Continuous Freeze Research Articles

Automated particle inspection of continuously freeze-dried products using computer vision

The pharmaceutical industry is progressing towards more continuous manufacturing techniques. To dry biopharmaceuticals, continuous freeze drying has several advantages on manufacturing and process analytical control compared to batch freeze-drying, including better visual inspection potential. Visual inspection of every freeze-dried product is a key quality assessment after the lyophilization process to ensure that freeze-dried products are free from foreign particles and defects. This quality assessment is labor-intensive for operators who need to assess thousands of samples for an extensive amount of time leading to certain drawbacks. Applying Artificial Intelligence, specifically computer vision, on high-resolution images from every freeze-dried product can quantitatively and qualitatively outperform human visual inspection. For this study, continuously freeze-dried samples were prepared based on a real-world pharmaceutical product using manually induced particles of different sizes and subsequently imaged using a tailor-made setup to develop an image dataset (with particle sizes from 50μm to 1 mm) used to train multiple object detection models. You Only Look Once version 7 (YOLOv7) outperforms human inspection by a large margin, obtaining particle detection precision of up to 88.9% while controlling the recall at 81.2%, thus detecting most of the object present in the images, with an inference time of less than 1 s per vial.

Freezing and thawing characteristics of seasonally frozen ground across China

Observations from 1,047 meteorological stations from September 1, 2006 to August 31, 2015 revealed regional differences in the freezing and thawing processes of seasonally frozen ground (SFG) across China. SFG generally undergoes a one-way freezing process (i.e., top-down), and the stations with a large freeze depth generally experienced long freeze durations. During the thawing process, soil is generally characterized by two-way thawing (i.e., top-down and bottom-up) in the region north of 35′N, especially north of 30′N (except in northeastern China). The onset of thawing from the bottom occurs earlier than that from the top at most stations in the two-way thawing region. The stations exhibiting one-way thawing (i.e., bottom-up) were mainly located on the southern edge of eastern China (east of 110°E) and in southern part of Xinjiang and southeast part of the Qinghai–Tibet Plateau. The freezing process lasts several days to more than four months longer than the soil thawing process, and this difference tends to be larger in high-latitude and high-altitude regions. All of the sites experienced a discontinuous freeze–thaw process, the station-average duration of which was less than a quarter of that of the continuous freeze–thaw process. Strong associations of soil freeze depth with air temperature (as characterized by the air freezing index and air thawing index) implied a dominant influence of air temperature on the soil freeze–thaw process. During the freezing process, this relationship was partially modulated by snow cover in snowy regions, such as northeast China, northwest China, and the eastern Tibetan Plateau. This paper provides the first overview of regional differences in the freezing and thawing processes of SFG over China, and the findings improve our understanding of the soil freeze–thaw process and provide important information to support research into regional landscapes, ecosystems, and hydrological processes.

Can a Hand-Held 3D Scanner Capture Temperature-Induced Strain of Mortar Samples? Comparison between Experimental Measurements and Numerical Simulations

The expected lifespan of cement-based materials, particularly concrete, is at least 50 years. Changes in the pore structure of the material need to be considered due to external influences and associated transport processes. The expansion behaviour of concrete and mortar during freeze–thaw attacks, combined with de-icing salt agents, is crucial for both internal and external damage. It is essential to determine and simulate the expansion behaviour of these materials in the laboratory, as well as detect the slow, long-term expansion in real structures. This study measures the expansion of mortar samples during freeze–thaw loading using a high-resolution hand-held 3D laser scanner. The specimens are prepared with fully or partially saturated pore structures through water storage or drying. During freeze–thaw experiments, the specimens are exposed to pure water or a 3% sodium chloride solution (NaCl). Results show contraction during freezing and subsequent expansion during thawing. Both test solutions exhibit similar expansion behaviour, with differences primarily due to saturation levels. Further investigations are required to explore the changing expansion behaviour caused by increasing microcracking resulting from continuous freeze–thaw cycles. A numerical analysis using a 3D coupled hygro-thermo-mechanical (HTM) model is conducted to examine the freeze–thaw behaviour of the mortar. The model accurately represents the freezing deformation during the freeze–thaw cycle.

