Introduction

Extended processing times in freeze drying contribute significantly to the high energy demand of this drying method. This is primarily due to the continuous operation required for energy-intensive components like the ice condenser’s cooling system and vacuum pumps throughout the entire drying process (Ambros et al., 2018; Duan et al., 2010; Jiang et al., 2013a, b; Ozkan et al., 2007; Wang & Xi, 2005). Microwave technology presents a viable approach to expedite and enhance traditional freeze drying methods, addressing limitations in heat transfer by volumetric and selective heating of water-rich segments, substantially reducing drying times compared to conventional methods. More precisely, in sectors like pharmaceuticals and food industries, where slow freeze drying hampers production capacity, microwaves have demonstrated the potential to cut drying times by 40–96% (Abbasi & Azari, 2009; Ambros et al., 2018; Gitter et al., 2018; Jiang et al., 2013a; Ozcelik et al., 2019). This makes microwave application a standout due to its ability to intensify processes, increase product output, lower energy consumption (Abbasi & Azari, 2009; Jiang et al., 2013a; Ozcelik et al., 2019), and save time (Abbasi & Azari, 2009; Ambros et al., 2018; Gitter et al., 2018; Jiang et al., 2013a, b; Ozcelik et al., 2019). Considering the escalating energy costs and the shift toward electrification, microwave application emerges as a promising alternative to conventional freeze drying.

Surprisingly, limited knowledge exists regarding the influence of processing parameters in microwave-assisted freeze drying (MWFD) on drying time and energy consumption. While the impact of microwave input power on drying time (Abbasi & Azari, 2009; Ambros et al., 2018; Chandrasekaran et al., 2013; Duan et al., 2010; Jiang et al., 2010, 2011, 2013a; Ozkan et al., 2007; Wang et al., 2009; Wang & Xi, 2005) and energy usage (Ambros et al., 2018; Duan et al., 2010; Jiang et al., 2010, 2011, 2013a; Wang et al., 2009) is well-documented indicating that higher input powers expedite the process and decrease energy consumption, the impact of maximum drying temperature in MWFD remains relatively unexplored. Wang et al. (2009) investigated the effect of maximum drying temperature on drying time, however; while the authors showed an accelerating effect of higher temperatures, the correlation between temperature and its impact on total energy consumption in MWFD remains unclear especially in combination with different settings of input power. Understanding the effect of maximum product temperature on the energy performance of MWFD becomes pivotal, considering how higher temperatures in conventional freeze drying significantly speed up the process particularly in desorption drying (Pikal et al., 1990; Wang et al., 2009), the final stage of MWFD where high temperatures prevail (Ambros et al., 2018; Duan et al., 2010).

However, even more significant is the assessment of MWFD concerning the new challenges microwaves introduce to freeze drying. Microwave processing often causes uneven heating due to the inherent inhomogeneous distribution of the microwave field within the drying chamber and the product. This creates localized “hot” and “cold” spots in the product, compromising product quality and safety by causing over-processing in some product areas and inadequate drying in others (Kalinke et al., 2022; Kalinke & Kulozik, 2023). While this phenomenon is well described in microwave heating applications (Chandrasekaran et al., 2013; Kalinke et al., 2023; Monteiro et al., 2011; Taghian Dinani et al., 2021), existing literature fails to elucidate the extent of inhomogeneity in MWFD. This neglect mainly stems from the complexity of describing inhomogeneity of temperature distribution in MWFD (Jiang et al., 2013b; Kalinke et al., 2022). While attempts have been made to quantify this inhomogeneity (Jiang et al., 2013b; Sickert et al., 2023a), such studies are limited in scope or miss crucial stages of the drying process, leaving the impact of processing parameters on inhomogeneity inconclusive. For instance, Jiang et al. (2013b) assessed inhomogeneity in MWFD of banana chips for a single MWFD procedure. The authors lacked to investigate the effect of variable processing parameters on inhomogeneity. Sickert et al. (2023a) addressed inhomogeneity in MWFD concerning changes in pressure and input power levels by comparing water contents among individual dried samples at a specific point in the MWFD process, namely, at 20% water removal (i.e., after 8% of the drying duration). However, it has been noted that inhomogeneity peaks towards the end of MWFD (Jiang et al., 2013b), particularly during the transition from the initial sublimation drying stage to the subsequent desorption drying stage, a critical period not covered in Sickert et al.’s evaluation. This could be a potential reason why no significant effect of pressure or input power on inhomogeneity could be identified in the study. Consequently, in light of existing research, the impact of specific processing parameters in temperature-controlled MWFD, such as microwave power input and maximum product temperature, on the overall extent of inhomogeneity during MWFD, remains unclear.

