Study on Kinetics and Moisture Migration Characteristics of Freeze–Thaw Pretreated Solar Hot-Air Drying of Mongolian Astragalus Slices

Abstract

This study investigated the effects of freeze–thaw pretreatment on the solar hot-air drying behavior, moisture migration, and microstructure of Mongolian Astragalus (Astragalus membranaceus var. mongholicus) slices. An L9 orthogonal design with slice thickness, diameter, air velocity, and drying temperature was used; drying kinetics, water-state distribution, and surface morphology were assessed by thin-layer models, apparent effective moisture diffusivity, LF-NMR, and SEM. The drying process showed no obvious constant-rate period and was mainly characterized by a falling-rate stage, indicating that dehydration was controlled by internal moisture migration. Freeze–thaw pretreatment redistributed the initial water fractions but did not uniformly accelerate drying; the longest drying time decreased from 130 to 100 min, showing a condition-dependent effect. Slice thickness was the dominant factor affecting the average drying rate. The preferred conditions were 1–3 mm thickness, 8–11 mm diameter, 1.0 m·s⁻¹ air velocity, and 50 °C for the control group, and 1–3 mm thickness, 11–14 mm diameter, 1.5 m·s⁻¹ air velocity, and 50 °C after freeze–thaw pretreatment. The Midilli model best fit the moisture-ratio data, and the apparent effective moisture diffusivity remained on the order of 10⁻⁹ m²·s⁻¹. LF-NMR showed that endpoint residual moisture was mainly bound water, with free water almost completely removed. SEM observations showed a looser surface with more visible pores and cracks after freeze–thaw pretreatment. Overall, freeze–thaw pretreatment mainly affected solar hot-air drying by regulating moisture migration, with effects depending on process conditions.

1. Introduction

Drying of Mongolian Astragalus (Astragalus membranaceus var. mongholicus) slices is a key link in its post-harvest processing, slicing, and storage, which directly affects storage stability, processing suitability, and product quality [1]. Mongolian Astragalus is mainly produced in northern China, especially in Inner Mongolia, where primary processing is closely associated with regional climatic and resource conditions. During drying, moisture removal from Astragalus slices becomes increasingly limited by internal diffusion as drying proceeds, which may prolong drying time and increase energy consumption [2]. Therefore, applying an appropriate pretreatment to improve internal heat and mass transfer is important for enhancing drying efficiency of Astragalus slices [3,4].

Solar hot-air drying is an environmentally friendly drying method that can utilize solar radiation resources and reduce dependence on conventional energy input [5]. For Inner Mongolia and other northern production areas with abundant solar radiation, this method has practical potential for the post-harvest processing of Mongolian Astragalus slices. However, Astragalus slices are plant tissue materials with complex internal structures, and the later stage of drying is usually controlled by internal moisture migration rather than surface evaporation alone. Thus, improving internal moisture transport is an important prerequisite for enhancing the solar hot-air drying performance of Astragalus slices [6].

In recent years, advanced green pretreatment technologies, such as pulsed electric field [7], ultrasound [8], and cold plasma [9], have been used to regulate cell membrane permeability, water distribution, and drying behavior of agricultural and food materials. Although these methods can improve moisture transfer, they generally require specialized equipment and controlled operating conditions. Compared with these technologies, freeze–thaw pretreatment may be more suitable for Mongolian Astragalus produced in cold regions, because natural low-temperature resources can be used to induce ice-crystal formation and thawing-related structural changes before solar hot-air drying.

Freeze–thaw pretreatment can affect the subsequent drying behavior by changing the cellular structure, water storage state and internal migration channels through the formation and ablation of ice crystals during the freezing and thawing process. It has been shown that this treatment can affect the drying rate, drying time and effective moisture diffusion coefficient in materials such as red dragon fruit [10], hawthorn [11], wolfberry [12], lotus root [13], onion [14], orange-fleshed sweet potato [15], apricot fruit [16], etc., but its effect is constrained by the characteristics of the material and the process conditions, and it does not always behave as a consistent promotion [17,18,19].

Meanwhile, LF-NMR has been widely used to characterize the internal moisture state and migration behavior of materials [20]. It has also been applied to the drying studies of Stropharia rugosoannulata [21], shiitake mushrooms [22], figs [23], wolfberries [24], and ginger [25], and some of them have been combined with quality indicators or modeling analyses in order to reveal the connection between moisture evolution and structural changes [26,27,28]. Nevertheless, limited information is available on how freeze–thaw pretreatment regulates the solar hot-air drying kinetics, apparent effective moisture diffusivity, moisture migration behavior, and microstructural changes of Mongolian Astragalus slices. In particular, the relationship between freeze–thaw-induced water redistribution and condition-dependent drying responses remains insufficiently clarified.

The main production areas of Mongolian Astragalus are mostly distributed in cold regions of northern China, such as Inner Mongolia, where the harvesting period is connected with the natural low-temperature period. This provides climatic conditions for low-cost pretreatment based on natural freezing and thawing. Meanwhile, this region has abundant solar radiation resources, which also provides favorable conditions for solar hot-air drying [29,30,31]. Based on these regional and process considerations, this study used Mongolian Astragalus slices as the research material and combined solar hot-air drying experiments, thin-layer drying model fitting, effective moisture diffusivity analysis, LF-NMR characterization, and scanning electron microscopy (SEM) observation to systematically investigate the effects of freeze–thaw pretreatment on drying kinetics, internal moisture migration, and microstructural characteristics. The aim was to clarify whether and how freeze–thaw pretreatment affects solar hot-air drying performance under different process conditions, thereby providing a theoretical basis for a low-cost and regionally adaptable drying process optimization of Mongolian Astragalus slices.

2. Materials and Methods

2.1. Materials

The experimental materials were fresh Mongolian astragalus, harvested from Wuchuan County, Hohhot City, Inner Mongolia Autonomous Region China (110°31′–111°53′ E, 40°47′–41°23′ N). After the samples were transported back to the laboratory, mechanically damaged, moldy and morphologically abnormal individuals were excluded, surface impurities were removed and the samples were washed with clean running water and then wiped dry with absorbent paper before slicing. No chemical disinfection was performed to avoid altering the initial moisture status and tissue structure of the samples. To ensure the consistency of the samples, Astragalus was cut into oblique slices and graded by thickness and diameter, where the thicknesses were set at 1–3, 3–5 and 5–7 mm and the diameters at 5–8, 8–11 and 11–14 mm in diameter, as shown in Figure 1. The initial moisture content of the samples was determined using the oven-drying method specified in General Rule 0832, Method 2, of the Pharmacopoeia of the People’s Republic of China (2025 edition) [32], and was expressed on a wet basis. The initial moisture content was 58.48% w.b.

