Mass Transfer Parameters Research Articles

Modeling of hydrogen permeation behavior through tungsten deposition layer growing on nickel substrate by hydrogen plasma sputtering

Tungsten (W) is a candidate material of plasma-facing walls for fusion reactors. When a W redeposition layer is formed on the plasma-facing wall by sputtering, the behavior of tritium in the in-vessel components is possible to be affected. Therefore, it is necessary to understand the tritium permeation behavior through the W deposition layer as well as W bulk. In the previous study, the hydrogen permeating through the W deposition layer growing on a nickel substrate was measured experimentally. In this work, the TMAP simulation code was used to analyze the time variation in the measured hydrogen permeation flux and mass transfer parameters were obtained. The results suggested that the permeation flux initially increased with increasing temperature but decreased when the thickness of the W deposition layer was greater than the hydrogen injection range. The obtained recombination coefficient was several orders of magnitude larger than that reported for W bulk. The obtained values were used to predict hydrogen isotope permeation through the plasma-facing wall in the DEMO reactor. The results suggested that the W deposition formed on the plasma-facing wall of the DEMO reactor significantly reduces tritium permeation rate.

Mass Transfer, Energy-Exergy Analysis, and Mathematical Modeling of Chili Pepper during Drying

There are no literature data on the effects of air velocity and relative humidity on moisture diffusivity, mass transfer coefficient, and energy-exergy analysis of chili pepper during cabinet-tray hot-air drying. This study tends to address this gap by presenting comprehensive drying kinetic, energy, and exergy analyses of a cabinet-tray hot-air drying for red chili pepper. Drying was conducted at varying levels of air temperature (40-70 oC), air velocity (0.5-2.0 m/s), and relative humidity (60-75%). The effect of drying conditions on drying time, drying coefficient, lag factor, drying efficiency, moisture ratio, effective moisture diffusivity, mass transfer coefficient, total energy consumption (TEC), specific energy consumption (SEC), energy utilization ratio (EUR), heat loss, energy efficiency, exergy loss, exergy efficiency, exergetic improvement potential (EIP), and exergy sustainability index (ESI)) was evaluated. Five different mass transfer models (Dincer-Dost, Bi-Di, Bi-S, Bi-G, and Bi-Re) were applied to determine the mass transfer parameters. A new drying mathematical model was developed for the prediction of drying kinetic, energy, and exergy parameters. Effective moisture diffusivity values of 1.58×10–8 - 5.10×10–8 m2/s and mass transfer coefficient values of 0.053×10–6 - 8.79×10–6 m/s over the drying conditions range were respectively obtained. The TEC, SEC, and EUR achieved over the range of drying conditions in the course of drying were in the range of 43.56-77.36 MJ, 49.0-87.02 MJ/kg, and 0.035-0.325, respectively. Heat loss and exergy loss varied from 0.16 to 2.39 MJ and from 0.026 to 0.622 kW, respectively. Drying, energy, and exergetic efficiency values obtained varied in the range of 2.80-8.25%, 2.69-7.91%, and 73-94.5%, respectively. EIP and the ESI values varied from 0.0068-0.114 kW and 3.70-18.18, respectively. The developed multivariate linear regression model provided an innovative model to predict drying kinetic, energy, and exergy parameters.

Modeling of hibiscus anthocyanins transport to apple tissue during ultrasound‐assisted vacuum impregnation

This study reports the mathematical modeling of hibiscus anthocyanins transport to apple tissues under various vacuum impregnation conditions (Control, VI 100, 250, and 500 mbar; ultrasound-assisted VI 100, 250, and 500 mbar). Azuara, Peleg, Diffusive, Z and L, and Weibull mathematical models were used to describe the water gain and anthocyanin gain's mass transfer kinetics. Azuara model successfully described the kinetic parameters of mass transfer during impregnation treatment. The equilibrium anthocyanin and water gain values predicted by the Azuara model varied between 38.4001–58.2536 and 24.0863–33.0245 mg/kg, respectively. Anthocyanin and water diffusion coefficients of the samples ranged between 0.406 × 10−9, −1.68 × 10−9, 0.117 × 10−9, and 0.715 × 10−9 m2/s, respectively. Ultrasound treatment increased moisture and anthocyanin gain during vacuum impregnation. At the end of the 30 min process, the highest anthocyanin content was determined as 38.85 mg/kg in samples treated ultrasound-assisted vacuum at 100 mbar. Novelty impact statement The studies on the modeling of bioactive components transport in the vacuum impregnation are limited although an increase is observed in the studies dealing with the enrichment of fruit and vegetable tissue with bioactive components. In the present study, Azuara model successfully described the kinetic parameters of mass transfer during impregnation treatment. In addition, ultrasound treatment increased anthocyanin content in the apple cubes during vacuum impregnation.