To address this knowledge gap, our study aims to assess the impact of microwave input power and maximum product temperature, on both energy efficiency and the inhomogeneity of processing. Consequently, MWFD trials were conducted at various settings of microwave input power (180 W, 200 W, 220 W, equivalent to 1.50 W/g, 1.67 W/g, 1.83 W/g of initial sample weight) and maximum product temperature (40 °C, 50 °C, 60 °C, 70 °C). The resulting drying time, energy consumption, and inhomogeneity of temperature distribution were evaluated. The process variables were adjusted within the common range reported for MWFD of food, following previous studies on input power (Abbasi & Azari, 2009; Ambros et al., 2018; Jiang et al., 2010; Wang et al., 2009; Wang & Xi, 2005) and maximum temperature variation (Wang et al., 2009). In agreement with these publications, the first hypothesis is that higher microwave input power and elevated product temperatures lead to shorter drying times due to higher heat transfer and increased temperature gradients, consequently reducing overall energy consumption in MWFD. This is because energy consumption in MWFD is mainly affected by the overall run time of the vacuum pump and ice condenser (Ambros et al., 2018; Jiang et al., 2013a) and thus by the effect of processing variables on drying time.

However, these higher settings might also induce higher inhomogeneities within the product, impacting product quality or safety and thus confidence in emerging MWFD. Therefore, we hypothesize that increasing maximum drying temperature (Tmax) and microwave power input (Pset) induces higher inhomogeneities within the product because faster drying rates restrict the time available for temperature equalization across different regions of the sample. In addition, water vapor transfer capacity across the product matrix might be limited, heightening the risk of undesirable ice crystal melting at higher drying rates. Consequently, this accelerated pace has the potential to amplify inhomogeneities. On the contrary, slower processing provides more time for heat conduction, facilitating temperature equalization and decreasing the risk of undesired melting of individual ice crystals. Individual melting of ice crystals leads to a substantial change in dielectric properties. This phenomenon takes place in the hot spots of the sample, contributing to the occurrence of a so-called thermal runaway of product temperature in these already hot product regions. This effect is known as the thermal runaway effect, a phenomenon held primarily responsible for the peaking inhomogeneities observed in MWFD in Jiang et al. (2013b).

This study aims to provide insights into the impact of processing parameters on both energy consumption and inhomogeneity, addressing the extent of uneven processing in MWFD. This knowledge is essential to instill confidence for successful integration of MWFD into commercial food processing. Specifically, unravelling the influence of these parameters on inhomogeneity is crucial for advancing our understanding and refining the optimization of processing conditions in MWFD. Through this research, we endeavor to contribute to the enhancement of efficiency and reliability in MWFD processes, paving the way for its effective utilization in the broader landscape of food processing technologies.

Materials and Methods

Sample Preparation

A maltodextrin foam sample was prepared as described in detail in Kalinke and Kulozik (2023). A model sample dispersion consisting of 6.0% w/w polysorbate 80 (Tween 80, GERBU Biotechnik GmbH, Heidelberg, Germany), 25% w/w maltodextrin DE-6 (Nutricia GmbH, Erlangen, Germany), 6.0% w/w ITC (TM-ICI-60-3513, Cheerful Kaki, Taoyuan City, Taiwan), and 63% w/w deionized water was prepared. Subsequently, 150 g of the dispersion was whipped at 220 rpm for 15 min in a commercial planetary mixer (KitchenAid ARTISAN 5KSM150, Whirlpool Corp., Greenville, USA; Geometry: K45WW, Whirlpool Corp., Greenville, USA). Immediately after the foam formation, 120 g was transferred to a glass Petri dish (Duran, Merck, Darmstadt, Germany) with a diameter of 22.5 cm. The sample was kept frozen at −80 °C (Freeze BF-U538, Buchner Labortechnik, Pfaffenhofen, Germany) until drying.