2.2. Freeze–Thaw Preconditioning

The samples were subjected to freezing at −20 °C for 3 h in a programmable constant temperature and humidity test chamber (BT-225L, Shenzhen Beite Instrument Equipment Co., Ltd., Shenzhen, China), after which they were allowed to thaw at room temperature (20–23 °C) for 3 h. The freezing temperature of −20 °C was selected because it is a commonly used condition for freeze–thaw pretreatment of plant materials before drying and is also close to the winter outdoor temperature in Inner Mongolia. This setting can induce ice-crystal formation and affect tissue structure and moisture transfer, as reported in previous studies on freeze–thaw-assisted drying of plant materials [33,34]. The freezing duration of 3 h was determined by considering the slice size and the short-term low-temperature exposure that may occur during postharvest handling and transportation. The subsequent thawing at 20–23 °C for 3 h was used to allow complete thawing and thermal equilibration before drying and LF-NMR measurement. After thawing, no visible ice crystals remained in the samples, and the sample temperature was considered to be close to the ambient temperature, approximately 20–23 °C. This step was used to avoid the influence of residual ice or a low initial sample temperature on the initial water-state distribution and subsequent drying behavior. The samples with the above treatments were used as the freeze–thawed group, and the non-freeze–thawed samples were used as the control group. Immediately after the freeze–thaw treatment, the solar hot-air drying test and LF-NMR measurement were carried out to minimize changes in the initial water-state distribution and migration characteristics of the samples during the resting process.

2.3. Experimental Design of Solar Hot-Air Drying

The drying experiments were carried out on a solar hot-air drying experimental bench (WGT-01). The device was jointly developed by China National Grassland Animal Husbandry Equipment Engineering Technology Research Center and Hohhot Branch of China Academy of Agricultural Mechanization Science. The test bench was equipped with an air-volume regulation system, a temperature-control unit, a temperature and humidity monitoring system, and an online weighing system. The main technical parameters of the system included a flow measurement accuracy of ±1%, a weighing accuracy of ±0.15%, a temperature measurement accuracy of ±0.5 °C, and a relative humidity measurement accuracy of ±3%. The fan speed range was 0–2900 r·min⁻¹, the wind pressure range was 0–1460 Pa, and the matched power was 22 kW. In order to improve the stability of air velocity distribution in the drying process, the ventilation structure of the device was adjusted, and only three screen plate vents were kept as effective ventilation channels, as shown in Figure 2. Before each drying experiment, the air velocity at the sample-layer position was checked using a hot-wire anemometer (TSI 9565-P-NB, TSI Incorporated, Shoreview, MN, USA), and the air-volume regulator was adjusted until the target air velocity was reached. During drying, the relative humidity inside the drying box was monitored by the built-in humidity sensor and remained close to the laboratory ambient level, but it was not independently regulated.

The experiment was conducted in an L9(3⁴) orthogonal design with three levels for slice thickness, diameter, air velocity and temperature, and the specific scheme is shown in

Table 1. Orthogonal experimental design.

Serial Number	A (Thickness, mm)	B (Diameter, mm)	C (Air Velocity, m·s−1)	D (Temperature, °C)
1	1–3	5–8	0.5	45
2	1–3	8–11	1	50
3	1–3	11–14	1.5	55
4	3–5	5–8	1	55
5	3–5	8–11	1.5	45
6	3–5	11–14	0.5	50
7	5–7	5–8	1.5	50
8	5–7	8–11	0.5	55
9	5–7	11–14	1	45

. The L9(3⁴) orthogonal design was selected because this study involved four factors with three levels each, allowing the effects of the main drying parameters to be evaluated with fewer experimental combinations than a full-factorial design. [35] The objective of this study was to screen the main effects of the selected drying factors and to compare the drying responses of the control and freeze–thaw-treated samples under the same experimental framework, rather than to construct a response surface model or obtain a mathematical global optimum. Compared with Box–Behnken and central composite designs, which are generally used for quadratic response surface modeling, interaction analysis, and numerical optimization, the L9 orthogonal design allowed the main effects of four factors at three levels to be evaluated with a relatively small number of experimental runs. Therefore, the preferred conditions reported in this study represent the best-performing combinations among the tested factor levels, rather than a global optimum outside the investigated parameter range. A control group and a freeze–thaw group were set up for each working condition. For each drying experiment, approximately 100 g of samples were evenly spread in a single layer on a circular screen tray with a radius of 12 cm. Each working condition was repeated three times. Throughout the drying experiment, the sample mass was monitored at fixed intervals, and drying was stopped when the wet-basis moisture content fell to below 10%. Moisture ratio, drying rate, average drying rate and apparent effective moisture diffusivity were calculated based on the mass change.

2.4. Calculation of Drying Kinetic Parameters

2.4.1. Moisture Ratio and Drying Rate

Moisture ratio (MR) is used to characterize the relative change in the water content state of the sample during the drying process and is calculated as follows [36]:

$$MR={\displaystyle \frac{M_t-M_e}{M_0-M_e}}$$

(1)

where: MR denotes the moisture ratio of Astragalus slices; M₀ is the initial moisture content on a dry basis, g·g⁻¹; M_t represents the dry-basis moisture content at drying time t, g·g⁻¹; and M_e is the equilibrium moisture content expressed on a dry basis, g·g⁻¹.

The equilibrium moisture content M_e is small relative to M₀ and M_t and can be approximately neglected, so Equation (1) can be simplified as follows [37]:

$$MR={\displaystyle \frac{M_t}{M_0}}$$

(2)

The drying rate is used to characterize the rate of change in the moisture content of the sample per unit of time and is calculated as formula [38]:

$$DR={\displaystyle \frac{M_{t1}-M_{t2}}{t_2-t_1}}$$

(3)

where: DR denotes the drying rate of the sample, g·g⁻¹·min⁻¹; M_t1 and M_t2 are the dry-basis moisture contents measured at drying times t₁ and t₂, respectively, g·g⁻¹; and t₁ and t₂ are represent two drying time points (min), with t₂ > t₁.

2.4.2. Average Drying Rate

To compare the overall drying efficiency of Astragalus slices under different drying conditions, the average drying rate $\left(\overline{DR}\right)$ was calculated based on the decrease in dry-basis moisture content over the whole drying period [39]:

$$\overline{DR}={\displaystyle \frac{M_0-M_f}{t_f-t_0}}$$

(4)

where: $\overline{DR}$ denotes the average drying rate of the sample, g·g⁻¹·min⁻¹; $M_0$ and $M_f$ are the initial and final dry-basis moisture contents of the sample, respectively, g·g⁻¹; and $t_0$ and $t_f$ are the initial and final drying times, respectively, min.