Uncertainty and sensitivity analysis of boundary conditions during water droplet phase change regimes

This paper presents the heat and mass transfer model of a liquid droplet in the consistently changing condensation, transit and equilibrium evaporation regimes, and iterative scheme of numerical simulation of the instantaneous temperature of a semi-transparent droplet in the case of complex radiative-convective heating. The whole cycle of the phase transition regimes of medium and large water droplets flowing in the flue gas was modeled, taking into account the application of water spraying into the flue gas of a biofuel furnace. Simulation results expressed as thermal, energy and phase transformation parameters of water droplets are analyzed in the universal Fourier time scale. The factors defining the change of heat transfer regime of a water droplet are termed as the suppression of droplet slipping in flue gas flow at initial phase transformation stage, and the decrease of radiation absorption at the final stage. Particular attention is paid to the evaluation of the influence of parameters defining the interaction of complex transfer processes on the droplet's phase transformations performing the sensitivity analysis of the heat and mass transfer parameters for the “hypothetical” droplet case (the diameter and the slipping velocity in to gas did not change). It is substantiated, that the main parameters defining the sensitivity of water droplets equilibrium evaporation temperature are flue gas humidity, droplets dispersity, flue gas temperature and droplets slipping velocity.The performed statistical uncertainty and sensitivity analysis showed that the uncertainty of heat and mass transfer parameters describing the phase transformations of a water droplet until equilibrium evaporation regime is affected mostly by droplet dispersity, slipping velocity, flue gas temperature and pressure. The size of droplets and their slip velocity in the flue gas flow were identified as very important parameters for the interaction of complex heat and mass transfer processes of a sprayed water. The main uncertainties were defined at the transition from condensing to transit evaporation regime, and it was defined that with a confidence interval of at least 95 % and accepting a tolerance limit with a probability of at least 95 %, the transit evaporation regime starts at the range Fo ≈ (0.02–0.1). The droplet surface temperature, i.e. parameter determining the droplet phase transformations and its dynamics, could be assessed with a mean error of ±10 %, accepting 95 % probability with 95 % confidence level.

Estimation of the Filled Two-Component Cold Curing Polymer System Performance as a Coating for Protecting Concrete Surfaces from the Aggressive Environment Exposure

A filled two-component polymer cold curingsystem (FTCPS) is discussed in the article. To assess its corrosion resistance and durability, the indexes of reagent resistance were determined in accordance with the sorption method. What is optimal, since this value depends on the parameters of mass transfer, the intensity of the reaction, the size of the product, the duration of exposure to aggressive media and other factors. As aggressive media were taken: water, 5% hydrochloric acid solution, 25% aqueous ammonia solution, 10% sodium hydroxide solution, saturated sodium chloride solution. The exposure time was 360 days. Reagent resistance evaluation of the developed FTCPScompositionswas carried out on the basis of guidelines for determining the anticorrosive properties of protective coatings of concrete and laboratory test methods. Changes in the mass of the samples and their reagent resistance as a result of exposure to chemical reagents simulating an aggressive environment during operation were evaluated. The change in the index of reagent resistance in laboratory conditions did not go beyond the value of 0.80, which makes it possible to ensure reliable protection and operation of polymer-coated products under conditions of exposure to these aggressive environments.

Finite element Soret Dufour effects on an unsteady MHD heat and mass transfer flow past an accelerated inclined vertical plate

AbstractThe present study is focused on the Soret and Dufour effects on magnetohydrodynamics unsteady fluid flow over an accelerated inclined vertical plate with thermal radiation and heat source. Solution of the nondimensional governing differential equations are worked out by the efficient Galerkin finite element method. The influence of several relevant flow parameters on velocity, temperature, and concentration distributions, as well as the numerical results, are studied and graphically displayed. The nondimensional skin friction and the rate of heat and mass transfer parameters are presented in the Tables 1‐3 below. Raising the Soret number results in growing concentrations, but the converse is true for the Schmidt number. Skin friction reduces when Soret and Dufour numbers increase. The present simulations apply to the processing of magnetic materials in the chemical and metallurgical industries.