Scaling up continuous eutectic freeze crystallization of lactose from whey permeate: A pilot plant study at sub-zero temperatures

Eutectic freeze crystallization is explored as an alternative to the state-of-the-art evaporation process for the recovery of lactose from whey permeate. At the so-called eutectic freezing point, both water (the solvent) and lactose (the solute) crystallize and can be removed continuously while continuously feeding whey permeate. This continuous process is demonstrated on a pilot scale at sub-zero temperatures. In the first instance, only freeze concentration of whey permeate took place at −4 °C. It was possible to reach a lactose concentration of 30 wt% and hardly any nucleation was observed. The resulting ice had high purity, with a lactose concentration of ±2 wt%. Next, the eutectic phase was reached, and lactose and ice crystallized simultaneously and were continuously removed from the system, the resulting crystals had parallelogram morphology with an average size of 10 µm. Ice was recovered at a rate of 60 kg/h and lactose was recovered at a rate of 16 kg/h, yielding over 80% of the feed lactose. A conceptional design was proposed for an improved yield and reduction of energy. Yields of at least 80% and up till 95% could be achieved. Compared to the state-of-the-art mechanical vapor recompression (MVR), EFC is 80% more energy efficient.

Intertidal mussels survive icy Canadian winters

For many biologists, the intertidal zone is a captivating place. At low tide, seawater collects in depressions and crevasses along rocky shorelines, leaving behind tidepools teeming with life. Tidepools are often packed wall-to-wall with anemones, barnacles and snails, among other intriguing marine taxa trying to stay wet long after the tide recedes. However, not all intertidal residents are fortunate enough to secure a tidepool refuge during low tide, which is particularly problematic in temperate regions that experience bitter, cold winters. When intertidal animals are immersed in seawater, they are protected from sub-zero air temperatures. Without a tide pool refuge, however, air-exposed creatures can freeze when the tide goes out, thawing only upon immersion when the tide returns. Remarkably, many intertidal residents can survive the formation of ice crystals in their body, but how do they tolerate repeated freeze-thaw cycles? In a fascinating new study led by Lauren Gill at the University of British Columbia, a team of researchers discovered how bay mussels (Mytilus trossulus) survive repeated freezing and thawing during harsh Canadian winters.Gill and her team first collected mussels from the rugged coastline in Vancouver, Canada, to investigate their survival rate under different freezing regimes: one continuous freeze lasting 8 h, two separate freezes lasting 4 h each or four separate freezes lasting 2 h each. The researchers induced freezing in the mussels by exposing them to air at –8°C. For mussels that underwent multiple freezing bouts, the team provided a 24 h recovery in 7°C seawater between each freeze to mimic the relief that they would experience with natural tides. The researchers predicted that repeated freezing and thawing would increase mussel mortality. However, much to their surprise, survival was almost 100% in mussels frozen four separate times (4×2 h) and a mere 25% in mussels frozen only once (1×8 h).At this point, the researchers were keen to uncover the physiological mechanisms that led to such high survival in their repeatedly frozen mussels. They suspected that two different proteins could be playing an important role. The first, heat-shock protein 70 (HSP70), is known to help the body deal with extreme temperature stress. Extremely hot and cold temperatures can denature (i.e. damage) proteins in the body, but HSP70 can help protect proteins from denaturation. Sure enough, the team discovered that in repeatedly frozen mussels, the expression of HSP70 increased considerably after freezing, thereby providing mussels with protection against subsequent freezing events. The second protein is ubiquitin, which tracks down any damaged proteins in the body and flags them for disposal. Interestingly, the researchers found that in repeatedly frozen mussels, the number of proteins flagged by ubiquitin increased after freezing, indicating that the mussels were working hard to repair any molecular damage caused by freezing.Taken together, Gill and her team found that mussels have a higher survival rate when they experience repeated freeze-thaw cycles compared with a single lengthy freeze of the same total duration. Furthermore, periods of thawing are critical for surviving sub-zero temperatures because they offer mussels an opportunity to make important proteins that protect against, and repair, molecular damage caused by freezing. So, the next time you’re out exploring the captivating tidepools of the intertidal, be sure to remember the creatures outside of these pools and the great lengths that they must go to in order to survive.

An LC-MS/MS Method for Analysis of Vitamin D Metabolites and C3 Epimers in Mice Serum: Oral Supplementation Compared to UV Irradiation.

