Fresh ginger roots were washed thoroughly with distilled water to remove surface impurities, manually peeled, and sliced using a custom-made stainless-steel slicing mold to ensure uniform thicknesses of 2, 3, and 4 mm. These thicknesses were selected to represent the typical range used in commercial dried ginger products and to systematically evaluate the influence of diffusion path length on heat and mass transfer during drying. After slicing, the samples were sealed in polyethylene bags and stored at 4°C. Prior to drying experiments, all samples were equilibrated to ambient conditions (25 ± 2°C) for at least 2 h to minimize the effect of initial temperature differences on drying kinetics. The initial moisture content of fresh ginger was determined using the standard oven-drying method at 105°C until constant mass was achieved and was found to be 94.17% (wet basis). The drying endpoint for all experiments was defined as a moisture content of ≤10% on a dry basis, which is widely accepted as a safe level for the storage and handling of dried ginger products.

For each run, 30 ± 0.5 g of ginger slices were evenly spread in a single layer on an aluminum tray and dried in an electric hot air oven. Drying temperatures of 50, 60, and 70°C were selected based on preliminary experiments. Temperatures below 50°C resulted in excessively long drying times, while temperatures above 70°C led to noticeable quality deterioration, particularly excessive surface browning and color degradation. During drying, sample mass was recorded at 30 min intervals until the target moisture content (≤10% d.b.) was reached. These conditions were chosen to represent conventional industrial hot air drying practices and to provide a baseline for comparison with microwave-based drying methods.

For microwave drying experiments, 30 ± 0.5 g of ginger slices were uniformly arranged on a glass plate and placed at the center of a laboratory microwave dryer. Preliminary trials indicated that microwave powers below 200 W resulted in slow moisture removal, whereas powers above 500 W caused localized overheating, uneven moisture distribution, and structural damage due to excessive internal vapor pressure buildup. Accordingly, microwave power levels of 200, 350, and 500 W were selected for systematic evaluation. The mass of the samples was recorded at 5 min intervals until the moisture content reached ≤10% (d.b.).

For MVD experiments, 30.0 ± 0.5 g of ginger slices were evenly spread on a glass plate and dried in a microwave vacuum dryer. Sample mass was measured at 5 min intervals throughout the drying process until the target moisture content was achieved. Preliminary tests demonstrated that vacuum levels lower than 0.02 MPa provided limited enhancement compared to atmospheric microwave drying, whereas a vacuum level of 0.08 MPa significantly promoted moisture removal by reducing the boiling point of water and enhancing internal vapor-driven mass transfer, while remaining within the safe operating range of the equipment. Therefore, vacuum degrees of 0.02, 0.05, and 0.08 MPa were selected.

To investigate the individual effects of key MVD parameters, initial single-factor experiments were conducted under the following conditions: (1)

Microwave power: 200, 350, and 500 W at a fixed vacuum of 0.05 MPa and slice thickness of 3 mm;

Given the strong coupling between microwave power, vacuum degree, and material geometry in MVD which leads to nonlinear heat and mass transfer behavior, response surface methodology (RSM) was employed to model and optimize the drying process. The experimental design and factor levels used in the RSM are presented in Table 1. All experiments were conducted in triplicate, and the average values were reported. The measurement uncertainties associated with key experimental parameters are summarized in Table 2.

(1)Mt=mt−mcmc×100%where m_t is the mass at time t, m_c is the mass of the dry sample.

The moisture ratio MR was calculated as: (2)MR=M−MeM0−Me

Since M_e is very small compared to M_t and M₀ and can be neglected, the above formula can be simplified to: (3)MR=MtM0×100%where M_t is the moisture content of the material at any time t, M₀ is the initial moisture content of the material, M_e is the equilibrium moisture content of the material.

(4)DR=ΔMΔt=Mt−Mt+ΔtΔtwhere ΔM is the difference in moisture content between adjacent samples, Δt represents the time gap between successive measurements of sample weight.

To quantitatively assess the energy utilization efficiency of different drying technologies, Specific Energy Consumption (SEC) was introduced as a key evaluation metric. SEC is defined as the electrical energy consumed to evaporate a unit mass of water, calculated based on the total energy consumption of the drying process and the mass of water removed: (5)SEC=Emωwhere E is the total electrical energy consumed during the entire drying process (kWh), obtained by real-time integration via a power recorder; and m_ω is the mass of water removed (kg), calculated from the mass difference of the sample before and after drying.