Identification of heat and mass transfer parameters in timber drying based on hybrid optimisation techniques

Identification of heat and mass transfer parameters in timber drying based on hybrid optimisation techniques

A Review on Gas-Liquid Mass Transfer Coefficients in Packed-Bed Columns

This review provides a thorough analysis of the most famous mass transfer models for random and structured packed-bed columns used in absorption/stripping and distillation processes, providing a detailed description of the equations to calculate the mass transfer parameters, i.e., gas-side coefficient per unit surface ky [kmol·m−2·s−1], liquid-side coefficient per unit surface kx [kmol·m−2·s−1], interfacial packing area ae [m2·m−3], which constitute the ingredients to assess the mass transfer rate of packed-bed columns. The models have been reported in the original form provided by the authors together with the geometric and model fitting parameters published in several papers to allow their adaptation to packings different from those covered in the original papers. Although the work is focused on a collection of carefully described and ready-to-use equations, we have tried to underline the criticalities behind these models, which mostly rely on the assessment of fluid-dynamics parameters such as liquid film thickness, liquid hold-up and interfacial area, or the real liquid paths or any mal-distributions flow. To this end, the paper reviewed novel experimental and simulation approaches aimed to better describe the gas-liquid multiphase flow dynamics in packed-bed column, e.g., by using optical technologies (tomography) or CFD simulations. While the results of these studies may not be easily extended to full-scale columns, the improved estimation of the main fluid-dynamic parameters will provide a more accurate modelling correlation of liquid-gas mass transfer phenomena in packed columns.

Magnetohydrodynamic Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Ferrofluids

In this research, the problem of magnetohydrodynamic flow and heat transfer over an exponentially stretching/shrinking sheet in ferrofluids is presented. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying suitable similarity transformations. These equations are then solved numerically using the shooting method for some pertinent parameters. For this research, the water-based ferrofluid is considered with three types of ferroparticles: magnetite, cobalt ferrite, and manganese-zinc ferrite. The numerical solutions on the skin friction coefficient, Nusselt number, velocity and temperature profiles influenced by the magnetic parameter, wall mass transfer parameter, stretching/shrinking parameter, and volume fraction of solid ferroparticle are graphically displayed and discussed in more details. The existences of dual solutions are noticeable for the stretching/shrinking case in a specific range of limit. For the first solution, an increasing number in magnetic and suction will also give an increment of skin friction coefficient and Nusselt number over stretching/shrinking sheet. For the skin friction coefficient only, it is showed a decreasing pattern after the intersection. Besides, the presence of ferroparticles in the fluids causes a high number of the fluid’s thermal conductivity and heat transfer rate.

Separation of multicomponent aromatic/aliphatic mixtures by simulated moving bed adsorption: Modeling and experiments

AbstractSimulated moving bed (SMB) adsorption has potential for efficient separation of many valuable chemical mixtures, but considerably less attention has been devoted to multicomponent feeds relative to binary mixtures. We take a rigorous experimental and modeling approach to study multicomponent separation of aromatics and aliphatics with a mesoporous silica adsorbent, which is relevant in many petrochemical applications such as separation of reformate and distillate streams. Our approach involves refining multicomponent adsorption, mass transfer, and SMB process parameters based upon detailed experimental inputs, with progressive addition of components. We develop a robust model that quantitatively predicts the influence of key operating parameters such as stream flow rates, desorbent/feed ratio, and switch time on the separation results and concentration profiles. The model is validated as a function of feed complexity by SMB experiments and column concentration profile measurements in a 16‐column mini‐plant. Furthermore, conditions for clear separation of each mixture are developed.