Drying Equipment

MWFD experiments were conducted in a pilot-scale microwave-freeze dryer (Model µVac0150fd, Püschner, Schwanewede, Germany) with two integrated vacuum pumps (Hena 61, Pfeiffer Vacuum, Aßlar, Germany; Ruvac WA501, Leybold, Cologne, Germany), an ice condenser (Dietz, Bremen, Germany) operated at −50 °C and a magnetron (MB2340A-140BW, Muegge, Reichelsheim (Odenwald), Germany) with a nominal operating frequency of 2450 MHz. The sample weight was detected along drying by an integrated balance (Soemer, Lennestadt, Germany) with an accuracy of 0.01 g. The sample temperature was continuously measured by an integrated infrared pyrometer (CT13.10, Heitronics, Wiesbaden, Germany). It had an accuracy of ± 0.8 °C plus 0.8% of temperature difference between sample and equipment (approximately 23 °C), a response time (t90) of 1 s, and a field-of-view diameter of 2.5 cm.

The drying process control was realized automatically using the software µWaveCAT (Püschner Microwave Power Systems, Schwanewede, Germany).

MWFD Experiments

MWFD experiments were conducted at 0.1 mbar, at parallel turntable rotation (revolution speed 1.5 min−1), at different microwave power input levels, namely Pset = 180 W, 200 W, and 220 W. These were equivalent to 1.50 W/g initial sample weight, 1.67 W/g initial sample weight, and 1.83 W/g initial sample weight. A temperature-controlled microwave-assisted freeze drying was conducted, meaning microwave power input was kept constant until maximum drying temperature setting (i.e., Tmax = 40 °C, 50 °C, 60 °C, 70 °C) was reached. Subsequently, microwave power was applied in a pulsed manner to maintain drying temperature at Tmax ± 1 °C. This means: Microwave power input was switched on and off, when drying temperature was falling below or exceeding ± 1 °C of Tmax. The drying was completed when product weight stayed constant for a duration of 10 min. All MWFD experiments were conducted at least in duplicate.

For better understanding of the drying procedure, an exemplary drying process at 220 W and Tmax = 70 °C is given in Fig. 1. Whereat, the moisture ratio (MR), representing a dimensionless parameter to describe the normalized product moisture along drying, is shown on the left axis. MR is calculated as given in the “Moisture Ratio and Drying Time” section. The right axes in Fig. 1 report (1) the drying temperature used for temperature control, detected by pyrometer temperature measurement during drying, and (2) the current input microwave power. Further details on the temperature detection during MWFD are noted in the “Process Temperature and Temperature Span” section.

Fig. 1
figure 1

Exemplary MWFD process at 220 W and Tmax = 70 °C showing the simultaneous progression of moisture ratio (1, left axis), product temperature (2, right axis), and microwave input power (3, right axis) in the two stages of constant and pulsed microwave power input

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In Fig. 1, the set microwave input power was constant at 220 W in the stage of constant microwave input. In the second stage of pulsed microwave power input after the drying temperature exceeded Tmax, microwave input power was either 220 W or 0 W to maintain maximum drying temperature Tmax. Switch-on power peaks common for magnetron microwave generator systems resulted in a power overshoot up to maximum magnetron input power (i.e., 1000 W).

Assessment of MWFD

Moisture Ratio and Drying Time

The moisture ratio (MR) represents a dimensionless parameter to describe the normalized product moisture along drying, as derived from literature (Ambros et al., 2018; Kubbutat et al., 2020; Ozcelik et al., 2019). It is calculated according to Eq. (1):

$$\mathit{MR}\left(t\right)=\frac{M_{\mathrm t}-M_{\mathrm e}}{M_0-M_{\mathrm e}}$$
(1)

Mt is the product mass at the time t (kg), Me is the equilibrium mass of the product (kg), and M0 is the product mass at the beginning of the drying process (kg).

Drying time was defined as the time span between vacuum application and reaching a MR of 0.005 [-].

Energy Performance of MWFD

The total energy demand of MWFD is derived from the total microwave energy input and the energy demand of plant peripherals. Detailed explanations of each component, along with the calculation of the energy efficiency of the microwave process, are provided in the following subsections. A visual overview is presented in Fig. 2 for clarity.

Fig. 2
figure 2

Visual overview of the energy performance evaluation process, illustrating the total energy demand of MWFD, composed of the energy demand of plant peripherals and the energy demand of microwave application. PAE describes the energy efficiency of the microwave input

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Total Microwave Energy Input and Total Energy Demand of Microwave Application

The total microwave energy input refers to the cumulative microwave power applied throughout the drying process, which is calculated by summing forward microwave input power value (PFWD) multiplied by its corresponding time interval. The PFWD at specific time points was recorded using the drying control software of the MWFD plant (µWaveCAT, Püschner Microwave Power Systems, Schwanewede, Germany).