Introduction: The most common forms of vitamin D in human and mouse serum are vitamin D3 and vitamin D2 and their metabolites. The aim of this study is to determine whether diet and sunlight directly affect the circulating concentrations of vitamin D metabolites in a mouse model. We investigated the serum concentrations of eight vitamin D metabolites—vitamin D (vitamin D3 + vitamin D2), 25OHD (25OHD3 + 25OHD2), 1α25(OH)2D (1α25(OH)2D2, and 1α25(OH)2D3)—including their epimer, 3-epi-25OHD (3-epi-25OHD3 and 3-epi-25OHD2), and a bile acid precursor 7alpha-hydroxy-4-cholesten-3-one (7αC4), which is known to cause interference in liquid chromatography-tandem mass spectrometry (LC-MS/MS) analysis. Method: The LC-MS/MS method was validated according to FDA-US guidelines. The validated method was used for the analysis of mouse serum samples. Forty blood samples from mice were collected and divided into three groups. The first group, the DDD mice, were fed a vitamin D-deficient diet (25 IU VD3/kg of diet) and kept in the dark; the second group, the SDD mice, were maintained on a standard-vitamin D diet (1000 IU VD3) and kept in the dark; and the third group, SDL, were fed a standard-vitamin D diet (1000 IU VD3) but kept on a normal light/dark cycle. LC-MS/MS was used for the efficient separation and quantitation of all the analytes. Results: The validated method showed good linearity and specificity. The intraday and interday precision were both <16%, and the accuracy across the assay range was within 100 ± 15%. The recoveries ranged between 75 and 95%. The stability results showed that vitamin D metabolites are not very stable when exposed to continuous freeze–thaw cycles; the variations in concentrations of vitamin D metabolites ranged between 15 and 60%. The overlapping peaks of vitamin D, its epimers, and its isobar (7αC4) were resolved using chromatographic separation. There were significant differences in the concentrations of all metabolites of vitamin D between the DDD and SDL mice. Between the groups SDD (control) and SDL, a significant difference in the concentrations of 3-epi-25OHD was noted, where C3 epimer was about 30% higher in SDL group while no significant differences were noted in the concentrations of vitamin D, 25OHD, 1α25(OH)2D, and 7αC4 between SDD and SDL group. Conclusions: A validated method, combined with a simple extraction technique, for the sensitive LC-MS/MS determination of vitamin D metabolites is described here. The method can eliminate the interferences in LC-MS/MS analysis caused by the overlapping epimer and isobar due to them having the same molecular weights as 25OHD. The validated method was applied to mouse serum samples. It was concluded that a standard-vitamin D diet causes an increase in the proportion of all the vitamin D metabolites and C3 epimers and isobar, while UV light has no pronounced effect on the concentrations of the majority of the vitamin D metabolites except 3-epi-25OHD. Further studies are required to confirm this observation in humans and to investigate the biochemical pathways related to vitamin D’s metabolites and their epimers.

Structure and Properties of the Hollow Cast Iron Castings Formed by Continuous Cyclic Freeze Casting

Structure and Properties of the Hollow Cast Iron Castings Formed by Continuous Cyclic Freeze Casting

Fabricating metal wicks by LMC-like continuous directional freeze casting

A novel continuous directional freeze casting technique derived from LMC (liquid metal cooling) is developed in the present study, which is named as “LMC-like freeze casting”. In this novel freeze casting method, a quartz mold containing slurry is dipped into a low-temperature bath with a constant rate to achieve directional freezing of the slurry. Under quasi-steady state conditions, the solidification front is kept above the liquid level of the low-temperature bath at a constant distance. The heat released during freezing is conducted downward axially within the solidified slurry, and then is conducted axially and radially to the low-temperature bath through the mold wall. As a result, the thermal resistance between the solidification front and the low-temperature bath is kept constant, and the solidification velocity is exactly the same as the dipping rate of the casting mold. With casting molds made from quartz, a good compromise between high casting rate and unidirectional freezing is achieved without introducing complex temperature control systems. To demonstrate the feasibility of the LMC-like freeze casting, long wicks (about 10 cm) with uniform pore size along the freezing direction are freeze-casted from aqueous nickel slurry. Permeabilities and capillary performance parameter of the fabricated wicks are measured, proving that LMC-like freeze casting technique is feasible to fabricate biporous metal wicks with aligned porosity.