Seasonal shifts in surface water-groundwater connections in a ferricrete-impacted stream estimated from electrical resistivity

The efficacy of the hyporheic zone (HZ) — where surface water and groundwater mix — for processing nutrients or the uptake of metals is dependent on the streambed hydraulic conductivity and stream discharge, among other characteristics. Here, we have explored electrical resistivity tomography (ERT) of hyporheic exchange in Cement Creek near Silverton, Colorado, which is affected by ferricrete precipitation. To quantify flows through the HZ, we have conducted 4 h salt injection tracer tests and collected time-lapse ERT of the streambed and banks of Cement Creek at high and low flow. We have installed piezometers to conduct slug tests, which suggest a low-permeability zone at 44 cm depth likely composed of ferricrete that cemented the cobbles together. Based on the ERT, the tracer released into the stream is constrained within the shallow streambed with little subsurface flow through the banks. The tracer is detected in the HZ for a longer time at high flow compared to low flow, suggesting that more flow paths were available to connect the stream to the HZ. The tracer is confined above the ferricrete layer during the high- and low-flow tests. Mass transfer and storage area parameters are calculated from combined analysis of apparent bulk conductivity derived from ERT and numerical modeling of the tracer breakthrough curves. The hyporheic storage area estimated at low discharge ([Formula: see text]) is smaller than that at high discharge ([Formula: see text]) and residence times are 2.7 h at low discharge and 4.1 h at high discharge. During high discharge, in-stream breakthrough curves display slower breakthrough and longer tails, which is consistent with the time-lapse electrical inversions and 1D transport with inflow and storage modeling. Our findings indicate that ferricrete reduces the hydraulic conductivity of the streambed and limits the areal extent of the HZ, which may lower the potential for pollutant attenuation from the metal-rich waters of Cement Creek.

Fixed-bed adsorption of bisphenol A onto organoclay: Characterisation, mathematical modelling and theoretical calculation of DFT-based chemical descriptors

Bisphenol A (BPA) is a noteworthy and ubiquitous chemical of concern. Up to this day, several methods of water remediation have already been tested, however, few studies have addressed the fixed-bed adsorption of this contaminant. In this regard, this work aimed to evaluate the continuous adsorption of BPA using an organoclay (Spectrogel® type-C) as an adsorbent. The material passed through a series of characterisation techniques to elucidate the impact of the contaminant uptake onto the organoclay. The effect of the operation conditions on the adsorption behaviour was evaluated through breakthrough curves and the calculation of mass transfer and efficiency parameters The system conducted at 0.6 mLmin−1 and 0.2 mmolL−1 obtained the highest removal (95%) until breakthrough point (19.29 h), as well as greater breakthrough and exhaustion adsorption capacities (0.0424 and 0.2151 mmolg−1, respectively). The breakthrough curves were correlated by five distinctive models and the modified dose response model showed the finest fitting to the data (R2 >0.97). Furthermore, the regeneration potential of the spent adsorbent was investigated. It was observed that NaOH solution was a satisfactory eluent. Moreover, density functional theory (DFT) calculations were studied to give further insights regarding BPA adsorption.

The Peculiarities of Mass Transfer in the Surface Layer of Materials under Extreme Heating

Possible causes of mass transfer acceleration of carbon atoms and alloying elements in the surface layers of steels and alloys under extreme heating, under pulsing laser irradiation in particular, are considered. The research shows that the anomaly accelerated mass transfer, including diffusion in particular, in steels and alloys under fast laser heating has a cooperative character and is a result of a simultaneous action of several processes of different physics. It is proved that the carbon atoms mass transfer parameters and alloying elements depend on the scale and the level of emerging tension, relaxation of which goes along with a local plastic deformation, and occurrence of increased number of linear defects in crystal structure.

Diffusion and kinetic modeling of water absorption process during soaking and cooking of chickpea

AbstractThe chickpea soaking and cooking processes were empirically studied in terms of water absorption. The effective moisture diffusivity (Deff) and the convective mass transfer coefficient (K) were determined by developing a mathematical model in spherical coordinates. According to the evaluation of mass transfer parameters, the values of Deff and K ranged from 0.91 × 10−12 to 1.49 × 10−10 m2/s, and 2.02 × 10−10 to 7.25 × 10−10 m/s, respectively. Also, the kinetic behavior of chickpea during soaking and cooking was successfully modeled by the commonly used predictive models such as Peleg, Page, two‐term, and Vega–Lemus. The statistical parameters including the coefficient of determination (R2) and sum of square error (SSE) were applied for comparison of mathematical models. The two‐term model was found to be the best predictive equation for describing the soaking behavior of chickpea. In the case of cooking, a proposed model in this study was introduced as the best equation in predicting the moisture content of chickpea against time. The approach that was applied in this work can support the development of diffusion and kinetic modeling in different types of legumes during soaking, cooking, and the other processes related to moisture absorption or removal.