2.4.3. Effective Water Diffusion Coefficient

The samples of Astragalus slices are flaky materials, and the moisture migration during the drying process mainly takes place along the thickness direction. In order to characterize the internal moisture migration ability of the sample, this paper approximates the Astragalus slices as flat materials, and calculates the apparent effective moisture diffusion coefficient based on Fick’s second law under the condition of neglecting volume contraction and assuming the diffusion coefficient to be constant [40]. Under the condition of internal diffusion control, its analytical equation can be expressed as:

$$MR={\displaystyle \frac{8}{{\pi }^2}}{\displaystyle \sum _{n=0}^{\mathrm{\infty }}}{\displaystyle \frac{1}{{\left(2n+1\right)}^2}}\mathrm{e}\mathrm{x}\mathrm{p}\left[-{\displaystyle \frac{{\left(2n+1\right)}^2{\pi }^2{D}_{eff}t}{4L^2}}\right]$$

(5)

where: D_eff is the apparent effective moisture diffusion coefficient of Astragalus slices, m²/s; L is the equivalent half-thickness of Astragalus slices, m; t is the drying time, s; and n is the number of graded terms, which is taken as a non-negative integer.

Under longer drying time conditions, only the first term of the series expansion is retained and Equation (5) can be simplified as [41]:

$$MR={\displaystyle \frac{8}{{\pi }^2}}\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{{\pi }^2{D}_{eff}t}{4L^2}}\right)$$

(6)

Taking the natural logarithm of Equation (6) and organizing it gives:

$$\mathrm{l}\mathrm{n}MR\approx \mathrm{l}\mathrm{n}{\displaystyle \frac{8}{{\pi }^2}}-{\displaystyle \frac{{\pi }^2{D}_{eff}t}{4L^2}}$$

(7)

In a linear regression of t with lnMR, where the slope of the regression line is noted as k, the apparent effective water diffusion coefficient can be expressed as:

$$D_{eff}=-{\displaystyle \frac{4L^{2}k}{{\pi }^2}}$$

(8)

This method is more widely used in the study of drying of flakes or thin layers of agricultural products, which provides insight into the evolution of internal resistance to moisture migration during drying, and is often used in the comparative analysis of the apparent effective moisture diffusion capacity under different drying conditions [42]. It should be noted that the calculated D_eff is an apparent parameter estimated from the moisture-ratio decay curve rather than a directly measured material constant. According to the calculation equation, D_eff is affected not only by the slope of the ln(MR)–time regression, but also by the square of the equivalent half-thickness (L²). Therefore, comparisons of D_eff among samples with different thicknesses should be interpreted together with MR, drying rate, average drying rate, and total drying time.

2.5. Thin Layer Drying Model Fitting

In order to characterize the changes in moisture ratio with drying time during solar-hot-air drying of Astragalus slices, the study used four typical thin-layer drying models to fit the experimental data nonlinearly, and the specific model forms are listed in

Table 2. Commonly used thin-layer drying models.

Model Serial Number	Model Name	Model Equation	References
1	Midilli	MR = a·exp(−ktn) + bt	[45]
2	Page	MR = exp(−ktn)	[46]
3	Henderson–Pabis	MR = a·exp(−kt)	[47]
4	Logarithmic	MR = a·exp(−kt) + c	[48]

. The fitting quality of each model was quantified using R², χ², and RMSE. Higher R² values, together with lower χ² and RMSE values, indicate greater agreement between the predicted and experimental moisture-ratio data. Comprehensive comparison of evaluation indices was used to select the most suitable drying kinetic model. The method of thin-layer drying model optimization based on the characteristics of moisture-ratio change has been widely used in the research related to solar drying and hot-air drying [43,44].

To quantitatively evaluate the fitting performance of the thin-layer drying models, the coefficient of determination (R²), chi-square (χ²), and root mean square error (RMSE) were calculated using the following equations [49]:

$$R^2=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^N}{\left(y_{\exp ,i}-y_{pre,i}\right)}^2}{{\displaystyle \sum _{i=1}^N}{\left(y_{\exp ,i}-{\overline{y}}_{\exp }\right)}^2}}$$

(9)

$${\chi }^2={\displaystyle \frac{{\displaystyle \sum _{i=1}^N}{\left(y_{\exp ,i}-y_{pre,i}\right)}^2}{N-z}}$$

(10)

$$RMSE={\left[{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}{\left(y_{pre,i}-y_{\exp ,i}\right)}^2\right]}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$$

(11)

where y_exp,i and y_pre,i denote the experimental and predicted values of the ith observation point, respectively; ȳ_exp denotes the mean of the experimental values; N denotes the number of observation points; and z denotes the number of model constants. In the thin-layer drying model fitting, the fitting variable is moisture ratio (MR); and in the linear regression used to calculate the effective moisture diffusion coefficient D_eff, the fitting variable is lnMR. Generally speaking, the higher R², the lower χ² and RMSE, which indicates better agreement between predicted and experimental values. Therefore, this paper evaluates the quality of fit of the thin-layer drying model fit and the linear regression used to estimate D_eff according to Equations (9)–(11).

2.6. LF-NMR Test Methods

The internal moisture status of Astragalus slices was determined using a low-field nuclear magnetic resonance (NMR) instrument (Minispec LF90, Bruker BioSpin GmbH, Rheinstetten, Germany). The samples were loaded into special NMR tubes and the T₂ relaxation signals were collected at room temperature. The internal water status of the samples was characterized according to the T₂ relaxation time distribution, where T₂₁ (0.01–10 ms), T₂₂ (10–100 ms), and T₂₃ (100–10,000 ms) corresponded to bound water, weakly bound water, and free water, respectively. Combining the T₂ spectrum peak location, distribution characteristics and peak area ratio of each interval of the samples with different treatments, we analyzed the effects of freeze–thaw pretreatment on the internal water state and moisture state and migration characteristics of Astragalus slices [50].

2.7. SEM Observation

To further examine the effect of freeze–thaw pretreatment on the microstructure of Astragalus slices, scanning electron microscopy (SEM) was performed after drying. Since the Astragalus slices were relatively small, the dried samples from the control and freeze–thaw groups were directly mounted on SEM specimen stubs using conductive adhesive tape without further cutting. The naturally exposed surface of the slices was selected for observation to compare the microstructural differences between the two groups. Before SEM observation, the samples were sputter-coated with gold using a GVC-2000P ion sputtering coater (Shanghai Hezao Electronic Technology Co., Ltd., Shanghai, China). The surface microstructure was then observed using a JSM-6510 scanning electron microscope (JEOL Ltd., Tokyo, Japan). Representative micrographs were obtained to compare the differences in surface morphology, pore structure, cracks, and tissue integrity between the control and freeze–thaw pretreated samples.

2.8. Experimental Data Processing and Statistical Analysis

All the experiments were set up with three parallel replications, and the results were analyzed by taking their average values. The moisture ratio, drying rate, average drying rate and effective moisture diffusion coefficient were calculated according to the dynamic changes of sample mass during the drying process. Python 3.8 was used to conduct nonlinear fitting of the thin-layer drying models and to estimate the corresponding model parameters. The fitting performance was assessed comprehensively based on R², χ², and RMSE. Excel 2021 was used for data collation, while Origin 2024 was employed for graphical presentation.