A proposal for restructuring the layout of continuous freezing tunnels of fresh sausages

Abstract Currently companies face a market extremely competitive, in this scenario, to achieve a significant profit margin, is essential to reduce costs and rework. This study was developed in the central food cooperative Aurora (Erechim- RS), in the continuous freezing tunnels, which are responsible for the biggest bottleneck of the company. The continuous freezing tunnels are very unstable, because the products are positioned on a rail, which can or cannot acquire the proper temperature for freezing, generating rework case do not meet the standards. Therefore, the objective was to restructure the current layout of continuous sausage freeze tunnels, based on temperature analyzes to evaluate compliance with the SAI-151-00 Internal Regulation, propose a new layout with static cages for the tunnels, present the budget for that change and to estimate a deadline to investment's payback. For this work were used approach methods qualitative and quantitative. As the purpose is classified as descriptive, methodological, and as to the means to be treated as field research, literature and case study. In order to perform the temperature analysis, the freezing conformity assessment methodology was used and the layout design methodology was used for the development of the new layout, in which a budget analysis was also developed according to the described methodology. With the completion of work was possible to developed a proposal for a new layout that will double capacity of freezing tunnels and meet all applicable standards. Also found through a budget analysis in less than five days of production in fresh pork the expenses will be paid off.

Production of components for special-purpose products at continuous freeze drying of plants

Experimental studies on freeze-drying of juices and fermented milk drinks at continuous plants were carried out. High-quality components comparable with raw materials for the production of special-purpose products are obtained.

Numerical analysis of in-flight freezing droplets: Application to novel particle engineering technology

The freezing of a stream of free-falling monodispersed droplets was simulated through the development of numerical models in this work. Prediction of the freezing time and temperature transition of a single droplet is beneficial for optimisation of novel continuous spray freeze drying (cSFD) processes. Estimations of the vertical free-falling distance of the droplets in a slip stream and predictions of the chances of droplet coalescence greatly enhance process understanding and can be leveraged to direct equipment design and process development. A design space of droplet diameters in the range from 100 μm to 400 μm and ambient temperatures from −120 °C to −40 °C was explored. The rate of supercooling within the design space was predicted to range from 48 to 830 °C s−1 depending on the ambient temperature and droplet size. A comparison of the vertical free-falling distances of solitary droplets and streams of droplets at different temperatures showed that the terminal velocity of a vertically falling stream of droplets is always in excess of the terminal velocity of a solitary droplet of the same size. A difference of 1.35 m was predicted for the free-falling distance of a 400 μm droplet compared to a stream of droplets at −42 °C. A comparison between flow rates for consecutively generated 100 μm droplets showed that droplet coalescence was predicted at 0.05 Lh−1, whilst at 0.02 Lh−1 a separation distance of 23 μm was maintained thus preventing coalescence.

Investigation of the processes of freezing and freeze-drying of bacterial concentrates for the dairy industry

This project is dedicated to the development of finishing equipment for the production of dry bacterial concentrates. One of the main objects is a quick-freezing apparatus designed for freezing bacterial concentrates, as well as a continuous vacuum freeze dryer. In this market, domestic production takes about 9 ... 12%. Creation of high-tech equipment of a new generation for the production of bacterial concentrates for dairy enterprises will allow to solve the problem of import substitution of this type of product. The main directions for the use of bacterial concentrates in the dairy industry. The analysis of used starter cultures, the range of products manufactured using bacterial concentrates. The classification of bacterial concentrates according to the method of storage and use is given. The methods of using bacterial concentrates at dairy enterprises are considered. The ways to improve the production of bacterial concentrates are proposed. To study the effect of technological parameters of vacuum freeze-drying on the quality of the final bacterial concentrate, a series of experiments was performed. Drying was carried out to a final moisture content of 3.0–3.2%, while the residual pressure in the chamber varied in the range of 10–50 Pa, and the heat flux density ranged from 1.2 to 1.8 kW / m2. The expediency of creating domestic production of baconconcentrates on an industrial scale is substantiated. The results of the study of the kinetics of the freezing of bacterial concentrates are given. The rational parameters of the freezing process and the optimal composition of the cryoprotective medium are proposed. Investigations of the process of vacuum-sublimation dehydration of bacterial concentrate in a layer and granulated form have been conducted. The quality indicators of dry bacterial concentrates are given. The results will allow to carry out engineering calculations and design of equipment for freezing and vacuum sublimation plants with various methods of energy supply.