Buoyancy effect on the chemically reactive flow of Cross nanofluid over a shrinking surface: Dual solution

Stagnation point flow of steady two dimensional Cross fluid by a shrinking surface is investigated with the influence of nanoparticles. With the help of Fourier's and Fick's laws, the heat and mass transport mechanisms are performed. The chemical reaction is also considered here. For the solution of the problem, the numerical technique is employed to explore the multiple solutions of the problem. Dual solutions exist in the range χc < χ and Sc < S in which χc and Sc are the critical points. The obtained numerical results are discussed for skin-friction, heat and mass transfers, velocity profiles, respectively. Results reveal that, the velocity profile enhances in the upper branch solution with the increment in buoyancy ratio parameter. Further, it is found that the skin friction coefficient increases in the upper branch solution as mass transfer parameter rises while reduces in the lower branch. Further, in both branches, the rate of heat transfer enhances by taking higher estimation of Prandtl number.

Experimental Comfort Evaluation of Baby Diapers In Terms of Liquid Accumulation, Moisture Management and Heat Transfer via Non Destructive Testing

The purpose of this paper is to provide an applied and objective analysis into heat transfer and mass transfer parameters such as relative water vapour permeability, thermal conductivity and thermal absorptivity as well as liquid accumulation of baby diapers which have critical importance on skin health using non-destructive Alambeta and Permetest instruments. SEM investigation was also carried out for characterization of breathable film layer of the diaper assembly. According to the water vapour transmission assessment, it was found that a few hours later, the composite diaper assembly becomes almost zero vapour permeable which results in discomfort and a poor breathability in baby diaper. It was also found that the liquid accumulation in diaper has increased in the course of time. The thickness of the diapers had an important effect on thermal parameters however production type of nonwoven top sheet and back sheet layers had a dramatic effect on these parameters.

Evaluating the heat and mass transfer effective coefficients during the convective drying process of paddy (Oryza sativa L.)

AbstractThis work investigates important heat and mass transfer parameters of a variety of paddy named Fajr, during a thin layer convective drying. The experiments on drying are conducted at air temperatures in the domain of 30–80°C with air velocities between 0.54 and 3.27 m s−1. Mathematical equations are developed to adjust the experimental data obtained for the thin layer drying. The drying results show that the Henderson and Pabis' model satisfactorily fit all the experimental data for the convective drying behavior of paddy. The effective diffusivity of moisture transfer, calculated by the Fick's second law of diffusion, varies from 1.109 × 10−11 to 5.858 × 10−10 m2 s−1 and the highest values of the Dincer, Biot, Reynolds, and Nusselt numbers obtained are 2.383 × 105; 0.2026; 1.833 × 107; and 8,434, respectively. The obtained results demonstrate that the coefficient of mass transfer (hm) for paddy lies between 5.118 × 10−8 and 4.807 × 10−6 m s−1, while the heat transfer coefficient (hc) ranges from 811 to 2,474 W m−2 K−1. Furthermore, the values of the energies of activation obtained for moisture diffusion (Ed) and convective mass transfer (Ec) are in the range of 50.538–61.825 kJ mol−1 and 72.325–87.386 kJ mol−1, respectively. Therefore, knowledge regarding to the determination process of heat and mass transfer characteristics can help to distinguish the suitable operating conditions for saving the maximum value of energy.Practical ApplicationsSome grains have a short shelf life that limits their commercialization as fresh products and increase postharvest losses. Drying is an interesting alternative to the development of new products of grains like paddy with added value. This research work involved the estimation of heat and mass transfer properties during convective drying by using two calculation methodologies, allowing estimating the diffusivity and the mass and heat transfer coefficients for paddy. Also, the activation energy for moisture diffusion and for convective mass transfer was determined, assuming that the temperature dependence of the diffusion coefficient and the mass transfer coefficient follows an Arrhenius type relationship. Therefore, also the study presents a simple method to greatly enhance the shelf life of wet paddy by convective drying and it can be applied for the better preservation of this product.