To model the drying kinetics of ginger slices under MVD, for which no established model currently exists, five classic empirical and semi-empirical mathematical models [21,22] were selected to fit the experimental drying curves. The coefficient of determination (R²) and root mean square error (RMSE) were employed to assess the goodness of fit for each model. The forms of the evaluated models are presented in Table 3.

In this experiment, several commonly used thin-layer drying models (Table 3) were employed to fit the experimental data. The goodness of fit for each model was evaluated using the coefficient of determination (R²), chi-square (χ²), and root mean square error (RMSE). A better fit is indicated by higher R² values coupled with lower χ² and RMSE values. These statistical parameters were calculated using the following equations: (6)R2=1−∑i=1N(MRexp,i−MRpre,i)2∑i=1N(MRexp,i¯−MRpre,i)2 (7)χ2=∑i=1N(MRexp,i−MRpre,i)2N−n (8)RMSE=1N∑i=1N(MRexp,i−MRpre,i)2where MR_exp,i and MR_pre,i represent the experimental and predicted MR values calculated from the i-th experimental data point, respectively; N denotes the number of experimental data points; and n represents the number of model parameters.

It is well-established that the drying characteristics of biological materials during the falling-rate period can be effectively modeled using Fick’s second law of diffusion. For materials with slab geometry, assuming a uniform initial moisture distribution, the analytical solution derived by Crank can be applied. The general form of this solution is given in Eq. (9), which is applicable to particles with slab geometry. (9)MR=8π2∑n=0∞1(2n+1)2exp⁡(−(2n+1)2π2Defft4L02)where D_eff is the effective diffusivity (m²/s); L₀ is the half thickness of slab (m). For long drying period, Eq. (9) can be further simplified to only the first term of the series. Then, Eq. (9) is written in a logarithmic form as follows: (10)ln⁡MR=ln⁡8π2−π2Defft4L02

The diffusion coefficient is usually determined by plotting the experimental drying data as lnMR against drying time t, as this plot will show a straight line, and its slope K is (π²D_eff)/(4L₀²).

The surface color of dried ginger slices was measured using a precision colorimeter operating under a D65 standard illuminant and the CIELAB color space. The color parameters L* (lightness), a* (red–green coordinate), and b* (yellow–blue coordinate) were recorded. Fresh ginger slices were used as the reference (control). For each sample, measurements were taken at three randomly selected positions on the surface, and the average values were reported to minimize local heterogeneity. The total color difference (ΔE) between dried and fresh ginger slices was calculated according to Eq. (11): (11)ΔE=(L∗−L0∗)2+(a∗−a0∗)2+(b∗−b0∗)2where L₀*, a₀* and b₀* are the color parameters of the fresh ginger slices.

The rehydration capacity of dried ginger slices was evaluated as an indicator of structural integrity and porosity development during drying. A known mass of dried sample (W_d) was immersed in an excess of distilled water at 25°C for 30 min under static conditions to ensure sufficient water availability. After rehydration, the samples were removed, gently blotted with filter paper to eliminate surface water, and weighed to obtain the rehydrated mass (W_r). The rehydration ratio (RR) was calculated using Eq. (12): (12)RR=(Wr−WdWd)×100%

To examine the microstructural evolution induced by MVD under different drying intensities, two representative MVD-treated samples—corresponding to the shortest drying time and the longest drying time—were selected for comparison, together with fresh ginger as a reference. The samples were fractured to expose the cross-sectional surface, freeze-dried to preserve internal structure, and sputter-coated with a thin layer of gold to enhance electrical conductivity. The cross-sectional morphology was observed using a scanning electron microscope (SEM, JEOL JSM-IT810, Japan) at an accelerating voltage of 5.0 kV. The observed microstructural features were used to qualitatively interpret differences in moisture migration behavior, structural collapse, and puffing phenomena under different MVD conditions.