Effect of Operating Conditions on Ice Characteristics in Continuous Eutectic Freeze Crystallization

AbstractThe efficacy of eutectic freeze crystallization (EFC) in crystallizers and in subsequent downstream washing or filtration steps is a direct function of size and morphology of the crystalline products. These product characteristics are influenced by supersaturation and residence time. To investigate the effect of residence time and supercooling on ice product characteristics in a continuous EFC process, crystallization experiments were performed in an EFC crystallizer with Na2SO4 aqueous solution. Crystal size distribution and morphology during the crystallization process were analyzed by digital image processing. Longer residence times enhanced the mean crystal size and disk‐shaped ice crystals were formed. Increasing supercooling resulted in a larger mean ice equivalent diameter.

Poly-l-Arginine Topical Lotion Tested in a Mouse Model for Frostbite Injury

Frostbite injury occurs when exposure to cold results in frozen tissue. We recently reported a novel mouse model for frostbite injury to be used in screening potentially therapeutic drugs and other modalities. We used the mouse skin frostbite model to evaluate the effect of poly-l-arginine contained in lotion (PAL) applied topically to involved skin. Sixty mice were studied in a randomized, double-blind method. Standardized 2.9-cm-diameter circles were tattooed on the mouse dorsum. Magnets snap frozen in dry ice (-78.5°C) were used to create a frostbite injury on skin within the circle as a continuous 5-minute freeze. Mice were treated with prefreeze placebo, postthaw placebo, combined prefreeze and postthaw placebo, prefreeze with PAL, postthaw with PAL, or combined prefreeze and postthaw with PAL. Appearance, healing rate, tissue loss, and histology were recorded until the wounds were healed. Application of PAL before inducing frostbite injury resulted in decreased tissue loss as compared with other treatment conditions. Applying PAL topically to frostbitten mouse skin caused decreased tissue loss. Poly-l-arginine should be studied further to determine whether it is a beneficial therapeutic modality for frostbite injury.

D- and G-optimal experimental designs for the partition coefficient in freeze concentration

A variety of D- and G-optimal experimental designs are developed for continuous freeze concentration experiments when the partition coefficient was determined from the experimental data. The experimental parameters under consideration were the rate of advancement of the solid–liquid interface and the rotation rate of stirring the liquid phase. The data analysis consisted of three model parameters that had to be estimated from the experimental data. The experimental designs developed included simply-supported pseudo-exact D-optimal, pseudo-continuous D-optimal, the corresponding minimax designs, simply-supported G-optimal, and minimax G-optimal designs. The resulting designs show that the minimax G-optimal design can be an efficient design when the model parameters are not well known. When the model parameters are well known, then either the D-optimal or G-optimal designs would be preferred.

A Novel Mouse Model for Frostbite Injury

Frostbite injury occurs when exposure to cold results in frozen tissue. To screen drugs and other field therapies that might improve the outcome for a frostbite victim, it would be helpful to have a reliable and cost-effective preclinical in vivo model. We sought to create a novel mouse skin model of induced frostbite injury. This model would allow quantification of the surface area of involved skin, histology of the wound, rate of wound healing, and skin loss in a standardized fashion after the frostbite injury. Thirty-six mice were studied. Standardized 2.9-cm diameter circles were tattooed on the mouse dorsum. Magnets frozen in dry ice (-78.5°C) were used to create a frostbite injury on skin within the circle, either as a continuous 5-minute freeze or as 3 repeated freeze (1-minute) and thaw (3-minute) cycles. Appearance, healing rate, skin surface area loss, and histology were recorded until the wounds were healed. The amount of skin surface area loss was approximately 50% for both freeze methods. Although the time to surface skin healing was similar for both freeze methods, the initial healing rate was significantly (P = .001) slower in mice exposed to the freeze-thaw cycles compared with the continuous freeze model. Histopathology reflected inflammatory changes, cell death, and necrosis. This novel in vivo mouse model for frostbite allows quantification of affected skin surface area, histology, healing rate, and skin loss and has the potential of being utilized to screen future treatment modalities.

