Process Parameters as Tools to Intensify the Freeze-Drying Process and Modify the Sorption Properties of the Obtained Freeze-Dried Products

Abstract

This study aimed to investigate the effect of the application of different freeze-drying conditions on the process’s kinetics and the sorption properties of dried apples. Slices of apples were frozen and subjected to a freezing-drying process with different combinations of shelf temperature (−20, 10, 20, and 30 °C) and pressure (37, 63, 103, and 165 Pa). During the freeze-drying, the temperature in the centre of the material was recorded. The moisture content in the dried material and changes in the water content in dried apples stored at a humidity of 75.3% were obtained. The Midilli et al. model was used to describe the drying kinetics of the freeze-drying with a good fit. Drying time increased from 660 (variant with a constant shelf temperature of 30 °C, pressure 63 Pa) to 1305 min (variants with temperatures −20:10:20:30 °C, pressure 63 Pa). For this reason, the most favourable experimental parameters were a temperature of 30 °C and a pressure of 63 Pa. However, applying these parameters caused higher absorption of water vapour during storage. Therefore, the selection of freeze-drying parameters should also be related to the expected properties of the final product.

1. Introduction

Freeze-drying is a process in which the free water contained in the product must remain frozen throughout its duration [1]. Freezing prevents the structure’s flow and deformation, allowing material preservation [2,3].

The freeze-drying process consists of three phases: (1) freezing, described as a change in the state of free water from liquid to solid; (2) sublimation, described as primary drying; and (3) desorption, as secondary drying [4,5,6]. In the primary (sublimation) period, the product temperature depends on the material properties, shelf temperature, chamber pressure of the freeze-dryer, sublimation rate, and container system. Therefore, it is not easy to optimize freeze-drying. The philosophy of primary drying is to select the optimal temperature for a given raw material, quickly bring the product to this temperature, and then keep the product temperature more or less constant throughout the primary drying period [1,7].

On the other hand, the temperature should be kept below the collapse temperature (Tc) for a given material, at which the material’s structure collapses during freeze-drying [7,8]. The sublimation phase ends when there is no more water in the material in the form of ice. The temperature of the material during this period must remain below the triple point—0 °C in the case of pure water and below that of a cryoscopic temperature in the case of solutions [7].

The second phase of freeze-drying is desorption drying. During this phase, water desorption occurs. This period occurs mainly after the end of sublimation, but it can begin at the beginning of the sublimation period in places (regions) where the ice has been removed. This is because, during the entire process, there are two regions in the dried material: one from which water has sublimated and the other in which water is frozen and its content is equal to the water content in the frozen product [9].

During desorption, non-freezing water is removed. After primary drying, an amorphous product still contains a fair amount of residual water (5–20% on a dried solid basis), depending on the formulation and structure [2,6]. Dried products in the food industry can be divided into two groups: plant or animal raw materials with a preserved cellular structure and processed products without a cellular structure. The final water content in freeze-dried juices, suspensions, or pulps may be less than 1%. However, the final moisture content of freeze-dried cellular materials is between 0.5 and 3% [10].

Cellular structure is fundamental in freeze-drying because the presence of the cell membrane resists the movement of heat and mass [11]. The cell membrane holds the cell fluid, whether frozen or liquid. Therefore, during freeze-drying of plant or animal tissues, it is difficult to notice whether the cell fluid has thawed or not [2,3]. The appearance of free water causes the material to flow, causing cell deformation and ultimately, shrinkage.

To avoid thawing the product during freeze-drying, selecting the appropriate parameters of the freeze-drying process is essential. The parameters that can be controlled during the freeze-drying process are [12]:

• working pressure,
• the flow of supplied heat (in the case of contact heating, the shelf temperature),
• safety pressure.

A freeze-dryer chamber’s working pressure is related to the material temperature through the thermodynamic equilibrium curve: the evaporation temperature of water versus ambient pressure (

Table 1. The dependence of evaporation temperature on pressure for water is a basis for selecting the pressure in the freeze-dryer chamber. This is based on data from the Alpha 1-4 (Christ) freeze dryer control system (Martin Christ Gefriertrocknungsanlagen GmbH, Osterode am Harz, Germany.

Temperature, °C	Pressure, Pa	Temperature, °C	Pressure, Pa
0	611.0	−30	37.0
−5	402.0	−35	22.0
−10	256.0	−40	12.0
−15	165.0	−45	7.0
−20	103.0	−50	4.0
−25	63.0	−55	2.1

). Therefore, the temperature of the material, which contains a lot of water, during the period of intensive sublimation depends on the value of the set pressure. For example, at a pressure of 63 Pa, with the material during intensive evaporation, the frozen product maintains a temperature of −25 °C. Theoretically, the pressure in the chamber of the freeze dryer should be below 610 Pa (water triple point parameter). For plant and animal cellular material with a high water content, the pressure in the chamber should be within the range of 63 to 124 Pa [13]. This is related to the composition of cell juice and osmotic pressure resulting from the presence of simple sugars and minerals as osmotically active substances influencing the freezing temperature [14,15].

Lowering the pressure lowers the water evaporation temperature and vice versa. Such a dependence occurs only when the resistance to mass transport inside the material is lower than the resistance to water vapor penetration from the material’s surface to the surroundings, similar to the first period of convective drying.

The temperature during primary drying must be maintained within certain limits, depending on the type of material, its chemical composition, and the glass transition temperature. To prevent melting or collapse of the structure, the product temperature should be several degrees lower than the glass transition temperature [16]. It should also correspond to the temperature at which 100% of the free water is frozen. For fruit, this is −25 to −30 °C. On average, free water constitutes about 96% of the total water in fruits [6]. In apples, non-freezing water constitutes about 3.7% of the total water content [17].

The temperature in the desorption drying phase may be increased, but apples at the end of desorption drying should not exceed 38 °C, i.e., the glass transition temperature for an apple containing 0.5% water [17].

By lowering the working pressure in the freeze-dryer chamber, the ability to sublimate is significantly reduced because the temperature difference between the condenser and the vapor above the evaporation surface, which is the driving force, decreases [1,18].

For sublimation to occur, providing heat for phase transfer is necessary. The heat source may be a shelf (contact heating), infrared radiation, or microwave heating. In the case of contact heating (most often used), the appropriate shelf temperature should be set to ensure the necessary heat flux [1]. The temperature of the material is the result of the temperature of the dry and ice regions. Therefore, it can only increase due to completing the sublimation process, not due to providing too high a heat flux. Since, as a result of reducing the amount of ice inside the material, the amount of vapor produced is limited, it is advisable that the amount of heat supplied gradually decreases during the process, which is used in industrial processing [12].