Fig. 2 illustrates the evolution of dry-basis moisture content of ginger slices dried under different microwave power levels (200, 350, and 500 W). In all cases, moisture content decreased monotonically with drying time. Increasing microwave power significantly shortened the total drying duration, with drying times of approximately 60, 50, and 30 min at 200, 350, and 500 W, respectively. The acceleration of drying at higher microwave power can be attributed to the increased volumetric energy absorption within the material. Under microwave heating, electromagnetic energy is directly converted into thermal energy within the moisture-containing matrix, leading to rapid temperature rise and enhanced internal vapor generation. The resulting increase in internal vapor pressure intensifies the moisture migration driving force, thereby reducing both evaporation time and internal mass transfer resistance. This behavior is consistent with the fundamental principle that microwave drying kinetics are governed primarily by the absorbed power density rather than by external heat transfer limitations. Similar trends have been reported for other high-moisture biological materials, such as Moringa leaves extract, where increased microwave power density markedly reduced drying time [23].

The corresponding drying rate curves under different microwave power levels are presented in Fig. 3. Although higher microwave power resulted in more pronounced fluctuations in drying rate, particularly at 500 W, all curves exhibited a similar overall pattern, characterized by a rapid initial increase followed by a continuous deceleration. The absence of a distinct constant-rate period indicates that moisture removal during MVD is predominantly controlled by internal vapor-driven transport rather than steady surface evaporation. The initial rapid increase in drying rate can be associated with the abundant availability of free and weakly bound water and the strong internal heating effect of microwaves, which promotes rapid vaporization throughout the sample volume. As drying proceeds, the depletion of easily removable moisture and the progressive strengthening of moisture binding within the solid matrix lead to a sharp decline in drying rate, marking the transition to a diffusion-dominated regime. At higher microwave power levels, this transition occurs earlier because free water is removed more rapidly, exposing the diffusion-controlled stage sooner. The observed drying rate fluctuations, particularly under high microwave power (500 W), are likely associated with intermittent puffing or localized structural disruption caused by rapid vapor generation and release. Such phenomena are commonly observed during microwave drying of moist biological materials and reflect the dynamic interaction between internal vapor pressure buildup, structural resistance, and momentary vapor escape. These transient events further highlight the inherently unsteady nature of heat and mass transfer during MVD.

Fig. 4 shows the evolution of dry-basis moisture content of ginger slices dried under different vacuum degrees (0.02, 0.05, and 0.08 MPa). The total drying times were approximately 70, 50, and 40 min, respectively, indicating that increasing the vacuum degree significantly accelerates the MVD process. The enhancement of drying performance at higher vacuum levels can be primarily attributed to pressure-induced thermodynamic and mass transfer effects. First, reducing the ambient pressure lowers the boiling point of water within the ginger matrix, allowing phase change to occur at lower temperatures. This facilitates internal moisture vaporization under milder thermal conditions, thereby reducing the thermal resistance required for evaporation and potentially mitigating heat-induced quality degradation. Second, an increased vacuum degree enlarges the water vapor partial-pressure difference between the product interior and the surrounding chamber environment. This amplified pressure gradient enhances vapor-driven moisture transport from the interior toward the surface and subsequently into the vacuum chamber. In contrast to atmospheric conditions, where surface evaporation may limit mass transfer, the low-pressure environment in MVD suppresses external resistance, enabling more efficient removal of internally generated vapor. Similar effects of vacuum-enhanced drying kinetics have been reported for tomato slices by Alvi et al. [24].

The corresponding drying rate curves under different vacuum degrees are presented in Fig. 5. At a vacuum degree of 0.08 MPa, the drying rate increased rapidly during the early stage, reached its maximum value earlier, and then declined sharply. Conversely, at 0.02 MPa, the drying rate exhibited a delayed peak with a lower maximum value and a more gradual decrease. These differences reflect the role of ambient pressure in governing the onset and intensity of internal vaporization. At higher vacuum levels, the reduced equilibrium vaporization temperature decreases the energetic barrier for phase change, enabling rapid moisture evaporation even at moderate internal temperatures. As drying progresses, the rapid depletion of free water leads to an earlier transition to a diffusion-dominated regime, resulting in a pronounced deceleration in drying rate. At lower vacuum degrees, vaporization is less intense, and moisture removal proceeds more gradually, delaying the peak drying rate and extending the overall drying duration.