On the Role of Aging, Washing, and Drying in the Synthesis of Polycrystalline Zinc Oxide by Precipitation: Combining Fast Continuous Mixing, Spray Drying and Freeze Drying to Unravel the Solid-State Transformations of the Precipitate

The continuous precipitation of zinc carbonates using aqueous solutions of zinc nitrate and sodium carbonate was quenched within a few seconds by combining a micromixer with a bench-top spray dryer. In this way, it was possible to monitor the slow phase transformation of the initially formed sodium zinc carbonate into zinc hydroxy carbonate during subsequent washing and drying. An increased stirring rate applied during washing was found to accelerate this phase transformation, thus influencing the specific surface areas and pore size distributions of the ZnO powder materials finally obtained after calcination.

Development of Continuous Freeze Concentration Equipment.

溶液の凍結濃縮を目的に氷片の連続生成機および連続遠心分離機から構成される連続凍結濃縮の装置を試作した．海水希釈液を原液として本装置の特性を検討した．試験の結果，氷片連続生成機から排出される氷片に含まれる塩素イオンの濃度（以下濃度とは塩素イオン濃度）および生成量が知られた．さらに，原液濃度0.62～0.67wt%，ドラムの冷却温度−11～−24°C，ドラムの1回転時間98～610s，連続遠心分離機内における氷片の滞留時間15～600sの条件において，連続遠心分離後の濃縮液の濃度が1.6～3.9wt%，分離氷に含まれる塩素イオンの濃度が0.27～0.55wt%，また分離氷の残液率が0.10～0.20の結果を得た．

Effect of Freeze–thaw Cycle on the Parameters of the Green and Ampt Infiltration Equation

In humid and temperate regions, application of hydrologic models based on the Green and Ampt infiltration equation, during the spring season, often creates problem due to freezing and thawing of soils. These climatic conditions result in significant changes in hydrological and hydraulic properties of the soil. Three soil properties which are used to estimate parameters of the Green and Ampt infiltration equation were measured on repacked soil cores after subjecting them to a number of freeze–thaw cycles. The saturated hydraulic conductivity, air entry potential and total porosity tests were conducted to determine the influence of repeated freeze–thaw cycles on these properties and to incorporate the interactive effect of soil type, bulk density and saturation on these variables. The three soil types chosen for the experiment were silt loam, clay loam and loamy sand. Saturated hydraulic conductivity was measured using a steady upward flow constant head permeameter. The air-entry potential was estimated from the relationship between soil matric head and volumetric water content. Volumetric water content at saturation was used to approximate total porosity. Results from factorial analysis of variance indicate that the means of saturated hydraulic conductivity, total porosity and air-entry potential proved to be significantly different among soil types and bulk density. Changes in saturated hydraulic conductivity values for the three different soil types by the impact of continuous freeze–thaw cycles is most severe at lower degree of saturation and reduces in severity as the degree of saturation increases.

Thermal Characteristics of a Hepatic Cryolesion Formedin Vitroby a 3-mm Implantable Cryoprobe

The objective of the investigation was to characterize the hepatic cryolesion formed with an implantable needle (3 × 100 mm) cryoprobe. This was used to produce cryolesions in isolated porcine liver tissue equilibrated to 37°C in a water bath. The shape, size, and temperature zones within the cryolesion and the effect of single versus repeated freeze–thaw cycles on cryolesion size were studied. The final shape of the cryolesion at 15–20 min freezing was cylindrical and its distal hemispherical end extended 8 mm beyond the tip of the cryoprobe. The rate of increase in maximum diameter was logarithmic and decreased from 4.7 mm/min during the first 5 min to 0.4 mm/min during the fourth 5-min period of freezing. By contrast, the rate of increase in volume was linear and ranged from 9.6 to 7.9 ml/min during the corresponding periods. The volume of the hepatic cryolesion after 20 min of continuous freezing was significantly greater than that of the cryolesion formed with 20 min of cumulative freezing interrupted by a 5-min spontaneous thaw. The ultimate temperatures reached and the cooling rates varied in different zones within the cryolesion depending on distances away from and alongside the cryoprobe. Diameter measurements taken in isolation do not reflect the actual growth rate of the cryolesion. Volume measurements define more accurately the amount of tissue frozen and leftin situ.Prolonged freezing beyond 20 min did not increase the diameter of the cryolesion. A single continuous freeze produces a larger cryolesion than two freeze–thaw cycles of the same freezing duration.