Magnetron generators typically possess an energy efficiency of 88% (Atuonwu & Tassou, 2018). The energy efficiency in combination with the required total microwave energy of the MWFD process was used in the quantification of total energy demand of microwave application.

Total Energy Demand of Plant Peripherals

The energy demand of the plant peripherals (i.e., vacuum pumps and ice condenser system) was measured using a power meter (3/16 MID, TiP, Thüringer Industrie Produkte, Ruhla, Germany).

Energy Efficiency of Microwave Processing

Energy efficiency of the microwave process was quantified by the proportion of absorbed microwave energy (PAE) in relation to the amount of input microwave energy, as derived from literature (Kalinke et al., 2023; Sickert et al., 2023b; Zhang et al., 2018). Consequently, the PAE value describes the relative microwave input energy being absorbed by the sample. A PAE value close to 1 corresponds to a high energy efficiency of the microwave application. The PAE is calculated according to Eq. 2.

$$\mathit{PAE}=\frac{P_{\mathrm{ABS}}}{P_{\mathrm{FWD}}}=1-\frac{P_{\mathrm{RFD}}}{P_{\mathrm{FWD}}}$$
(2)

Herein, PRFD describes the reflected microwave power measured by a reflection detector (µWReflAmp1.3 000337 provided with the plant), which was continuously documented during the MWFD process using the drying control software (µWaveCAT, Püschner Microwave Power Systems, Schwanewede, Germany). The forward microwave power (PFWD) was obtained from the magnetron generator system (MB2340A-140BW, Muegge, Reichelsheim (Odenwald), Germany) during MWFD. The absorbed microwave power (PABS) is determined by the difference between PFWD and PRFD.

Process Temperature and Temperature Span

Online temperature measurement was realized using the stationary integrated pyrometer of the drying unit (CT13.10, Heitronics, Wiesbaden, Germany) in combination with the drying control software µWaveCAT (Püschner Microwave Power Systems, Schwanewede, Germany). The emissivity of the pyrometer was pre-set by the drying plant manufacturer. It is acknowledged that emissivity changes during the drying process (Kalinke et al., 2022). However, constant adjustment of the pyrometer emissivity throughout drying was not feasible. Therefore, a static emissivity setting was employed. The static emissivity was well suited for temperature measurement of the dry, unfrozen product towards the end of drying—the point in time where inhomogeneity assessment based on pyrometer data was performed.

Oscillation of temperature data is caused by turntable-induced sample rotation relative to the stationary pyrometer measurement position within the microwave cavity. As the measuring spot (diameter of 2.5 cm) was located 4 cm outside the rotation axis of the sample, the measuring spot described a circular path on the sample surface, leading to oscillating temperature data resulting from inhomogeneous temperature distribution on this circular path on the sample surface. To enhance clarity and facilitate a better understanding, the measurement principle was further illustrated in Fig. 3.

Fig. 3
figure 3

Visual overview of the inline inhomogeneity measurement process, utilizing pyrometer temperature measurement and evaluating temperature oscillations. These oscillations result from the combined effects of sample rotation and temperature spot measurement outside the rotation axis. The measurement spot traces a circular path on the sample surface, and the span of oscillations expands with rising temperature inhomogeneity along this circular measurement path

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To quantify the extent of the resulting temperature oscillation and thus the range of temperature values on the surface at one point in time, the maximum temperature oscillation span (TO,span) between maximum (TO,max) and minimum (TO,min) temperature of one oscillation was extracted. This was equivalent to the maximum sum of the absolute amplitude in positive and negative direction. Herein, t is the time when Tspan is maximum. Tspan is calculated according to Eq. 3.

$$T_{O,span}\;\left[K\right]=T_{O,max}\left(t\right)-T_{O,min}\left(t\right)$$
(3)