Fig. 6 illustrates the variation in dry-basis moisture content of ginger slices with different thicknesses (2, 3, and 4 mm). The total drying times were approximately 40, 50, and 60 min, respectively. The nearly linear increase in drying time with slice thickness indicates that geometric factors, particularly the internal moisture diffusion path length, play a dominant role in governing the overall drying duration. Thinner slices provide a shorter migration distance for moisture transport from the interior to the surface, thereby reducing internal mass transfer resistance. In addition, the larger surface-area-to-volume ratio of thinner slices facilitates more efficient vapor release into the surrounding low-pressure environment, which is especially beneficial under microwave vacuum conditions. These combined effects result in faster moisture removal and shorter drying times. Similar thickness-dependent drying behavior has been reported for Persimmon slices under microwave-assisted drying conditions [25].

The corresponding drying rate curves for different slice thicknesses are shown in Fig. 7. Thicker slices exhibited a lower maximum drying rate and a more prolonged deceleration stage compared with thinner samples. This behavior can be attributed to the increased internal diffusion resistance associated with longer moisture transport pathways and a reduced surface-area-to-volume ratio. Moreover, in thicker slices, the central regions tend to experience slower temperature rise during the early stage of drying, resulting in lower internal vapor generation rates and a weaker vapor-driven mass transfer driving force. These results highlight that slice thickness primarily influences MVD performance through geometric constraints on moisture transport, rather than by enhancing intrinsic mass transfer properties. Therefore, optimizing slice thickness is essential to suppress diffusion-limited behavior and to maximize drying efficiency in microwave vacuum drying of ginger.

Figs. 8 and 9 compare the drying behavior of ginger slices under hot air drying (HAD) at 50, 60, and 70°C. As shown in Fig. 8, increasing the drying temperature significantly reduced the total drying time, which decreased from approximately 7 h at 50°C to 5 h at 60°C and 3 h at 70°C. This trend reflects the enhanced convective heat transfer and increased vapor pressure gradient at elevated air temperatures. Despite this temperature-dependent acceleration, HAD remained substantially slower than MVD. Under comparable moisture endpoints, the total drying time required for MVD was approximately one-sixth of that required for HAD at 70°C. This pronounced difference arises from the fundamentally different heat and mass transfer mechanisms governing the two processes. In HAD, heat is supplied externally and must be transferred from the hot air to the product surface and subsequently conducted into the interior. As drying progresses, the formation of a dried outer layer and the depletion of surface free water increase internal mass transfer resistance, causing a progressive decline in drying rate. A significant portion of the supplied thermal energy is therefore consumed in heating the solid matrix rather than directly driving moisture evaporation, particularly during the later stages of drying. By contrast, MVD combines volumetric microwave heating with a low-pressure environment, allowing energy to be deposited directly within the moisture-containing regions of the material. This internal energy generation promotes rapid vapor formation throughout the sample volume, generating a strong internal vapor pressure gradient that accelerates moisture transport toward the surface. Consequently, MVD effectively mitigates thermal lag and surface hardening phenomena commonly observed in HAD.

The drying rate curves shown in Fig. 9 further highlight these differences. HAD exhibited an accelerating stage followed by a prolonged deceleration stage, with no distinct constant-rate period. This behavior has been widely reported for agricultural products dried by hot air, including Daqu [26] and Red Onion Slices [27], and reflects the dominance of internal diffusion resistance once surface moisture is rapidly depleted. Overall, the comparison demonstrates that the superior performance of MVD over HAD is primarily attributable to the shift from externally limited heat transfer to internally driven vapor transport.

Fig. 10 presents the moisture ratio curves of ginger slices dried by conventional microwave drying (MD) at power levels of 200, 350, and 500 W. The total drying times required to reach the target moisture content were approximately 70, 65, and 55 min, respectively. Under the same microwave power settings, MVD consistently achieved shorter drying times, with an average reduction of approximately 25% compared to MD. This improvement highlights the synergistic effect of combining microwave heating with vacuum conditions. While both MD and MVD rely on volumetric microwave energy absorption, the presence of vacuum in MVD lowers the boiling point of water and reduces the external vapor pressure. As a result, moisture vaporization can occur at lower internal temperatures, enhancing vapor-driven mass transfer and reducing thermal stress on the product.