The safety pressure protects against excessive heat flow and, thus, against the melting of the ice. Once it is reached, the heating is turned off, which limits the amount of heat supplied and protects the material against undesirable temperature increases. Its value is usually set at a level that ensures an acceptable increase in the temperature of the frozen material (usually by 2 to 5 °C compared to the temperature resulting from the working pressure) [7].

The condenser temperature is a result of the design of the freeze dryer and is not an adjustable value. Usually, it is a temperature of −50 to −60 °C; in solutions for the pharmaceutical industry, it reaches a value of −90 °C [12].

Analysing the works presented in the literature, most authors do not justify their freeze-drying parameters, and often even omit them (Table 2). In some cases, these parameters seem unreasonable. Examples of freeze-drying parameters used for drying fruit and vegetables are presented in Table 2.

Gianfrancesco et al. [19] used variable heating shelf temperature. They concluded that the product temperature should be maintained below the collapse temperature during the primary drying step. During desorption, the temperature should gradually increase following the glass transition line to accelerate dehydration.

Taking into account the need to adjust the freeze-drying parameters to a given stage of the freeze-drying process [19], a theory was put forward that the course of the freeze-drying process and the quality of the dried product can be influenced by linear or step changes in the processing parameters (the working pressure and shelf temperature).

Analysing the data from Table 2, it can be stated that some authors do not attach importance to the precise specification of the lyophilization parameters, e.g., [20,21,22,23]; do not specify the heating intensity, e.g., [24]; use a very high shelf temperature, without controlling the temperature of the lyophilized material [25,26]; or carry out the process for a set time instead of until the equilibrium water content is determined [22,27]. They occasionally differentiate the parameters for the primary and secondary periods [28]. Only in one of the found works were variable parameters used to increase the heating intensity during the process [19]. However, this work concerned a model system, not a natural raw material.

When designing the research for this work, the authors aimed to show how the processing parameters, when even slightly changed, are essential for the course of the process and sorption properties of freeze-dried material. We also wanted to draw attention to the fact that:

• changes in parameters, even slight changes, can significantly affect the kinetics of the process,
• measurement of the material temperature can be a tool for assessing the adequacy of the process,
• too high a material temperature, especially in the initial freeze-drying period, results in the presence of free water in the material, which changes the process from freeze-drying to vacuum drying.

Table 2. Some examples of controlled freeze-drying parameters.

Material	Sample Preparation	Freeze-Drying Parameters	Ref.
Apple	slices 4 and 8 mm	T (condenser) = −48 °C IR lamp (T = lack of data), Pressure = 13.3 Pa Material T control: no	[24]
Apple	slices 5 mm	T shelf variable during the process: 20_45_55_50 °C, T (condenser) = −40° Pressure = 100 Pa, Time 15 h Material T control: yes	[29]
Apple puree gel	cylinder with d = 13.5 mm, height of 13.7 mm	T (shelf) = 20 °C Pressure = 63 Pa, Time = 24 h Material T control: no	[25]
Banana	cylindrical shape with a d = 20 mm and thickness from 10 to 20 mm	Temperature of IR radiator range of 50–70 °C Pressure = 0.5 Pa Time = 6 h Material T control: no	[30]
Blackberries	Juice with carrier agents	T = −84 °C (shelf or condenser T-not reported) Pressure: 4 Pa, Time: 48 h Material T control: no	[26]
Carrot	3–4 mm slices	T (shelf) = 30 °C, T (condenser) = −60 °C Pressure = 6 Pa, Time = n/a Material T control: no	[20]
Carrot and horseradish	0.5 cm slices	Primary drying: T (shelf) = −35 °C, Pressure = 50 Pa Secondary drying: Pressure = 4 Pa, T rising continually to +18 °C Material T control: no	[28]
Guava and papaya	1 × 1 × 1 cm cubes	T (shelf) = 10 °C Pressure = less than 613.2 Pa, Time = 24 h Material T control: no	[31]
Pumpkin, green bell pepper	samples of 2 × 2 cm	T = between −47 and −50 °C (shelf or condenser T-not reported), Pressure = 0.67 Pa, Time 38 h Material T control: no	[32]
Model instant powder solution	model spheres (d = 2 cm) with sucrose coating	Isotherm at T = (−7) °C (12 h) Isotherm at T = (−3) °C (12 h) Isothermal drying at T = −27 °C (5 h) T ramp from −27 °C to 20 °C at 1 °C/min T ramp from −70 °C to 20 °C at 4 °C/h Isotherm at T = −60 °C for 20 h T ramp from −60 °C to 20 °C at 4 °C/h T ramp from −60 °C to −40 °C at 0.5 °C/h T ramp from −40 °C to 20 °C at 1.25 °C/h Pressure 20 Pa, Material T control: no	[19]
Pineapple, cherry, guava, papaya	pulp, thickness of 1 cm	T = −30 °C (shelf or condenser T-not reported), Pressure = 130 Pa, Time 12 h Material T control: yes	[21]
Strawberry	slices 5 or 10 mm, or whole fruits	T shelf (30, 40, 50, 60 and 70 °C) T (condenser) = −92 °C Vacuum level of less than 5 mL Time: 12 h—slices and 24 and 48 h—whole fruits Material T control: yes	[22]

Table 2. Some examples of controlled freeze-drying parameters.