3. Results

3.1. Drying Characterization

3.1.1. Changes in Moisture Ratio

Under different process combinations, the moisture ratios of Astragalus slices in both the control group and the freeze–thaw group decreased continuously with the prolongation of drying time, and the overall performance was characterized by a faster decline in the early stage and a gradual slowdown in the later stage, as shown in Figure 3. The error bars represent the standard deviations of three repeated measurements, providing a visual indication of the repeatability of the drying experiments. This MR trend was consistent with a drying process dominated by a falling-rate period, which was further supported by the subsequent drying-rate analysis. In the later stage of drying, moisture removal was mainly limited by the internal moisture migration capacity. Differences in curve trends and drying endpoints between different experimental groups indicate that the way thickness, diameter, air velocity and temperature are combined affected the dehydration behavior of the samples.

In the control group, the moisture-ratio curves corresponding to each process combination were more obviously differentiated, with Experiment 1 and Experiment 2 decreasing faster and reaching the drying endpoint earlier, while Experiment 9 had the slowest decrease and the longest drying time, reflecting that thinner slices and better heat and mass-transfer conditions were more favorable to the dehydration of the samples.

Compared with the control group, the changes in the moisture ratios of the experimental combinations after freeze–thaw treatment did not show a consistent promoting effect, but showed an obvious condition-dependence, with some combinations showing an accelerated drying process after freeze–thawing and some experiencing a delayed process, which suggests that the effect of freeze–thaw pretreatment on the drying behavior of Astragalus slices was not simply enhanced or weakened, but depended on the matching relationship between the sample state and the process parameters.

For the treatment with the longest drying duration, the time required for Experiment 9 to reach the drying endpoint was shortened from approximately 130 min in the control group to approximately 100 min after freeze–thaw pretreatment, indicating that freeze–thaw pretreatment could shorten the total drying time under specific process conditions. Overall, the effect of freeze–thaw pretreatment on the mid- to late-stage dehydration behavior was more apparent, indicating that it affects the drying process mainly by regulating the internal mass-transfer conditions rather than simply increasing the rate of water loss in the early stage.

3.1.2. Changing Law of Drying Rate

In order to reveal the stage-by-stage water loss characteristics of Astragalus slices in the process of solar hot-air drying, the change rule of drying rate with time was analyzed under different experimental combinations, and the results are shown in Figure 4. The drying rates of both the control group and the freeze–thaw group samples rapidly increased and peaked at the early stage of drying, and then continued to decline, and overall there did not appear to be an obvious constant speed drying stage, indicating that the solar hot-air drying process of Astragalus slices was dominated by the falling-rate period, and the later dehydration was mainly limited by internal moisture migration.

As can be seen from the comparison between the different treatments, the freeze–thaw pretreatment did not show a consistent enhancement of the peak drying rate, and only Experiments 7 and 9 showed a slight increase after freeze–thaw, while Experiments 5 and 6 showed a more pronounced decrease, suggesting that its effect on the initial transient water loss capacity was significantly condition-dependent.

In contrast, the freeze–thaw treatment regulated the mid- to late-stage drying rate decay more clearly in most experimental combinations, with a relatively gentle and less fluctuating curve decline, suggesting that the freeze–thaw action was not mainly to enhance the pre-surface evaporation but to regulate the water loss process in the rate reduction stage by improving the internal water migration path and alleviating the mass-transfer resistance in the late stage.

The effect of freeze–thaw pretreatment on the change rule of drying rate of Astragalus slices is mainly reflected in the middle and late stage of rate reduction, rather than the initial peak stage, and its role is essentially manifested in the stage of internal moisture redistribution and mass-transfer process regulation.

3.1.3. Average Drying Rate and Orthogonal Analysis

The average drying rate was used as an indicator to compare the overall moisture removal performance of Astragalus slices under different process combinations in the control and freeze–thaw groups. The average drying rate represents the mean decrease in dry-basis moisture content per unit drying time over the whole drying process. As an integrated indicator covering the whole drying process, the average drying rate reflects the combined heat and mass-transfer performance of the samples and helps characterize how freeze–thaw pretreatment influences solar hot-air drying behavior.

As can be seen from

Table 3. Average drying rates of Astragalus slices in the control and freeze–thaw groups.

Serial Number	Thickness (mm)	Diameter (mm)	Air Velocity (m·s−1)	Temperature (°C)	Control Group (g·g−1·min−1)	Freeze–Thaw Group (g·g−1·min−1)
1	1–3	5–8	0.5	45	0.05317 ± 0.00076	0.05051 ± 0.00244
2	1–3	8–11	1	50	0.08560 ± 0.00049	0.08422 ± 0.01000
3	1–3	11–14	1.5	55	0.07231 ± 0.01431	0.08615 ± 0.00429
4	3–5	5–8	1	55	0.02963 ± 0.00003	0.01766 ± 0.00248
5	3–5	8–11	1.5	45	0.02376 ± 0.00028	0.01321 ± 0.00051
6	3–5	11–14	0.5	50	0.02287 ± 0.00087	0.01955 ± 0.00061
7	5–7	5–8	1.5	50	0.01467 ± 0.00018	0.01625 ± 0.00128
8	5–7	8–11	0.5	55	0.01477 ± 0.00012	0.01353 ± 0.00009
9	5–7	11–14	1	45	0.01007 ± 0.00006	0.01245 ± 0.00060

Note: Values are presented as mean ± standard deviation (n = 3).

, the average drying rates of Astragalus slices in the control and freeze–thaw groups varied among the nine process combinations, indicating that the combinations of thickness, diameter, air velocity, and temperature affected the overall water loss efficiency of the samples. The values ranged from 0.01007 to 0.08560 g·g⁻¹·min⁻¹ in the control group and from 0.01245 to 0.08615 g·g⁻¹·min⁻¹ in the freeze–thaw group, showing clear numerical variations among different treatments.

The variation ranges of the average drying rate of different treatment groups were generally close to each other, but the response trends under each experimental combination were not consistent, indicating that the freeze–thaw pretreatment did not simply produce a uniform increase in the average drying rate of Astragalus slices, but changed the response pattern of the samples to process parameters.

The average drying rate was higher for combinations with smaller thicknesses and lower overall for combinations with larger thicknesses, suggesting that thickness is a key factor limiting the dehydration efficiency of Astragalus slices. The statistical contribution of each factor was further evaluated by orthogonal range analysis and ANOVA in the subsequent analysis.

In order to clarify the degree of influence of each factor on the average drying rate, the control group and the freeze–thaw group were analyzed by polar analysis, and the results are shown in

Table 4. Extreme variance analysis results.