The drying rate profiles of MD and MVD differ markedly, as shown in Fig. 11. Under atmospheric conditions, MD exhibited a characteristic multi-stage drying behavior, consisting of an initial rapid increase in drying rate, a pronounced constant-rate period, and a final falling-rate stage. The existence of a constant-rate period is associated with the high initial free-water content of ginger slices, during which absorbed microwave energy sustains a relatively steady evaporation rate at the surface. Similar drying kinetics have been reported for other high-moisture agricultural materials, such as lychee [28]and Castanea henryi [29]. In contrast, MVD drying rates displayed a sharp initial peak followed by continuous deceleration, without a prolonged constant-rate stage. The reduced ambient pressure and volumetric microwave heating jointly intensify internal vapor generation from the onset of drying, leading to rapid moisture expulsion and an earlier transition to a diffusion-controlled regime. This direct transition reflects the dominance of internal vapor pressure–driven transport over surface evaporation control under vacuum conditions.

A direct comparison of MD and MVD at 350 W (Fig. 12) further emphasizes three key distinctions: (i) a steeper decline in moisture ratio under MVD, indicating faster moisture removal; (ii) the absence of the extended constant-rate plateau observed in MD; and (iii) a higher initial peak drying rate for MVD, reflecting enhanced mass transfer under reduced pressure. Collectively, these differences explain the shorter drying time achieved by MVD and suggest its potential advantages for reducing overall thermal exposure during ginger drying.

Energy consumption is a critical factor in evaluating the economic feasibility and environmental sustainability of drying technologies. In this study, the specific energy consumption (SEC) of HAD, MD, and MVD was calculated based on Eq. (5) for identical ginger slice samples dried to the same target moisture content. The detailed results are summarized in Table 4. From a drying kinetics perspective, MVD exhibited a clear advantage in terms of processing time. For example, under comparable drying endpoints, MVD (350 W, 0.08 MPa, 3 mm) required only 22.2% of the drying time needed for HAD at 70°C and approximately 61.5% of that required for MD at 350 W. This substantial reduction reflects the intensified internal heat and mass transfer achieved by combining volumetric microwave heating with vacuum conditions. However, the energy consumption analysis reveals a different trend. As shown in Table 4, MVD generally exhibited higher SEC values than MD under most investigated conditions, primarily due to the system-level energy demand of MVD, which includes not only the microwave power input but also the continuous operation of the vacuum pump and associated auxiliary components. HAD, although requiring the longest drying time, exhibited moderate SEC values, particularly at higher temperatures (e.g., 17.68 kWh/kg at 70°C), which are comparable to or slightly higher than MD but still lower than high-power MVD. This can be attributed to its simple system configuration and the absence of energy-intensive auxiliary equipment.

These results highlight an inherent trade-off between drying speed and energy efficiency among the investigated drying methods. MVD is particularly suitable for applications where rapid processing is critical and where the higher energy cost can be justified by product quality requirements or high added value. Conversely, when minimizing overall energy consumption is the primary objective, atmospheric MD or high-temperature HAD may represent more economical alternatives. The quantitative SEC data provided in this study offer a practical basis for selecting appropriate drying technologies for ginger slices under different production priorities.

MVD is a multivariable and highly nonlinear process influenced by microwave power, vacuum degree, and slice thickness. Response Surface Methodology (RSM) was therefore employed to quantitatively model the combined effects of these factors and to optimize drying performance with a limited number of experiments. It should be noted that the second-order polynomial model adopted in RSM represents a local approximation of the response surface within the investigated experimental domain, and its applicability is therefore confined to the defined factor ranges. Based on single-factor results, a three-factor, three-level Box–Behnken design was constructed using Design-Expert 13, with drying time, color difference, rehydration rate and specific energy consumption as the responses. The experimental matrix and corresponding responses are listed in Table 9.