Material	Sample Preparation	Freeze-Drying Parameters	Ref.
Apple	slices 4 and 8 mm	T (condenser) = −48 °C IR lamp (T = lack of data), Pressure = 13.3 Pa Material T control: no	[24]
Apple	slices 5 mm	T shelf variable during the process: 20_45_55_50 °C, T (condenser) = −40° Pressure = 100 Pa, Time 15 h Material T control: yes	[29]
Apple puree gel	cylinder with d = 13.5 mm, height of 13.7 mm	T (shelf) = 20 °C Pressure = 63 Pa, Time = 24 h Material T control: no	[25]
Banana	cylindrical shape with a d = 20 mm and thickness from 10 to 20 mm	Temperature of IR radiator range of 50–70 °C Pressure = 0.5 Pa Time = 6 h Material T control: no	[30]
Blackberries	Juice with carrier agents	T = −84 °C (shelf or condenser T-not reported) Pressure: 4 Pa, Time: 48 h Material T control: no	[26]
Carrot	3–4 mm slices	T (shelf) = 30 °C, T (condenser) = −60 °C Pressure = 6 Pa, Time = n/a Material T control: no	[20]
Carrot and horseradish	0.5 cm slices	Primary drying: T (shelf) = −35 °C, Pressure = 50 Pa Secondary drying: Pressure = 4 Pa, T rising continually to +18 °C Material T control: no	[28]
Guava and papaya	1 × 1 × 1 cm cubes	T (shelf) = 10 °C Pressure = less than 613.2 Pa, Time = 24 h Material T control: no	[31]
Pumpkin, green bell pepper	samples of 2 × 2 cm	T = between −47 and −50 °C (shelf or condenser T-not reported), Pressure = 0.67 Pa, Time 38 h Material T control: no	[32]
Model instant powder solution	model spheres (d = 2 cm) with sucrose coating	Isotherm at T = (−7) °C (12 h) Isotherm at T = (−3) °C (12 h) Isothermal drying at T = −27 °C (5 h) T ramp from −27 °C to 20 °C at 1 °C/min T ramp from −70 °C to 20 °C at 4 °C/h Isotherm at T = −60 °C for 20 h T ramp from −60 °C to 20 °C at 4 °C/h T ramp from −60 °C to −40 °C at 0.5 °C/h T ramp from −40 °C to 20 °C at 1.25 °C/h Pressure 20 Pa, Material T control: no	[19]
Pineapple, cherry, guava, papaya	pulp, thickness of 1 cm	T = −30 °C (shelf or condenser T-not reported), Pressure = 130 Pa, Time 12 h Material T control: yes	[21]
Strawberry	slices 5 or 10 mm, or whole fruits	T shelf (30, 40, 50, 60 and 70 °C) T (condenser) = −92 °C Vacuum level of less than 5 mL Time: 12 h—slices and 24 and 48 h—whole fruits Material T control: yes	[22]

2. Materials and Methods

2.1. Materials

The Granny Smith apples were purchased at the local market (E. Leclerc, Warsaw, Poland) and used in the investigations. This variety of apples was selected due to its year-round availability. The fruits were stored at refrigeration conditions at a temperature of 5 °C. This research was carried out on one batch of apples over a short period (three weeks) to limit the impact of raw material variability on the obtained results.

Whole fruits were cut into slices with a thickness of 10 mm using the Robot Coupe CL50 slicer (Vincennes, France). The outer slices of apples were not used; only the samples with a diameter of approximately 70 mm were subjected to freezing.

2.2. Freezing of Samples

The slices of apples were frozen to a temperature of −40 °C for 2 h using a convention freezer with forced air circulation (Irinox HC 51/20, Corbanese, Italy). Thermocouples with a wireless logger (TrackSense^®, Ellab, Hilleroed, Denmark) were placed inside some slices of the material (before freezing) to record the temperature at 2 min intervals during the freeze-drying process.

2.3. Freeze-Drying of Apple Slices

The freeze-drying process was carried out using a Gamma 1-16 freeze-dryer (Martin Christ Gefriertrocknungsanlagen GmbH, Osterode am Harz, Germany). The dryer shelves were cooled to a temperature of −40 °C before placing the frozen samples to avoid the ice melting during pressure reduction. The freeze-dryer software controlled the temperature and pressure of the process.

Different conditions of the process (pressure and shelf temperature) were applied. When selecting the range of parameters used, the following was considered: the need for complete freezing of free water, which is observed for apples at a temperature of −25 °C (corresponding to a pressure of 63 Pa). Therefore, the pressure of 63 Pa was the base, concerning which modifications were made from 37 to 165 Pa. In turn, the shelf temperature range of 10 to 30 °C was selected based on our own experience [14] as a range that allows for the supply of such an amount of heat to the apple that will be used exclusively for the phase change but will not cause an excessive increase in the apple’s temperature. The attempt to modify the parameters during the process aimed to adjust the size of the heat flux supplied to the demand under the given pressure conditions. It was, therefore, possible to observe their effect on the material temperature (as a parameter allowing for the determination of the lack of ice in the freeze-dried material) during freeze-drying and on the kinetics of the process.

Table 3. Applied parameters during freeze-drying.

Variant No	Variant Code	Shelf Temperature	Pressure
1	T10, P63	Isotherm at 10 °C (24 h)	Isobar at 63 Pa
2	T10/30, P63	Ramp * from 10 °C to 30 °C; 0.2 °C/h Isotherm at 30 °C (14 h)	Isobar at 63 Pa
3	T–25/10/30A, P63	Ramp from −25 °C to 10 °C; 8.75 °C/h Ramp from 10 °C to 30 °C; 0.2 °C/h Isotherm at 30 °C (10 h)	Isobar at 63 Pa
4	T30, P63	Isotherm at 30 °C (24 h)	Isobar at 63 Pa
5	T–25/10/30B, P63	Ramp from −25 °C to 10 °C; 35 °C/h Isotherm at 10 °C (5 h) Ramp from 10 °C to 30 °C; 2.5 °C/h Isotherm at 30 °C (10 h)	Isobar at 63 Pa
6	T–25/10/20/30, P63	Ramp from −25 °C to 10 °C; 35 °C/h Ramp from 10 °C to 20 °C; 0.55 °C/h Ramp from 20 °C to 30 °C, 3.33 °C/h Isotherm at 30 °C (2 h)	Isobar at 63 Pa
7	T10/30, P63/103/37	Ramp from 10 °C to 30 °C; 0.2 °C/h Isotherm at 30 °C (14 h)	Ramp from 63 to 103 Pa; 40 Pa/h Isobar 103 Pa (10 h) Ramp from 103 to 37 Pa, 4.72 Pa/h
8	T30, P63/103	Isotherm at 30 °C (24 h)	Ramp from 63 to 103 Pa; 40 Pa/h Isobar 103 Pa (23 h)
9	T–25/10/30B, P63/103	Ramp from −25 °C to 10 °C; 35 °C/h Isotherm at 10 °C (5 h) Ramp from 10 °C to 30 °C; 2.5 °C/h Isotherm at 30 °C (10 h)	Ramp from 63 to 103 Pa; 8 Pa/h Isobar 103 Pa (19 h)
10	T–25/10/30A, P63/165/103	Ramp from −25 °C to 10 °C; 8.75 °C/h Ramp from 10 °C to 30 °C; 0.2 °C/h Isotherm at 30 °C (10 h)	Ramp from 63 to 165 Pa; 25.5 Pa/h Ramp from 165 to 103 Pa; 6.2 Pa/h; Isobar 103 Pa (10 h)

* Ramp means a linear change of process parameters.

describes the procedure for parameter changes during freeze-drying. The variants 1–6 were characterised by different shelf temperatures with a constant pressure of 63 Pa. Variants 7–10 showed the process’s condition with different pressure and temperature ranges (Table 3). Table 3 shows that the same procedures of ramp temperature changes were applied for variants: 2 and 7 (from 10 °C to 30 °C), 4 and 8 (30 °C), and 3 and 10 (from −25 °C to 10 °C and from 10 to 30 °C) at different pressures.