Image Acquisition and Processing

Inhomogeneity of MWFD was assessed using an established method applying an irreversible thermochromic color-component (ITC) (Kalinke & Kulozik, 2023). Thereby, the applied ITC provided a particular color intensity profile as a function of temperature (40–70 °C) with an increasing change from colorless to magenta with temperature, as described in detail in Kalinke and Kulozik (2023). A spatially resolved evaluation of the temperature-induced color intensity pattern of the sample allows for a spatially resolved assessment of the exposure to differing maximum temperatures of the drying process within one sample. This provides insight into the inhomogeneity of a MWFD process. The color intensity resulting from the temperature-induced ITC activation using L*a*b*-color-values in the CIELab color space. Thereby, a* represents the green to magenta ratio of the respective color to be described. A higher a*-value corresponds to a stronger color change of the ITC to magenta and thus an exposure to higher processing temperatures in the respective sample segment. The distribution of resulting a*-values on the sample surface post MWFD was evaluated using an automated image analysis procedure in Matlab R2019a software (MathWorks, Natick, MA, USA). This analysis involved processing visual photos captured immediately after the MWFD process.

The photos were taken within a photo box (Fositan, Shenzhen, China) using a visual photo camera (EOS 1100D with Canon Image Stabilizer EFS 18–55 mm, Canon, Tokyo, Japan) with specific camera settings (Manual, 55 mm, F11, ISO 1600, 1/125). For more comprehensive information about the methodology and the respective measurement procedure, please refer to Kalinke and Kulozik (2023).

In Fig. 4, a processed image illustrates the color intensity pattern caused by temperature effects on the sample. The variation of a*-values is represented using a pseudo-color scale spanning from blue to yellow. Elevated a*-values signify regions in the sample where the thermochromic ITC experienced greater activation, indicating exposure to higher temperatures throughout the drying process.

Fig. 4
figure 4

(adapted from Kalinke and Kulozik (2023)

Visual overview of the ITC inhomogeneity measurement process following MWFD: The methodology involves employing a visual photo camera and assessing temperature-induced color changes, transitioning from colorless to magenta as a function of temperature. Automated image analysis yields the distribution of the a*-value on the sample, in the following referred to as color intensity pattern. Higher a*-values correspond to higher regional process temperatures in MWFD

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Statistical Analysis

All drying experiments were conducted at least in duplicate. Indicated error values refer to the mean error of replicates. The significance of the effect of Tmax or Pset on the given data was evaluated performing analyses of variance (ANOVA) with post hoc Bonferroni test. To analyze the significance of a trend, we conducted t-tests. Differences were considered significant for p < 0.05. Statistical analysis of data was carried out using OriginPro 2019 software (OriginLab Corp., Northampton, MA, USA).

Results and Discussion

Impact on Drying Time

Drying time plays a pivotal role in the assessment of MWFD processes (Abbasi & Azari, 2009; Ambros et al., 2018; Chandrasekaran et al., 2013; Duan et al., 2010; Jiang et al., 2010, 2011, 2013a; Ozkan et al., 2007; Wang et al., 2009; Wang & Xi, 2005). Figure 5 outlines the duration of MWFD under different Tmax (40–70 °C) and Pset (180–220 W) settings. A significant decreasing trend of drying time with increasing Tmax was observed (t-test, p < 0.05). Although higher Pset was anticipated to expedite the drying process due to enhanced heat and thus water vapor transfer, our study did not find a significant acceleration within the investigated power range (ANOVA, p < 0.05). Nevertheless, the highest input power level (220 W) resulted in the shortest drying time across all Tmax settings (excluding 40 °C). This was in alignment with existing literature findings (Abbasi & Azari, 2009; Ambros et al., 2018; Chandrasekaran et al., 2013; Duan et al., 2010; Jiang et al., 2010, 2011, 2013a; Ozkan et al., 2007; Wang et al., 2009; Wang & Xi, 2005). However, this effect of shorter drying times for higher levels of Pset was neither stringent nor significant. While for Tmax of 40 °C and 70 °C, drying with 200 W resulted in slightly faster drying compared to 180 W, as expected, for Tmax values of 50 °C and 60 °C, drying at 200 W was slightly slower than drying at 180 W, contrary to expectation. As there is no clear explanation for this observation of longer drying times at 180 W at Tmax = 50 °C and 60 °C compared to drying at 200 W, it is reasonable to assume this was coincidental. This assumption is supported by the size of the error bars reported in Fig. 5, which may appear elevated, but fall within the documented error range for MWFD, as highlighted in previous studies (Ozcelik et al., 2019; Wang et al., 2009). These deviations could have arisen from acknowledged issues regarding the reproducibility of magnetron-driven microwave processes (Atuonwu & Tassou, 2018), which are the subject of this study, as well as fluctuations in surrounding equipment temperature.