Preprocessing		A	B	C	D
Control group	K1	0.07036	0.03249	0.03027	0.029
	K2	0.02542	0.041377	0.041767	0.041047
	K3	0.01317	0.035083	0.036913	0.038903
	R	0.05719	0.008887	0.011497	0.012047
Freeze–thaw group	K1	0.073627	0.02814	0.027863	0.025390
	K2	0.016807	0.036987	0.03811	0.040007
	K3	0.014077	0.039383	0.038537	0.039113
	R	0.05955	0.011243	0.010673	0.014617

Note: A, B, C and D represent thickness, diameter, air velocity and temperature, respectively. K1, K2 and K3 represent the mean values of the average drying rate at levels 1, 2 and 3 of each factor, respectively; R represents the range value, calculated as the difference between the maximum and minimum K values.

. In different treatment groups, the K value and R value of each factor at different levels differed, among which the R value of factor A was always the largest, indicating that the thickness was the dominant factor influencing the average drying rate of the Astragalus slices. In contrast, factors B, C and D are less influential than factor A. However, their order of action varied between the two treatments, with the order of influence being A > D > C > B in the control group and A > D > B > C in the freeze–thaw group, suggesting that the freeze–thaw pretreatment did not change the predominance of thickness, but altered the relative contributions of diameter, air velocity and temperature to the mean drying rate, particularly enhancing the moderating effect of the diameter factor. The optimal level combinations of the two treatment groups were A₁B₂C₂D₂ and A₁B₃C₃D₂, respectively, further indicating that freeze–thawing changed the response characteristics of Astragalus slices to external process parameters.

The results of ANOVA were generally consistent with the conclusions of the extreme variance analysis, as shown in

Table 5. ANOVA results.

Preprocessing	Factors	SS	df	MS	F	Significance
Control group	A	0.016321	2	0.008161	206.87	**
	B	0.000376	2	—	—	—
	C	0.000600	2	0.0003	7.60	**
	D	0.000744	2	0.000372	9.43	**
	error	0.000789	20	3.945 × 10−5	—	—
Freeze–thaw group	A	0.020347	2	0.010174	686.62	**
	B	0.000631	2	0.000316	21.31	**
	C	0.000657	2	0.000329	22.18	**
	D	0.001208	2	0.000604	40.76	**
	error	0.000267	18	1.48 × 10−5	—	—

Note: SS, df, MS and F denote the sum of squares, degrees of freedom, mean square and F-value, respectively; “—” indicates not applicable. ** denotes a highly significant effect at p < 0.01. In the control group, factor B had a relatively small effect and was incorporated into the error term for ANOVA.

. In the control group, factors A, C and D all reached highly significant levels, with factor A having the highest F-value, indicating that thickness was still the dominant factor influencing the average drying rate of Astragalus slices, while the role of factor B was relatively weak. In the freeze–thaw group, factors A, B, C and D all reached highly significant levels, with factor A still dominating, but factor B shifted from a weak to a highly significant role, indicating that the freeze–thaw pretreatment significantly enhanced the moderating effect of the diameter factor on the mean drying rate. The freeze–thaw treatment did not change the dominant control of thickness on average drying rate, but reinforced the effect of structural scale differences on the drying process under different diameter conditions.

As can be seen in Figure 5, the main effect curves for factor A showed a marked downward trend in both treatment groups, again indicating that thickness was the primary determinant of average drying rate. In the control group, factors B, C and D performed better around the intermediate level, while in the freeze–thaw group, factor B maintained a higher response at a higher level, and the optimal response intervals of factors C and D were also shifted. This suggests that freeze–thaw pretreatment altered the adaptability of Astragalus slices to diameter, air velocity and temperature conditions and resulted in a more pronounced parameter-matched characterization of their drying behavior.

3.2. Thin-Layer Drying Kinetic Model Fitting and Optimal Model Checking

3.2.1. Model Fitting Results and Optimal Model Screening

The moisture-ratio curves of Astragalus slices during solar hot-air drying were analyzed using four thin-layer drying models, including Midilli, Page, Henderson–Pabis, and Logarithmic. These four models were selected because they are commonly used empirical or semi-empirical models in thin-layer drying studies and can describe nonlinear moisture-ratio changes with different model structures and parameter forms. These models were separately applied to the nine experimental datasets obtained from the control and freeze–thaw groups.

The results summarized in

Table 6. Thin layer drying model fitting results for control and freeze–thaw groups.

Model	Experiment	Control Group			Freeze–Thaw Group
		R2	χ2	RMSE	R2	χ2	RMSE
Midilli	1	0.99988	0.00007	0.00366	0.99797	0.0012	0.01547
	2	0.99855	0.00072	0.01196	0.99876	0.00052	0.01016
	3	0.99996	0.00002	0.002	0.99892	0.00047	0.00971
	4	0.99929	0.00012	0.00816	0.99977	0.00002	0.00424
	5	0.99975	0.00003	0.00463	0.99986	0.00001	0.00325
	6	0.99964	0.00005	0.00561	0.9998	0.00002	0.00408
	7	0.99979	0.00002	0.00391	0.9999	0.00001	0.00263
	8	0.99984	0.00002	0.00359	0.9999	0.00001	0.00287
	9	0.99973	0.00002	0.00446	0.99989	0.00001	0.00281
	Mean	0.9997	0.00005	0.00486	0.99958	0.00018	0.00505
Page	1	0.99705	0.00054	0.01797	0.99796	0.0004	0.01551
	2	0.99908	0.00037	0.01104	0.9993	0.00023	0.00882
	3	0.9963	0.00092	0.02143	0.99928	0.00025	0.00917
	4	0.9978	0.00027	0.01436	0.99345	0.00059	0.02258
	5	0.9932	0.00072	0.02419	0.9961	0.00034	0.01745
	6	0.99496	0.00052	0.02082	0.99184	0.00082	0.02639
	7	0.99494	0.00042	0.01941	0.99412	0.00049	0.02066
	8	0.99304	0.00062	0.02336	0.99486	0.00047	0.02044
	9	0.99359	0.00051	0.02171	0.99349	0.00054	0.02203
	Mean	0.99555	0.00054	0.01937	0.9956	0.00046	0.01812
Henderson–Pabis	1	0.98989	0.00185	0.03328	0.98823	0.00232	0.03728
	2	0.99066	0.0037	0.03513	0.9942	0.00195	0.02546
	3	0.99502	0.00124	0.02486	0.99141	0.00302	0.03175
	4	0.9969	0.00037	0.01704	0.99383	0.00055	0.02192
	5	0.99228	0.00081	0.02579	0.99618	0.00033	0.01727
	6	0.99413	0.00061	0.02248	0.98857	0.00115	0.03123
	7	0.99518	0.0004	0.01893	0.99223	0.00064	0.02375
	8	0.99315	0.00061	0.02317	0.99341	0.0006	0.02313
	9	0.9943	0.00045	0.02048	0.99398	0.0005	0.02118
	Mean	0.9935	0.00112	0.02457	0.99245	0.00123	0.02589
Logarithmic	1	0.99977	0.00006	0.00504	0.99599	0.00118	0.02176
	2	0.99778	0.00055	0.01481	0.99821	0.00037	0.01221
	3	0.99721	0.00139	0.01862	0.99848	0.00033	0.01155
	4	0.999	0.00014	0.0097	0.99536	0.00045	0.01901
	5	0.99772	0.00027	0.014	0.99831	0.00016	0.01148
	6	0.99843	0.00018	0.01163	0.9984	0.00018	0.01169
	7	0.99602	0.00036	0.01721	0.99227	0.00069	0.02368
	8	0.99689	0.0003	0.0156	0.99904	0.00009	0.00884
	9	0.99759	0.0002	0.01331	0.99626	0.00033	0.01669
	Mean	0.99783	0.00036	0.01314	0.99652	0.00044	0.01616