After the freeze-drying, the temperature measurement results were downloaded from a TrackSense logger with the software ValSuite Basic 2.4.5 (Ellab, Hilleroed, Denmark). The profiles of temperature changes in the centre of the material during freeze-drying were plotted.

2.4. Kinetics of the Freeze-Drying at Different Process Parameters

During the freeze-drying, the weight loss of the apples was measured and recorded online with the application of a weight system (model SWL025, Mensor, Warsaw, Poland). The measurement was carried out according to the procedure described by Nowak and Jakubczyk [15].

The recorded weight loss during the freeze-drying was used to calculate the moisture ratio MR (dimensionless) as follows:

$$\mathrm{M}\mathrm{R}={\displaystyle \frac{u-u_e}{u_o-u_e}}$$

(1)

where u is the water content at the time, u_o is the initial water content, and u_e is the equilibrium water content (g water/g d.m.), which was determined when the mass of the sample did not differ over the drying time interval (15 min).

The drying curves were created to present the changes in moisture ratio over time. Regression analysis was conducted using the Table Curve v. 5.01 program (Systat Software Inc., Palo Alto, CA, USA). The Midilli et al. model (2) was used to describe the drying curves for different conditions of the freeze-drying process. The parameters of fit, namely the determination coefficient (R²) and the root mean square error (RMSE), were calculated as follows [33]:

$$\mathrm{MR}=a\cdot \exp \left(-k\cdot t^n\right)+b\cdot t$$

(2)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^N{\left({\mathrm{MR}}_{i,p}-{\mathrm{MR}}_{i,e}\right)}^2}}{N}}}$$

(3)

where a, k, n, and b are parameters of the Midilli et al. equation, t is the time of drying (min), MR_i,p is the predicted moisture ratio, MR_i,e is the experimental moisture ratio, and N is the number of experimental data.

Based on the data obtained with the Midilli et al. model, the Table Curve v. 5.01 program (Systat Software Inc., Palo Alto, CA, USA) was applied to calculate the drying rates as the first derivate dMR∙dt⁻¹. The curves describing the changes in drying rate (min⁻¹) versus drying time (min) were plotted.

The moisture content of the freeze-dried apples (%) was investigated according to the procedure described by Nowak and Jakubczyk [15]. The samples were dried at a pressure of 2 kPa and a temperature of 70 °C for 24 h using a vacuum dryer (VO200, Memmert GmbH, Büchenbach, Germany).

Based on the drying curves and profiles of temperature changes in the material during freeze-drying, drying times required to reach −2 °C and −10 °C inside the material were determined. Additionally, the water content (g water g⁻¹ dry matter) in the dried material was obtained at these times. Also, the final drying time was noted (when the water content reached equilibrium, approximately 0.05 g water/g d.m.).

2.5. Water Sorption Kinetics

The water sorption kinetics was carried out according to the protocol described for freeze-dried materials [23,27]. A slice of apple was weighed every 2 min during storage in a chamber with a relative humidity of 75.3% at a temperature of 25 °C. The data were recorded during 24 h of sorption process using PW-Win 2004 software (Radwag, Warsaw, Poland). The water sorption kinetics curves were plotted as water uptake by the material (g water/g d.m.) during the sorption time.

2.6. Statistical Analysis

All experiments were performed in triplicate. The regression analysis was applied to describe the drying curves and obtain the selected model’s constants. The model parameters are presented as mean with standard error of the estimate. Regression analysis was conducted using the Table Curve v. 5.01 program (Systat Software Inc., Palo Alto, CA, USA).

One-way ANOVA analysis and Tukey’s Honest Significant Difference method (The Statistica v 13.3 StatSoft Inc., Tulsa, OK, USA) with a confidence level of 95% were applied to evaluate the statistical difference between the obtained data (final moisture content and drying time, water content and drying time after reaching a temperature of −10 and −2 °C in the centre of the material, water uptake after 24 h of storage at an environment with a humidity of 75.3%) for different conditions of the freeze-drying process.

3. Results and Discussion

3.1. Freeze-Drying Kinetics of Apple Slices under Different Processing Conditions

The freeze-drying kinetics of apple slices under different processing conditions were described by the model of Midilli et al. This model was selected based on the results of our previous experiments with freeze-drying of apples with PEF treatment [15]. Also, other investigations of the freeze-drying process of different fruits [34,35] showed that the Midilli et al. model coincided very closely with experimental data. Krzyczkowski et al. [36] observed that the Midilli model best fitted the experimental data of freeze-drying curves obtained at different shelf temperatures from 30 to 70 °C. The Midilli et al. model is a semiempirical model obtained from Fick’s law for diffusion [37]. Modelling process parameters can reduce the number of experiments required during drying process design [38]. Also, it is important to select the drying conditions and equipment design for the improvement of food quality [39]. Proper management of the drying parameters can reduce the extent of damage of material related to heat and mass transfer during drying [40]. Knowledge of the kinetic model and its parameters is crucial because these models have already been used to assess changes in the nutritional characteristics and colour quality of food products [40,41]. A model with a very high value of determination coefficient R² and a very low value of the root mean square error RMSE can explain the drying characteristics [34,42].

Table 4. The parameters and goodness of fit of the Midilli et al. model for freeze-drying of apple slices under different processing conditions.