Development of a Sensitivity Analysis method to highlight key parameters of a dry Anaerobic Digestion reactor model

Global sensitivity analysis enables to identify model parameters that have the most significant impact on model outputs and therefore require an estimation effort. This work demonstrates the reliability of a global sensitivity analysis methodology based on Definitive Screening Design and multiple linear regression analysis that requires a low number of runs. The method is applied to a simplified anaerobic digestion model. The model is firstly used to simulate a case study of a thermophilic dry anaerobic digestion of a potential agricultural waste. Then, the influence of the kinetic and mass transfer parameters of the model on the biogas flowrate, the percentage of methane in the biogas and the pH are estimated and discussed. The sensitivity analysis reveals that the slow hydrolysis constant and the upper pH inhibition limit of the hydrolytic biomass are decisive in correctly describing the biogas flowrate. The methane percentage in the biogas slightly varies with kinetic parameters, between 53 % and 55 %. Moreover, the mass transfer coefficient has significant impact on the pH through CO2 desorption. The method simplicity and reliability make its application easy to any type of model.

Hydrodynamic and mass transfer parameters for CO2 absorption into amine solutions and its blend with nano heavy metal oxides using a bubble column

ABSTRACT In this work, hydrodynamic and mass transfer of CO2 absorption into metal oxide nanofluid includes TiO2, ZnO, and ZrO2 nanoparticles at Piperazine (Pz) solution in the bubble column was studied. The novel rigorous correlations were extended based on the variable parameters for the calculation of gas holdup, enhancement factor, and mass transfer coefficients in the reactive absorption processes using the π-Buckingham method. The correlations were constructed based on dimensionless numbers, including nanoparticle loading, film parameter, CO2 partial pressure ratio to the total pressure, the film thickness of phases, CO2 loading, and ratio of diffusion coefficients of CO2 in the gas and liquid phases. Experimental data were used to calculate the correlations, consisting of Pz concentration, CO2 partial pressure, nanoparticle loading, and stirrer speed in the range of 0.1–0.5 mol/l, 16.0–35.2 kPa, 0.0–0.1 wt%, and 0–300 rpm, respectively. The film parameter was applied to exert the influence of chemical reactions on the performance of absorption. The mean squared error (RMSEP), the average absolute error (%AARD), and the coefficient of correlation of the results (R2 ) for the correlations were in the range 0.021–2.604, 3.78–18.14, and 0.861–0.980, respectively, which represents the excellent accuracy of the proposed correlation.

Ultrasound-assisted osmotic dehydration of litchi: effect of pretreatment on mass transfer and quality attributes during frozen storage

Litchi (Litchi chinensis Sonn.), fruits being the perishable and high amount of moisture content, are very susceptible to fruit deterioration and reduced shelf life. A novel method of ultrasound-assisted osmotic dehydration can improve fruit quality by increasing mass transfer rate and maintaining texture characteristics. Therefore, this study aimed to investigate the effect of ultrasound-assisted osmotic dehydration on the mass transfer parameters, physicochemical and microbiological qualities of litchi fruits during frozen periods. For this purpose, litchi fruits were subjected to ultrasound-assisted osmotic dehydration as a pretreatment prior to the freezing step. The pretreatment consisted of three processing conditions: the use of osmotic dehydration at 50% (w/w) of sucrose (OD); ultrasound in an osmotic solution for 10 min before osmotic dehydration (US10 + OD); and ultrasound in an osmotic solution for 15 min before osmotic dehydration (US15 + OD). All samples were frozen and stored at − 18 °C. The obtained results indicated that ultrasound pretreatment effectively increases water loss (28.73 ± 3.25%) and solid gain (45.44 ± 6.85%) levels of litchi fruit. During the frozen storage for 90 days, the use of ultrasound, remarkably, US10 + OD treatment reduced the moisture content (76.46 ± 1.38%), drip loss (15.93 ± 1.01%), and microbial load (2.58 ± 0.06 log CFU/g) of the frozen litchi while increasing the firmness (1.46 ± 0.24 N), and a total soluble solid (17.50 ± 0.87 oBrix) amount of the samples in comparison to their controls (p < 0.05). Therefore, these results demonstrated that ultrasound-assisted osmotic dehydration could significantly improve the quality of litchi fruit in freezing and thawing processes.