Note: R² denotes the coefficient of determination, χ² denotes the chi-square value, and RMSE denotes the root mean square error. The fitting indices in Table 6 were calculated based on the mean moisture-ratio values of three independent replicates under each experimental condition. Therefore, each value represents the goodness of fit of the averaged drying curve rather than a direct replicate measurement. The standard deviations of the experimental drying data are presented by error bars in the corresponding figures.

indicate that the four selected thin-layer drying models could effectively characterize the moisture-ratio variation of Astragalus slices during drying solar hot-air drying, suggesting good agreement with the experimental data. Considering R², χ², and RMSE together, the Midilli model exhibited the best fitting performance in both the control and freeze–thaw groups. For the control group, the Midilli model yielded average R² and RMSE values of 0.99970 and 0.00486, respectively, while the corresponding values for the freeze–thaw group were 0.99958 and 0.00505. These results were superior to those obtained with the Page, Henderson–Pabis, and Logarithmic models, indicating that the Midilli model was more appropriate for describing the solar hot-air drying behavior of Astragalus slices. The Midilli model is more suitable for characterizing the nonlinear water loss process of Astragalus slices under solar hot-air drying conditions.

Freeze–thaw pretreatment did not change the type of optimal model, and in this paper the optimal model for both treatment groups was the Midilli model, indicating that the freeze–thaw effect mainly affected the drying parameter response and the water loss process without changing the basic descriptive framework of the drying kinetics of Astragalus slices. Therefore, this paper recommends that the Midilli model can be selected subsequently for further characterization and prediction of the solar hot-air drying process of Astragalus slices.

3.2.2. Tests of the Effectiveness of the Optimal Model Fit

The predictive performance of the optimal model was further examined by comparing the Midilli-predicted moisture ratios with the corresponding experimental values during solar hot-air drying of Astragalus slices, as shown in Figure 6 The Midilli model showed close agreement with the experimental data for both the control and freeze–thaw groups, indicating its ability to accurately describe the time-dependent variation in MR during the drying of Astragalus slices. The model effectively captured both the sharp decrease in MR at the initial stage and the subsequent gradual reduction in the drying rate during the middle and later stages.

Comparing the two treatment groups, it can be seen that although the difference in drying response between the different process combinations after freeze–thaw pretreatment was more obvious, the Midilli model was still able to fit the experimental data of each group stably and did not show obvious systematic bias. Combined with Table 6 and Figure 6, it can be seen that the Midilli model has high fitting accuracy and good applicability in both treatment groups, and can be used as the optimal thin-layer drying kinetic model to characterize the solar hot-air drying process of Astragalus slices.

3.3. Analysis of Apparent Effective Moisture Diffusivity

As can be seen from

Table 7. Effective water diffusion coefficients of control and freeze–thaw groups.

Experiment	Control Group				Freeze–Thaw Group
	Deff (×10−9 m2·s−1)	R2	χ2	RMSE	Deff (×10−9 m2·s−1)	R2	χ2	RMSE
1	1.00338 ± 0.02031	0.95902	0.05898	0.17168	1.05033 ± 0.03020	0.97244	0.04837	0.15877
2	1.41860 ± 0.02515	0.98742	0.02813	0.09678	1.09795 ± 0.06807	0.99051	0.01369	0.07162
3	1.19193 ± 0.11636	0.98464	0.03157	0.10271	1.20478 ± 0.03894	0.99008	0.01591	0.07257
4	1.72008 ± 0.02215	0.99843	0.00048	0.01646	0.98440 ± 0.07504	0.99938	0.00012	0.00906
5	1.23090 ± 0.00663	0.99592	0.00093	0.02442	0.77769 ± 0.00989	0.99916	0.00015	0.01072
6	1.21800 ± 0.02446	0.99732	0.00059	0.01982	1.03933 ± 0.01222	0.99649	0.00073	0.02237
7	1.90530 ± 0.03851	0.99789	0.00044	0.01834	1.97167 ± 0.13752	0.99844	0.00033	0.01567
8	1.83849 ± 0.03189	0.99784	0.00040	0.01750	1.71912 ± 0.02047	0.99777	0.00042	0.01790
9	1.32122 ± 0.02692	0.9984	0.00029	0.01487	1.58814 ± 0.09493	0.99923	0.00013	0.00948

Note: D_eff values are expressed as mean ± SD (n = 3, ×10⁻⁹ m²·s⁻¹). R², χ², and RMSE were obtained from the linear regression of ln(MR) versus drying time.

, the apparent effective moisture diffusion coefficients of Astragalus slices in both control and freeze–thaw groups were in the order of 10⁻⁹ m²/s, indicating that both groups of samples were dominated by internal diffusion mass transfer in the drying process. D_eff ranged from 1.00338 × 10⁻⁹ to 1.90530 × 10⁻⁹ m²·s⁻¹ in the control group and 0.77769 × 10⁻⁹ to 1.97167 × 10⁻⁹ m²·s⁻¹ in the freeze–thaw group, which indicated that there were clear differences in the internal water migration capacity of the samples under the different combinations of processes. To further evaluate the reliability of D_eff estimation, the fitting indices of the linear regression between lnMR and drying time were added in Table 7. Except for Experiment 1 in both groups, the R² values were higher than 0.98, and the corresponding χ² and RMSE values were generally low, indicating that the linear fitting used for the D_eff calculation was acceptable.

The maximum values of both groups appeared in Experiment 7, with D_eff values of 1.90530 × 10⁻⁹ m²·s⁻¹ and 1.97167 × 10⁻⁹ m²·s⁻¹ in control and freeze–thaw groups, respectively, and the minimum values appeared in Experiments 1 and 4, respectively. The relatively high D_eff in Experiment 7 did not mean that thicker slices had higher overall drying efficiency. D_eff was estimated from the ln(MR)–time regression based on the slab model and was affected by both the regression slope and the square of the equivalent half-thickness. Therefore, a higher apparent D_eff may occur in thicker slices under specific combinations of sample size and drying conditions. In Experiment 7, the larger thickness was combined with a smaller diameter and higher air velocity, which may have promoted moisture-ratio decay during the falling-rate stage.