Variants	a	10−5 × b	10−3 × k	n	R2	RMSE
T10, P63 (1)	1.005 (0.002) *	−190.0 (0.9)	1.4 (0.1)	1.069 (0.012)	0.9994	0.0043
T10/30, P63 (2)	0.996 (0.002)	−12.7 (0.7)	0.7 (0.0)	1.214 (0.011)	0.9995	0.0044
T–25/10/30A, P63 (3)	0.984 (0.002)	−18.0 (0.9)	0.2 (0.0)	1.350 (0.014)	0.9992	0.0042
T30, P63 (4)	1.009 (0.003)	−18.0 (1.0)	1.6 (0.1)	1.125 (0.013)	0.9995	0.0044
T–25/10/30B, P63 (5)	1.010 (0.002)	−15.0 (0.6)	1.3 (0.0)	1.059 (0.010)	0.9994	0.0044
T–25/10/20/30, P63 (6)	1.002 (0.001)	−5.7 (0.2)	1.2 (0.0)	1.080 (0.005)	0.9991	0.0010
T10/30, P63/103/37 (7)	1.007 (0.002)	−19.0 (1.0)	0.8 (0.0)	1.160 (0.015)	0.9997	0.0051
T30, P63/103 (8)	1.009 (0.003)	−19.5 (1.3)	1.9 (0.1)	1.089 (0.015)	0.9991	0.0053
T–25/10/30, P63/103 (9)	0.998 (0.002)	−14.1 (0.7)	0.3 (0.0)	1.330 (0.012)	0.9991	0.0045
T–25/10/30, P63/165/103 (10)	0.996 (0.001)	−9.8 (0.4)	0.06 (0.0)	1.560 (0.008)	0.9993	0.0010

* Numbers in the brackets represent standard errors of the estimates.

shows the constants of the Midilli et al. model and statistical parameters describing the goodness of fit. As can be observed, all samples showed values of R² higher than 0.999, and the very low values of RMSE ranged from 0.0020 to 0.0053. Benlloch-Tinoco et al. [34] also applied this model to describe the kinetics of freeze-drying microwaved or hot pre-dried kiwifruit puree and obtained RMSE values between 0.0011 and 0.0061. Also, Igual et al. [35] reported the low RMSE values (0.0025–0.0062) of this kinetics model for freeze-dried grapefruit formulations, which is in agreement with our results.

In kinetics models, the k constant can be linked with the drying rate, but the n parameter is mainly affected by the initial water content or drying pre-treatment [34,43,44]. The effect of drying temperature on the n parameter was inconclusive in the case of dried almonds. Increasing the drying temperature from 40 to 50 °C caused the n value to decrease from 0.6014 to 0.4467, but at a drying temperature of 60 °C, the parameter reached a value of 0.6399 [45]. Parameter n describes the shape of the drying curve, and if the n value is higher than 1, the curve has a sigmoid-type shape. All analysed variants of the drying curves were described by n values between 1.069 and 1.560 (Table 4). Buzrul [39] emphasised that some model parameters could not have a specific and interpretable meaning. However, the effect of the processing parameters on the curve’s shape should be well recognised. Higher values of k can indicate a higher drying rate and a shorter time required for the process [44]. The highest values of k 1.9 and 1.6 were obtained for variants (8) and (4), respectively (Table 4). In both freeze-drying variants, the shelf temperature was the same (30 °C), but the applied pressure was different. The results presented in

Table 5. Final drying time and moisture content in freeze-dried apples.

Variants	Drying Time, min	Moisture Content, %
T10, P63 (1)	930 ± 4 a*	3.46 ± 0.02 a
T10/30, P63 (2)	855 ± 3 b	3.26 ± 0.06 b
T–25/10/30A, P63 (3)	915 ± 3 c	3.26 ± 0.02 b
T30, P63 (4)	660 ± 2 d	2.74 ± 0.01 c
T–25/10/30B, P63 (5)	1050 ± 5 e	3.31 ± 0.08 b
T–25/10/20/30, P63 (6)	1305 ± 3 f	3.29 ± 0.21 ab
T10/30, P63/103/37 (7)	870 ± 4 g	2.74 ± 0.03 c
T30, P63/103 (8)	735 ± 3 h	2.77 ± 0.08 c
T–25/10/30, P63/103 (9)	820 ± 4 i	3.13 ± 0.08 b
T–25/10/30, P63/165/103 (10)	945 ± 3 j	3.55 ± 0.18 a

* Data presented as mean ± standard deviation; the different letters in the column indicate significant differences between the parameters, p ≤ 0.05.

also showed that the shortest times of the process were recorded for these two samples. Additionally, the course of the drying curves indicated that the application of these processing conditions (temperature 30 °C, pressure 63 Pa, or pressure ramp of 63–103 Pa) accelerated the dehydration process (Figure 1a,b). The highest n parameter was obtained for variant (10) with a shelf temperature increase from −25 to 30 °C and pressure changes in the sequence of 63_165_103 Pa during freeze-drying. The highest value of the n parameter was related to the lowest value of the k constant of the model (Table 4). A decrease of k may compensate for an increase in the n parameter. It may lead to a similar course of drying kinetics for different values of the constants. However, both constants can be affected by different process variables [35,46]. In the case of our studies for variants 7 and 9, the use of different pressure and temperature conditions during drying led to obtaining different model parameters (Table 4), especially for the values of k (0.8 and 0.3) and n (1.160 and 1.330). Still, the drying curves almost coincided (Figure 1b). However, the greatest difference in the course of the curves was observed between 60 and 300 min of the process when lower water content values were recorded in variant 7. In this variant, the set pressure of 103 Pa was achieved after just one hour, while in the case of variant 9, after 5 h. In the desorption stage of freeze-drying, the pressure was reduced to 37 Pa in the case of variant 7. This caused the material to dry 50 min longer than variant 9, for which the pressure was constant at this stage (103 Pa). Therefore, the material’s response to the given pressure was observed.

Figure 1a presents the experimental drying curves obtained during the freeze-drying of apples at a constant pressure and different temperatures. The variants T10, P63 (1) and T10/30, P63 (2) had a similar course of drying curves. However, an increase in temperature from 10 to 30 during the first 10 h of drying for variant (2) caused shortening of the drying time from 930 to 855 min. Application of a shelf temperature of 30 °C during the entire process accelerated lyophilisation and the drying time was 660 ± 2 min. A gradual increase of the shelf temperature from −25 to 30 °C at different intervals extended the drying time by 2-fold for variant T–25/10/20/30, P63 (6). Egas-Astudillo et al. [47] observed during freeze-drying of grapefruit puree with or without the addition of biopolymers that an increase of the shelf temperature from 20 to 40 °C reduced the drying time up to 57.5%. A two-fold shortening of drying time was also observed for the freeze-drying of mulberry fruits due to an increase of the heating plate from 30 to 70 °C [36].

