and 1300 °C in air. The damage mechanisms were investigated by AE online monitoring and fractured morphology offline analysis. The tensile strength of 2D-C/SiC decreases with increasing thermal cycles. However, the modulus only decrease within 40 cycles. Due to oxidation, with the decrease in heating rate, the residual properties of the material decrease more obviously. Meanwhile, the results of AE online monitoring and fracture analysis show that the matrix damage is more serious at higher heating rate and that more delamination occours in tensile fractures. The above results indicate that for the thermal shock of 2D C/SiC composites in air, oxidative damage plays a key role in the residual properties.

Non-monotonic dose dependence of thermoluminescence in spatially correlated systems

TL dose dependences were simulated following the semi-localized transitions (SLT) model and the model with cluster defects which contain TL-active electron traps, luminescence centers and deep hole traps. Monte-Carlo method was used to calculate cluster occupancy at the irradiation and relaxation stages. At the heating stage, TL yield was calculated with Monte-Carlo method and with the proposed analytical approach. This approach expressed TL yield via cluster occupancy after relaxation stage. The results showed that non-monotonic dose dependence emerges in both models when the excited level of TL-active trap is deep enough. The reported effect was demonstrated to be directly related to intracluster non-radiative recombination of electron at the excited level of the trap and hole in the luminescence center. The intracluster competition between hole centers makes dose response less non-monotonic. When the heating rate decreases, TL yield at high doses drops and TL dose dependence becomes more non-monotonic.