In contrast, drying rate and average drying rate directly describe the overall moisture removal rate and are more strongly affected by diffusion path length and total drying time. Therefore, the trends in drying rate and apparent D_eff were not completely consistent.

Further comparison of the same process combinations showed that freeze–thaw pretreatment did not increase D_eff under all conditions; D_eff was higher than that of the control group only in Experiments 1, 3, 7 and 9, whereas it decreased in the remaining combinations. It indicates that the effect of freeze–thawing on the internal diffusion ability of Astragalus slices has obvious condition-dependence, and its effect depends on the matching relationship between the organizational state of the samples and the external drying parameters.

Combined with the moisture ratio, average drying rate and drying rate change rule, it can be seen that the freeze–thaw pretreatment did not change the basic characteristics of the drying process of Astragalus slices, which was mainly controlled by internal diffusion, but through the regulation of the internal tissue structure and moisture storage state, it changed the mass-transfer ability of the sample and its response to the external process conditions.

3.4. LF-NMR Characterization of Moisture Migration

3.4.1. Initial Moisture State Before Drying

Before the start of drying, the T₂ relaxation signals of samples with different diameters of Astragalus slices were mainly concentrated in the T₂₂ region, indicating that the initial moisture of the samples was dominated by weakly bound water, as shown in Figure 7. The largely overlapping main peak regions observed in the control and freeze–thaw groups indicate that freeze–thaw pretreatment did not fundamentally change the initial moisture distribution pattern of Astragalus slices, which was still mainly characterized by weakly bound water. Nevertheless, the treatment modified the proportional distribution among different water fractions.

In the control group, samples of different diameters showed some differences in initial water storage, with a relatively high proportion of bound water in the 5–8 mm group, a high proportion of free water in the 8–11 mm group, and an in-between proportion of free water in the 11–14 mm group, suggesting that the change in sample size has affected the water storage status within the Astragalus slices. This indicates that the change in sample size has affected the internal water storage status of Astragalus slices. After the freeze–thaw treatment, the main peak of T₂ in each diameter group is still located in the T₂₂ zone, but the proportion was redistributed, mainly in the form of a decrease in the proportion of bound water and an increase in the proportion of weakly bound water, while the change in free water is relatively limited. This result suggests that the effect of freeze–thawing on the initial moisture state of Astragalus slices is mainly reflected in the redistribution of water among existing moisture states rather than the fundamental change in the dominant moisture type. The freeze–thaw pretreatment may reshape the mass-transfer basis at the initiation stage of drying by altering the internal local structure and moisture distribution characteristics of the samples, and further influence the subsequent moisture migration behavior.

3.4.2. Moisture Distribution at the Drying Endpoint

In order to evaluate the residual moisture status inside the Astragalus slices at the drying endpoint, the LF-NMR T₂ relaxation characteristics and the ratio of the peak area of each moisture component of the samples with different diameters at the drying endpoint were analyzed, and the results are shown in Figure 8.

The T₂ relaxation peaks of each group of samples at the end of drying were mainly distributed in the short relaxation time interval, and the main peaks were concentrated in the region of bound water. The weakly bound water signal was weak, and the free water signal nearly disappeared, which indicated that most of the migratable water in the samples had been removed after the solar hot-air drying, and the residual water mainly existed in the form of bound water. Compared with the initial state, the T₂ spectra of all groups became more similar, indicating that the differences in the initial water storage between samples of different treatments and diameters were significantly weakened at the end of the drying period, as shown in Figure 8a. Further combined with Figure 8b, it can be seen that the proportion of bound water in each group of samples was 96–97%, the weakly bound water only accounted for 2–4%, and the free water was close to 0, and there were only slight fluctuations between different treatments and different diameters, indicating that the residual moisture composition of Astragalus slices generally converged after reaching the same drying endpoint. It can be seen that the freeze–thaw pretreatment did not change the basic pattern of residual moisture at the end of drying. Its effect was mainly reflected in regulating moisture migration behavior during drying, especially during the middle and late stages of mass transfer, rather than changing the final residual moisture composition.

3.5. SEM Characterization of Dried Astragalus Slices

To provide supplementary morphological evidence for the effect of freeze–thaw pretreatment on moisture migration and mass-transfer behavior, SEM observations were conducted on representative matched dried samples from the orthogonal experiment. The SEM analysis was not used as an independent evaluation of the effect of slice size, but was intended to compare the microstructural differences between the control and freeze–thaw groups under matched treatment combinations. Therefore, samples with the same diameter level of 8–11 mm were selected to reduce the influence of slice diameter on microstructural observation. For each matched pair, the control and freeze–thaw-treated samples had the same slice size and drying parameters, except for freeze–thaw pretreatment. The microstructures were observed at 500× magnification, and the results are shown in Figure 9.

The SEM micrographs showed that the dried samples in the control group generally exhibited a relatively compact surface morphology, with local shrinkage and fewer visible cracks or pores. In contrast, the freeze–thaw-treated samples showed a looser tissue structure, with more evident cracks, pores, and discontinuous surface morphology. These structural differences may be related to ice crystal formation and melting during freeze–thaw pretreatment, which could partially disrupt tissue continuity and provide additional pathways for moisture migration. Therefore, the SEM results provide supplementary morphological evidence that freeze–thaw pretreatment affected the drying behavior of Astragalus slices by modifying the microstructure and internal mass-transfer channels. However, this comparison was based on representative matched samples and should not be interpreted as an independent analysis of the effect of slice size.

4. Discussion

Igbozulike et al. [51] reported that drying process variables affected the effective moisture diffusivity and activation energy of African oil bean seeds, indicating that the dehydration of plant materials is controlled not only by external temperature and air-flow conditions but also by internal moisture migration. Gonzalez-Camacho et al. [52] also used Fick’s diffusion model to describe moisture migration within beetroot slices. Compared with these seed or fruit-and-vegetable slice materials, Mongolian Astragalus is a root-type medicinal plant with more complex vascular tissues, fibers, and cell wall structures. Therefore, the internal moisture migration pathway and tissue compactness may exert a stronger limitation on the drying process. Accordingly, the solar hot-air drying behavior of Astragalus slices should not be explained only by external heat supply, but should also be interpreted in relation to sample geometry and internal diffusion resistance.