Variants (9) and (10) were obtained at similar steps in the temperature changes but at different pressure conditions (Figure 1b). Applying more pressure intervals with a higher pressure caused an increase in drying time from 820 ± 4 min (variant 9) to 945 ± 3 min (variant 10). Variations in the chamber pressure from 0 to 26.6 Pa had little or no effect on the drying time and rate during the secondary drying of a solution of mannitol and moxalactam [48]. A similar course of drying curves was observed for material dried at different conditions of pressure and temperature (variants: T10/30, P63/103/37 (7) and T–25/10/30, P63/103 (9)). This may indicate that a similar course of the drying process can be obtained by modifying the values of the pressure and temperature parameters at different intervals.

The drying time was different for applied variants of the process, but the final moisture content in the dried material differed slightly and was in the range between 2.74 to 3.55% (Table 5).

Figure 2 presents the changes in drying rate during the freeze-drying of apples. Drying rate curves were obtained by the differentiation of the Midilli et al. model. The highest drying rate was observed for variant T30, P63 (4) during the first 200 min of the process with a maximal value of 0.0028 min⁻¹ (Figure 2a). At the end of the process, the drying rate for this variant was reduced by four times. The application of the ramp increases the temperature from 10 to 30 °C (variant 2), causing a decrease in the maximum and final drying rate to 0.0019 min⁻¹ and 0.0004 min⁻¹, respectively. Also, more steps in the changes of shelf temperature (a slower increase of temperature) between −25 and 30 °C (variants 5 and 6) slightly reduced the drying rate, especially after 400 min of drying. However, materials obtained with the same intervals of shelf temperature increased −25:10:30 °C (variants 3 and 5) but different durations of some temperature ramps showed different courses of the drying rate curve (Figure 2a). The slower drying rate was observed for variant 3 during the first 3 h of the process (when the shelf temperature increased from −25 °C to −10 °C over 4 h) than for variant 5 (when the same range of temperatures was obtained over 1 h). After this drying stage, the faster changes in shelf temperatures from 10 to 30 °C for variant 3 led to a higher drying rate than observed for variant 5. Additionally, an almost constant drying rate was obtained for variant 3 for a drying time between 145 and 290 min, which was not observed for variants with constant pressure (Figure 2a). It may be concluded that the rate of changes in shelf temperature can also be crucial in intensifying the freeze-drying process. Optimal conditions for freeze-drying of apples were obtained for variant 4 (T30, P63) with a shelf temperature of 30 °C. The highest and constant shelf temperature resulted in a significant increase in the drying rate and a reduction in the processing time. More temperature steps and a slower heating rate resulted in a reduced water removal rate. Gui et al. [49] observed that the drying rate increased by increasing the freeze-drying temperature from −4 °C to 0 °C. However, when the temperature was too high, the ice crystals in the dumplings melted and collapsed, which led to a decrease in the drying rate. The selection of the appropriate shelf temperature during freeze-drying is crucial for the kinetics of drying, but it also affects the final structure of the product. In the case of some biological materials, an increase in the heating temperature decreased the freeze-dried material’s porosity [50].

In the case of changes in the pressure and shelf temperature, a variant with the highest shelf temperature and two steps in pressure change T30, P63/103 (8) had the highest drying rate (0.0028 min⁻¹) (Figure 2b). More changes in pressure 63:165:103 Pa for variant 10 caused a decrease in the drying rate compared to variant 9 with pressure changes 63_103 Pa (during the first 400 min). Variant 9 was dried longer at a lower pressure than variant 10, which increased the drying rate (Figure 2b). This is in agreement with an investigation in which the lowering of pressure from 0.5 to 0.1 mbar caused an increase in the drying rate from 5.47 to 8.40 g/h for strawberries [51]. The authors concluded that the lower the pressure, the greater the heat energy generated in the pressure chamber, which increased the amount of evaporated water from the surface of the freeze-dried tissue. A decreased pressure also caused a decrease in hardness and an increase in the porosity of freeze-dried strawberries. In our investigation, the samples obtained at the lowest pressure (variant 4) and with a small number of pressure changes (variant 8) were characterized by high drying rates.

3.2. Effect of Changes in the Set Freeze-Drying Parameters on the Material Temperature

3.2.1. Effect of Changes in the Set Shelf Temperature

The assumption of this part of the experiment was to select the most favourable shelf temperature profile, which, on the one hand, allowed for a shorter freeze-drying time, and on the other hand, ensured that the water in the material was kept in an ice state. Usually, at the beginning of the process, the evaporation surface is equal to the external surface of the material. Intercellular spaces are exposed during evaporation, which increases the evaporation surface and the sublimation rate (Figure 3). This justifies the proposal to increase the shelf temperature during sublimation (primary drying). Haseley and Oetjen [12] recommended increasing the shelf temperature during desorption. This is justified by the intensification of the desorption process. However, an increase in temperature, often associated with a decrease in pressure, can lead to the removal of bound water. This water usually acts as a stabilizer of the protein structure, and its removal can cause the deactivation of proteins. Therefore, when selecting the freeze-drying parameters, the properties of the material subjected to freeze-drying should be considered.

Figure 3 shows the changes in the material temperature during sublimation and the desorption experiments conducted at a constant or variable shelf temperature and a constant pressure of 63 Pa. When the set shelf temperature was 10 °C (T10, P63 (1), Figure 3, blue line), the material temperature changed within the range of −25 to −22 °C during the first 10 h of the process. After this time, almost 87% of the water was removed from the material (Figure 1a).

Figure 4 shows changes in the moisture ratio and temperature of the material during the freeze-drying. Based on the course of the curves, the drying times required to `reach a temperature of −2 °C (the cryoscopic temperature for apple [14]) and −10 °C (the temperature at which 85% of the water from the apple is removed [12]) were determined (

Table 6. Drying time and water content in freeze-dried apples after reaching a temperature of −10 and −2 °C in the centre of the material.