Fig. 5
figure 5

Drying time in response to Tmax (40, 50, 60, 70 °C) for different settings of Pset (180 W, 200 W, 220 W); the dashed line shows the significant decreasing trend of drying time with increasing Tmax irrespective of Pset setting; whereat the effect of different Pset on drying time was not significant, the effect of Tmax was significant

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Furthermore, the relatively small range of Pset investigated in combination with an additional damping effect of temperature-controlled processing might be responsible for a lacking stringent, significant accelerating effect of increasing Pset on drying time. More precisely, the higher Pset mainly affected the first drying stage of constant microwave input. After that, the microwave power was applied in a pulsed manner, as shown in Fig. 1. During this pulsed microwave stage, the impact of Pset (180, 200, or 220 W) was minimal. In response to a higher Pset level, the pulse duration until product temperature reached Tmax + 1 °C was shortened, resulting in the same amount of microwave input energy per pulse independent of the individual Pset level. Thus, different levels of Pset did not substantially alter absolute microwave power input in the second stage of pulsed microwave power input. They could only influence drying time in the stage of constant microwave input. This is expected to be mainly responsible for the small observed effect of Pset on drying time in this study.

Nevertheless, increasing Tmax had a significant accelerating effect on drying time, as highlighted by the dashed trend line in Fig. 5. As Pset had no significant effect on drying time, the trend line in Fig. 5 highlights the decreasing trend of drying time irrespective of Pset. This expedited effect aligns with literature findings, suggesting that elevated drying temperatures in MWFD, particularly during desorption drying, the second phase of MWFD, lead to a decrease in drying duration (Wang et al., 2009) due to an increase in temperature gradient and thus water vapor pressure gradient (Pikal, 1994).

Impact on Microwave Energy Utilization

In addition to assessing the drying time, the impact of MWFD settings on the efficacy of microwave energy input was evaluated. This evaluation focused on two parameters: the total microwave energy input during drying and the proportion of this energy absorbed by the sample. The latter is expressed as PAE (proportion of absorbed energy), where a PAE of 1 is considered ideal. Hence, a PAE of 1 indicates that all input microwave energy was absorbed by the sample without energy reflection back into the generator system. Therefore, minimizing the discrepancy between input and absorbed energy is advantageous, as reflected microwave energy does not contribute to heat transfer into the sample and thus does not aid in the drying process (Sickert et al., 2023b). Further, it needs to be compensated by actively cooling the generator system to prevent equipment damage (Bardineshin, 2023). An energy-efficient MWFD process aims for low total microwave input energy, while striving for a high PAE value (close to 1) (Kalinke et al., 2023).

Therefore, the impact of Pset and Tmax on both the total microwave energy input and the PAE value of MWFD was assessed. The results are depicted in Fig. 6, where Fig. 6A represents the total microwave energy input and Fig. 6B illustrates the corresponding PAE values.

Fig. 6
figure 6

A Total microwave energy input of the MWFD process as a function of Tmax (40, 50, 60, 70 °C) for different Pset (180, 200, 220 W); The dashed line depicts the significant increasing trend of total microwave energy input with increasing Tmax irrespective of Pset. Whereat the effect of different Pset on total microwave energy input was not significant, the effect of Tmax was significant; B PAE value of MWFD for different settings of Pset irrespective of Tmax. Whereat the effect of different Pset was significant, the effect of different settings of Tmax was not significant

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From Fig. 6A, it is evident that the total microwave input energy for different Pset (i.e., 180, 200, 220 W) did not show significant differences, a result supported by ANOVA analysis (p < 0.05). This aligns with our expectations, as altering the power input (Pset) and, consequently, the energy delivered per unit of time was not expected to have a significant impact on the amount of heat required for the drying process. Therefore, our findings were consistent with existing literature (Ambros et al., 2018).

Nevertheless, a notable trend emerged: there was a significant increase in total microwave energy input with raising Tmax (t-test; p < 0.05), denoted by a gray dashed trend line in Fig. 6A. Consequently, higher Tmax settings demanded more microwave energy input due to the need to heat and maintain the sample at higher product temperatures, leading to an overall higher energy demand for the microwave part of the MWFD process. This association between higher Tmax and increased microwave energy input represents a novel finding in light of existing literature, where the effect of Tmax on total microwave energy input has been overlooked so far.