From the perspective of process factors, the effect of freeze–thaw pretreatment on the drying behavior of Astragalus slices should not be simply regarded as direct drying acceleration, but rather as a regulation of internal mass-transfer pathways. Liu et al. [53] found that contact ultrasound-assisted hot-air drying affected the drying characteristics and quality attributes of Sichuan pepper by modifying its microstructure. Ye et al. [54] also indicated that changes in cell wall structure and water distribution influenced the drying quality of asparagus lettuce. Unlike ultrasound and other externally applied physical fields, freeze–thaw pretreatment mainly depends on cell damage, pore formation, and tissue loosening induced by ice crystal formation and melting. Moderate structural disturbance may help reduce internal diffusion resistance during the middle and later drying stages; however, when sample size, air-flow rate, and temperature are not well matched, local collapse, shrinkage, or uneven moisture redistribution may also occur. Therefore, the preferred combinations obtained from the L9 orthogonal design should be interpreted as optimized results within the selected factor levels, rather than absolute optima in the sense of response surface optimization.

The applicability of thin-layer models should also be interpreted in relation to material properties and drying conditions. Stephenus et al. [55] reported that drying temperature affected drying rate, model parameters, and quality retention during the drying of plant materials, indicating that model applicability is closely associated with material type and drying method. Therefore, the Midilli model can be considered suitable for describing the nonlinear changes in the moisture ratio of Mongolian Astragalus slices within the experimental range of this study, but it should not be generalized as the universally optimal model for all Astragalus drying methods or processing conditions. The model-fitting results mainly reflect the moisture-ratio variation under the specific combination of sample size, freeze–thaw condition, air-flow rate, and drying temperature used in this work, rather than a universal judgment for all processing scenarios.

The inconsistent trends between effective moisture diffusivity and drying rate do not indicate contradictory results. DR reflects the actual moisture removal capacity per unit time and is influenced by sample thickness, exposed surface area, moisture state, and total drying time. In contrast, D_eff is an apparent parameter estimated from the ln(MR)–t fitting based on Fick’s diffusion assumption, and its value is also affected by the square of the equivalent half-thickness, the selected fitting range, and tissue heterogeneity. Therefore, some thicker slices may show relatively higher apparent D_eff values due to the thickness term or local diffusion-channel changes, but this does not necessarily mean higher overall drying efficiency. D_eff is more appropriate for characterizing internal moisture migration capacity under model assumptions and should be interpreted together with MR curves, DR, average drying rate, and drying time.

LF-NMR and SEM analyses further help explain the effect of freeze–thaw pretreatment on moisture migration pathways. Yi et al. [56] used LF-NMR to analyze moisture migration and distribution during nut drying, demonstrating that changes in different water states can reflect internal mass-transfer behavior in plant materials. Zhou et al. [57] further combined LF-NMR with structural and quality changes during black tea drying, showing that moisture migration behavior is closely related to tissue status. Yue et al. [58] also emphasized that heat and mass transfer during Astragalus root drying were associated with tissue structure and water distribution. Based on these findings, the effect of freeze–thaw pretreatment on Mongolian Astragalus slices should be understood as the modification of tissue structure and water state through ice-crystal damage, thereby affecting mass-transfer resistance during the middle and later drying stages, rather than simply changing the residual moisture composition at the drying endpoint.

In addition, solar radiation input, fan power, auxiliary heating energy consumption, freeze–thaw energy consumption, and specific energy consumption were not recorded in real time in this study. Therefore, it is not possible to directly determine whether the combined freeze–thaw and solar hot-air drying process reduced the total energy consumption. The shortened drying time observed under some treatment conditions only suggests the potential to reduce energy consumption during the drying stage, whereas whether the freeze–thaw process itself increases the overall energy input still requires further verification. Future studies should combine energy/exergy analysis, quality evaluation, and scale-up experiments to further assess the comprehensive applicability of this combined drying strategy in terms of efficiency, product quality, and energy utilization.

5. Conclusions

This study investigated the effects of freeze–thaw pretreatment on the solar hot-air drying behavior, moisture migration, and microstructural characteristics of sliced Mongolian astragalus. The drying process was comprehensively evaluated through solar hot-air drying experiments, L9(3⁴) orthogonal analysis, thin-layer drying kinetics model fitting, analysis of the apparent effective moisture diffusion coefficient, and LF-NMR and SEM characterization. The main conclusions are as follows:

(1)

The solar hot-air drying process of Mongolian Astragalus slices was dominated by a falling-rate period, with no distinct constant-rate drying stage observed. Freeze–thaw pretreatment did not consistently promote drying under all experimental conditions; its effect was condition-dependent. Within the range of factor levels set in this study, slice thickness was the dominant factor influencing the average drying rate. The parameter combination yielding the highest average drying rate in the control group was: thickness 1–3 mm, diameter 8–11 mm, airflow velocity 1.0 m/s, and drying temperature 50 °C; the parameter combination yielding the highest average drying rate in the freeze–thaw group was: thickness 1–3 mm, diameter 11–14 mm, airflow velocity 1.5 m/s, and drying temperature 50 °C. The above results indicate that the L9(3⁴) orthogonal design is suitable for screening the relative effects of process factors and identifying optimal combinations; however, the resulting combinations should be interpreted as preferred outcomes within the specified range of factor levels, rather than as absolute optimal parameters in the sense of global response surface optimization.

(2)

Among the four thin-layer drying models, the Midilli model best describes the variation in the moisture content of Mongolian Astragalus slices under the experimental conditions of this study. The apparent effective water diffusion coefficients for both the control group and the freeze–thaw group were in the order of 10⁻⁹ m²/s. The trend of D_eff does not always fully align with the drying rate; this is because D_eff is an apparent parameter calculated under the assumptions of a diffusion model and is influenced by factors such as sample thickness, the fitting interval, and tissue heterogeneity. Therefore, D_eff should be interpreted in conjunction with the MR curve, drying rate, average drying rate, and drying time, and should not be used alone as a basis for evaluating drying efficiency.

(3)

LF-NMR results indicate that freeze–thaw pretreatment altered the distribution of the initial water states in the samples prior to drying, but did not fundamentally change the dominant water state characteristics during the drying process. At the end of drying, the residual moisture in the samples primarily existed as bound water, while free water was essentially removed. SEM observations further indicated that freeze–thaw pretreatment altered the microstructure of the Astragalus slices, providing additional evidence for its influence on moisture migration. Overall, freeze–thaw pretreatment primarily affects the moisture migration process during the middle and late stages by altering internal mass-transfer pathways, rather than simply increasing the surface evaporation rate at the beginning of drying.

Overall, freeze–thaw pretreatment can influence the solar hot-air drying process of Astragalus mongholicus slices by modulating tissue structure and internal moisture migration pathways, demonstrating potential for application in the primary processing of medicinal materials in cold-climate production areas. However, since this study did not conduct a full-process energy consumption evaluation, its energy-saving effects still require further verification in subsequent research through energy consumption/power analysis, quality preservation assessments, and scale-up experiments.