	Drying Time, min		Water Content, g Water/g d.m.
Variants	at −10 °C in the Centre of the Material	at −2 °C in the Centre of the Material	at −10 °C in the Centre of the Material	at −2 °C in the Centre of the Material
T10, P63 (1)	756 ± 3 a,*	812 ± 4 a	0.195 ± 0.002 a	0.100 ± 0.001 a
T10/30, P63 (2)	620 ± 2 b	664 ± 2 b	0.550 ± 0.010 b	0.394 ± 0.007 b
T–25/10/30A, P63 (3)	590 ± 2 c	670 ± 2 b	1.101 ± 0.007 c	0.620 ± 0.004 c
T30, P63 (4)	356 ± 1 d	458 ±1 c	1.401 ± 0.005 d	0.701 ± 0.003 d
T–25/10/30B, P63 (5)	524 ± 2 e	638 ± 3 d	1.809 ± 0.044 e	1.211 ± 0.029 e
T–25/10/20/30, P63 (6)	530 ± 2 e	744 ± 2 e	1.661 ± 0.022 f	0.891 ± 0.009 f
T10/30, P63/103/37 (7)	420 ± 2 f	554 ± 3 f	1.681 ± 0.018 f	0.874 ± 0.010 f
T30, P63/103 (8)	346 ± 1 g	404 ± 2 g	1.428 ± 0.041 d	0.998 ± 0.029 g
T–25/10/30, P63/103 (9)	624 ± 3 b	684 ± 3 h	0.477 ± 0.012 b	0.258 ± 0.007 h
T–25/10/30, P63/165/103 (10)	566 ± 2 h	696 ± 2 i	1.232 ± 0.062 g	0.594 ± 0.030 c

* Data presented as mean ± standard deviation; the different letters in the column indicate a significant difference between the parameters, p ≤ 0.05.

). The cryoscopic temperature was determined in the work of Nowak [14] by measuring it with an Osmometer (Marcel OS3000). The measurement was made for juice obtained from the same apple variety.

Reaching the cryoscopic temperature means the lack of water in the frozen state of the material. Above this temperature, sublimation can no longer occur, so it can be considered the end of the primary period. In a proper lyophilization process, there should only be desorption.

Additionally, the moisture content in material obtained at these freeze-drying times is presented in Table 6. When the cryoscopic temperature was reached after 812 min of the process, the material contained 0.100 ± 0.001 g water/g d.m. (98.2% of the water removed) (Table 6). This means that practically all free water and partly adsorbed water were removed from the material during this period. The amount of supplied heat was used entirely for sublimation and desorption, not for heating the material. The final temperature of the material was close to 20 °C, which resulted from the freeze dryer being at ambient temperature, so a specific heat flow to heat the material was taken from the environment. It should also be remembered that the ambient temperature of the freeze-dryer chamber is a few degrees lower than the temperature outside the dryer. This is an additional source of heat. Therefore, a sublimation process that is too slow does not allow for maintaining a low temperature of the material.

When the set shelf temperature was 30 °C (T30 P63 (4); Figure 3, grey line), the material temperature increased within the first 1 h to nearly −20 °C. The material reached cryoscopic temperature within the first 458 min of the process. About 13% water was still left in the material (0.701 ± 0.003 water/g d.m.) (Table 6). This amount is within the limits of the amount of adsorbed water, meaning that some ice did not melt. When the set shelf temperature increased from 10 to 30 °C within 10 h (T10/30, P63 (2); Figure 3, red line), the material temperature changed within the range of −25 to −22 °C within the first 7 h of the process and 71% of the water was removed from the material. At the time of reaching the cryoscopic temperature (after 664 min of the process), the water content in the material was about 0.394 ± 0.007 g water/g d.m. (about 93% of the water removed) (Table 6). These values also indicate that the water evaporated from the frozen state. The linear increase in shelf temperature from 10 to 30 °C within 10 h shortened the sublimation time (compared to the process T10, P63 (1) by about 20%, without disturbing the sublimation process. When the initial shelf temperature was −25 °C, and it was programmed to increase to 10 °C within the initial 5 h of the process (T–25/10/30A, P63 (3), Figure 3, brown line), the material temperature increased faster than in the case of processes (1) and (2) (markings in Table 3). This means that the heat supplied to the material was too low. The cooling effect caused by sublimation was too weak, so the material temperature increased. The temperature of −2 °C was reached after 670 ± 2 min of the process. About 11% of the initial amount of water was still in the material (0.620 ± 0.004 g water/g d.m.) (Table 6).

In the case of variant T–25/10/30B, P63 (5), the temperature profile used in the T–25/10/30A, P63 (3) experiment was modified. The time to reach the shelf temperature of 10 °C was shortened, then it was maintained at a constant level for 5 h, after which the temperature was ramped up to 30 °C and maintained at a constant level for the next 10 h of the process (Table 3). The changes in the material temperature in this experiment are shown by the green line in Figure 3. The applied modifications did not cause any beneficial changes during the course of the process. Although the cryoscopic temperature was achieved after a similar time (638 min), only a minor part of the water was removed from the material—about 80%. The average water content of 1.211 water/g d.m. suggests that some free, unadsorbed water was present in the material, which may indicate the material’s melting (Table 6). In variant 6 (T–25/10/20/30, P63 Figure 3, pink line), in which the heat supply was slowed down in the first hour of the process, the material temperature increased to −20 °C, which is higher than the equilibrium temperature corresponding to a pressure of 63 Pa. The temperature of −2 °C was reached after 744 ± 2 min. The water content in the material was 0.891 ± 0.009 g water/g d.m. (Table 6). This is relatively high, although it is within the limits specified for the end of freeze-drying [6].

The course of the curve with the material temperature changes shows a good reaction to changes in the shelf temperature in the desorption process and the possibility of influencing the final water content. After 19 h of the process, after reaching a shelf temperature of 20 °C, the average water content stabilized at 0.10 g water/g d.m. (Figure 3, Table 6). The increase in shelf temperature increased the material temperature, which reduced the water content in the material to the range of 0.04 g water/g d.m. (Table 6). This shows the possibility of controlling the final water content in the freeze-dried material.

3.2.2. Effect of Changes in the Set Pressure

The variable pressure was programmed for four selected variants of shelf temperature profiles. The effect of the pressure changes is shown in Figure 5.

In the experiment shown in Figure 5A, instead of a constant pressure of 63 Pa, a pressure of 103 Pa was set in the sublimation period and a pressure of 37 Pa in the desorption period. The increase in pressure, following the theory (Table 1), caused the material temperature to increase to −20 °C. The material reached the cryoscopic temperature after 554 ± 3 min of the process but with a higher water content of 0.874 ± 0.010 g water/g d.m. (Table 6). The decrease of the pressure in the desorption period increased the water removal rate from the material but did not affect the final water content. Increasing the pressure to 103 Pa in the experiment, in which the shelf temperature was 30 °C, did not practically affect the course of the temperature change curve (Figure 5B). The cryoscopic temperature was reached after 404 ± 2 min of the process, and the water content in the material, after this time, was about 20% higher compared to variant 4 (Table 6). However, the course of the temperature change curve showed a decrease in the material temperature due to increased pressure. This was caused by a decline in the temperature of the water vapour generated, and thus an increase in the temperature difference between the water vapour and the condenser. This increased the amount of heat used for sublimation [1]. The pressure modification practically did not affect the final water content or the final time of freeze-drying (Table 5).