Quadratic polynomial regression models were developed for four response variables—drying time (Y₁), total color difference (Y₂), rehydration ratio (Y₃), and specific energy consumption (Y₄)—as functions of microwave power (A), vacuum degree (B), and slice thickness (C). The corresponding ANOVA results are summarized in Table 10, and the regression equations are presented below.(13)Y1=50.8−24.25A−19.5B+9.25C+2.75AB−3.25AC−3.02A2 (14)Y2=9.08+2.34A−1.4B+1.99C+1.05A2+0.4225B2 (15)Y3=260.14−18.74A−8.8B−4.26C+2.82AB−3.6A2 (16)Y4=97.86−9.82A−22.2B+11.53C+7.53AB−4.28AC−9.04A2−9.74B2−6.74C2

All four models were statistically significant (p < 0.0001), indicating that the selected model terms adequately describe the primary effects and interactions within the experimental design space. Importantly, the lack-of-fit tests for all responses were non-significant (p > 0.05), demonstrating that the models provide an acceptable empirical approximation of the experimental data within the investigated parameter ranges. The coefficients of determination (R²) ranged from 0.9914 to 0.9968, reflecting strong agreement between predicted and experimental values. In addition, Adequate Precision values for all models exceeded the recommended threshold of 4, supporting their ability to navigate the design space and to identify meaningful response trends.

Analysis of variance further clarified the relative influence of the process parameters. Microwave power (A) was identified as the most influential factor, exerting a highly significant effect (p < 0.01) on all responses, particularly drying time, color difference, and rehydration ratio. Vacuum degree (B) also exhibited a significant impact, especially on specific energy consumption. Slice thickness (C) significantly affected drying time and energy consumption, mainly by governing the effective moisture diffusion path length. Significant interaction effects were observed, most notably between microwave power and vacuum degree (AB) and between microwave power and slice thickness (AC), highlighting the coupled and nonlinear nature of heat and mass transfer during MVD.

Overall, the regression analysis established statistically adequate second-order polynomial models for all four responses. Within the investigated experimental domain, these models provide a sound empirical basis for response surface analysis and multi-objective optimization, while acknowledging the inherent limitations of polynomial approximations for highly nonlinear drying processes.

Based on the developed quadratic regression models, three-dimensional response surface and contour plots were generated to visualize the interactive effects of process parameters on drying time (Figs. 15–17). These graphical representations provide an intuitive means to interpret the combined influence of microwave power, vacuum degree, and slice thickness within the investigated experimental domain.

Fig. 15 illustrates the interaction between microwave power (A) and vacuum degree (B) at a fixed slice thickness of 3 mm. Drying time decreases markedly with increasing microwave power and vacuum degree, indicating that both parameters contribute to drying intensification. The curvature of the response surface and the elliptical contour lines are consistent with a synergistic interaction between these two factors, reflecting the combined enhancement of internal heat generation and vapor pressure driving force under higher power and stronger vacuum conditions.

Fig. 16 presents the interaction between microwave power (A) and slice thickness (C) at a vacuum degree of 0.05 MPa. Increasing microwave power significantly reduces drying time, whereas increasing slice thickness prolongs the process. The pronounced surface curvature suggests that slice thickness modulates the effectiveness of microwave heating by altering the internal moisture diffusion path length, which is characteristic of diffusion-controlled drying behavior.

Fig. 17 shows the interaction between vacuum degree (B) and slice thickness (C) at a microwave power of 350 W. Drying time decreases with increasing vacuum degree, whereas thicker slices require longer drying times. Compared with the other interaction plots, the response surface is relatively smooth, indicating a weaker interaction between these two factors within the studied range.

Based on the established regression models, a multi-objective numerical optimization was conducted using the desirability function approach, with the aims of minimizing drying time, total color difference, and specific energy consumption, while maximizing the rehydration rate. The predicted optimal conditions are summarized in Table 11. For practical implementation, the predicted values were adjusted to the nearest feasible operating levels: a microwave power of 200 W, a vacuum degree of 0.08 MPa, and a slice thickness of 2 mm. Validation experiments performed under these conditions yielded a drying time of (40 ± 5) min, a color difference of (5.0 ± 0.4), a rehydration rate of (265.8 ± 5.5)%, and a specific energy consumption of (38.2 ± 1.5) kWh/kg. The close agreement between predicted and experimental values demonstrates that the developed RSM models provide a reliable basis for identifying favorable operating conditions within the studied parameter space.