An increase in the ramp pressure from 63 to 103 Pa during the first 6 h of the process (variant 9) resulted in a decrease in the material temperature to below −20 °C (Figure 5C). After 684 ± 3 min, the cryoscopic temperature was reached, with a very low water content of 0.258 ± 0.007 g water/g d.m., almost 5 times lower than the corresponding variant conducted at a constant pressure of 63 Pa (Table 6). In the following variant (10), the pressure was increased to 165 Pa, corresponding to an equilibrium temperature of −15 °C (Figure 5D). In this case, the material temperature increased during the sublimation period, compared to the corresponding variant without pressure changes, by about 6–8 °C. The amount of water removed in the period until the cryoscopic point was reached (after 696 ± 2 min) was nearly 89% of the initial amount of water, which was a similar value compared to the corresponding variant conducted at a constant pressure of 63 Pa (Table 6).

3.3. Sorption Kinetics of Freeze-Dried Apples

Figure 6 presents the changes in water content during the storage of dried apples in a constant environment with a humidity of 75.3%. The initial water content of the dried apples was similar, and after 24 h of sorption, the moisture content of the materials changed significantly, but to a different extent.

The highest water uptake, 0.337 ± 0.009 g water/g d.m. during water sorption (after 24 h of storage), was observed for variant T–25/10/30A, P63 (3). Also, variants T10/30, P63 (2) and T30, P63 (4) showed high hygroscopicity. The lowest water content (0.159 g ± 0.001 water/g d.m.) after storage was obtained for variants T–25/10/20/30, P63 (6) and T10/30, P63/103/37 (7). Variant 8 had a slightly higher water content of 0.178 ± 0.004 g water/g d.m. An increase in final shelf temperature from 10 (variant 1) to 30 °C (variant 2–5) led to an intensification of the sorption process. However, many temperature changes during the freeze-drying for variant T–25/10/20/30, P63 (6) reduced water absorption. Ohori and Yamashita [52] observed that freeze-drying of amorphous-based cake with trehalose at fast ramp cycles of temperature led to the formation of a uniform porous microstructure with lower shrinkage than for variants dried at slow ramp cycles. An increase of the temperature of the process promoted a porosity increase during the freeze-drying of grapefruit puree [47]. It can be assumed that a lower shelf temperature and slower heating with many temperature intervals could have contributed to forming a porous open structure more susceptible to water sorption. In cases of continuous changes in shelf temperature and pressure (variant 7–10), the results were not consistent. The combination of temperature and pressure parameters for variants 6, 7, and 8 resulted in lower water absorption. This may indicate greater changes in the material structure and the creation of lower porosity of the final product. Analysis of different plant tissue freeze-dried at different conditions showed that temperature, as well as pressure, affected their porosity and the size of the pores [50,53]. At low pressure, the porosity was the highest and it decreased with increasing pressure for potatoes, mushrooms, and strawberries [54].

3.4. Critical Evaluation of Applied Parameters during Freeze-Drying

The effect of freeze-drying can be assessed by various parameters. Most often, the total freeze-drying time is evaluated as the basic parameter determining the energy consumption of the process. The total process time varied considerably in the experiments, from 660 to 1305 min (Figure 7). For this reason, the most favourable experimental parameters were T30 and P63 (4).

Most of the water was removed in primary drying using the parameters T10, P63 (1), T10/30, P63 (2), and T–25/10/30, P63/103 (9). The average water content in the material at the moment of obtaining the cryoscopic temperature was 0.100 ± 0.001, 0.394 ± 0.007, and 0.258 ± 0.007 g water/g d.m., respectively. Also, during these processes, the lowest water content was found when the material reached a temperature of −10 °C (Table 6). In these processes, the desorption drying time was the shortest, accounting for 12.5 to 22% of the total freeze-drying time (Figure 7). Therefore, the above parameters should be recommended when assessing the process as the most favourable one.

When assessing the final water content, it should be stated that the obtained values ranged from 0.028 to 0.037 g water/g d.m., with the highest value obtained in experiment T10, P63 (1) (Table 5), i.e., when during the desorption period, the heat was taken from the environment and not supplied by the heating shelf.

Due to their sorption properties, the least hygroscopic were the lyophilizates from experiments T–25/10/20/30, P63 (6), T10/30, P63/103/37 (7), and T30, P63/103 (8). The other materials had almost twice the water absorption capacity (Figure 6).

The final recommendation must, therefore, refer to the assumed priority goal of the process.

4. Conclusions

In order to shorten the freeze-drying time, the most advantageous parameters among those tested were a shelf temperature of 30 °C and a pressure of 63 Pa. The freeze-dried product obtained in this experiment was very hygroscopic and had the lowest final water content. Therefore, these parameters can be recommended for freeze-drying apples and other fruits with a similar tissue structure and chemical composition when a material with good sorption properties and insensitive to intense dehydration is desired. Low shelf temperature in the primary period can result in an extension of the freeze-drying time by up to two times.

The tests and analyses showed how important the selection of appropriate process parameters (pressure in the freeze-dryer chamber and the amount of heat supplied) is for the proper freeze-drying operation. It is crucial to provide a sufficiently large amount of heat in the first hour of the sublimation process. To maintain a sufficiently low temperature of the material, a sufficiently large amount of heat necessary for the phase change must be provided. Too low a shelf temperature may limit sublimation and, consequently, increase the temperature of the material resulting from heat exchange with the environment. The freeze-drying process is susceptible to the set parameter values, especially temperature. A change of these parameters significantly affects the process, including the freeze-drying speed, process time, and sorption properties of the obtained material. Therefore, the selection of freeze-drying parameters should also be related to the expected properties of the freeze-dried product, e.g., whether the material should hydrate quickly or whether it is essential to limit its sorption properties. It has also been shown that a controlled increase in pressure during the sublimation period can increase its intensity. By increasing the adsorption drying temperature, the final water content in the material was reduced. Therefore, when the freeze-drying material is sensitive to high dehydration, desorption drying should be carried out at an appropriately low temperature. These recommendations can be applied to plant materials with a chemical composition and structure similar to apple tissue.