In contrast to this, Fig. 6B shows that while Tmax had no significant effect on PAE, the PAE value significantly decreased with increasing Pset (ANOVA, p < 0.05). This implies that with higher Pset values, a smaller portion of the total microwave energy input was absorbed by the sample. This relationship between increasing Pset and declining PAE value was in agreement with previous findings, reported by Taghian Dinani et al. (2020) for microwave heating with a magnetron generator. Magnetron systems are prone to erratic changes in excitation frequency (Atuonwu & Tassou, 2018; Luan et al., 2017; Soltysiak et al., 2011). Varied excitation frequencies are noted to significantly impact the PAE value (Atuonwu & Tassou, 2018; Kalinke et al., 2023; Sickert et al., 2023b; Yakovlev, 2018; Zhou et al., 2023). Therefore, Taghian Dinani et al. (2020) suggested that higher Pset affected the magnetron generator’s excitation frequency and consequently the distribution of the microwave field within the cavity. This was investigated across a power range of 0–600 W using a magnetron generator with a maximum input power level of 1000 W in a commercially available household microwave oven, as outlined by the authors.

These shortcomings in reproducibility of magnetron systems likely explain the observed change in PAE with increasing Pset in our study, as also a magnetron system with a maximum power of 1000 W within the range of 180–220 W was used. This effect is not desirable as lower PAE values not only imply inefficient utilization of microwave input power but also indicate surplus energy being reflected back into the generator. This excess energy requires dissipation as heat through the generator’s cooling system.

Interestingly, despite the lower proportion of input energy absorbed by the sample (PAE) at higher Pset values, this did not correspond to an observable, stringent increase in the total microwave energy input with increasing Pset in Fig. 6A. This finding was unexpected, as one would typically anticipate that the reduction in absorbed energy and, consequently, the energy supporting the drying process would necessitate a compensatory increase in total microwave input. This adjustment would be required to uphold a consistent absolute amount of absorbed energy across all Pset settings, despite varying PAE values. The absence of this correlation lacks clarity; however, it appears likely that factors other than the effect of varying PAE values for different Pset exert more dominant influence on the total microwave energy input. In this scenario, the recognized issue of inconsistent operation in magnetron systems, as described above, is worth considering (Atuonwu & Tassou, 2018; Celuch et al., 2020; Luan et al., 2017; Soltysiak et al., 2011). This inconsistency can impact the reproducibility of MWFD experiments, increasing variability between repetitions and potentially overshadowing any slight effect of varying PAE values that might be present.

Energy Demand of MWFD

In this section, the impact of processing variables on MWFD’s overall energy performance was evaluated. The drying time plays a pivotal role in the context of energy performance of MWFD, being closely linked to the run time and thus the energy demand of the main consumers (Ambros et al., 2018; Jiang et al., 2013a). In our case, running the plant without microwave input (in idle) required an energy demand of 2.8 ± 0.1 kWh, which was multiplied by the drying time of each MWFD process to calculate the total energy demand attributed to running the plant peripherals (such as ice condenser cooling and vacuum pumps). Using the energy efficiency in combination with the required total microwave energy input from the “Impact on Microwave Energy Utilization” section resulted in the quantification of the portion of total energy demand allocated to microwave application. The combination of these two components constituted the total energy demand of MWFD, as depicted in Fig. 7.

Fig. 7
figure 7

Total energy demand as function of Tmax (40, 50, 60, 70 °C) and a slope of mTED. The total energy demand represents the sum of the primary energy demand of the microwave generator (referred to as the microwave part with a slope of mMW) and the energy demand of the remaining MWFD plant (referred to as the plant peripherals part with a slope of mPP). All indicated slopes (mTED, mPP and mMW) showed significant deviations from zero. Pset did not exert a significant effect on the total energy demand and their individual parts; therefore, all depicted trends were calculated independent of Pset

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As discussed in the “Impact on Drying Time” and “Impact on Microwave Energy Utilization” sections, only Tmax had a significant impact on the drying time and total microwave input energy required for the MWFD process. Therefore, only Tmax had a notable impact on the portion of energy demand for microwave application and plant peripherals and thus, the total energy demand of MWFD. Consequently, the observed significant rise in the total energy demand for microwave application with increasing Tmax contrasted with the significant reduction in the energy demand for plant peripherals. These opposing trends stemmed from the observed increase in total microwave input energy alongside the decrease in drying time with increasing Tmax, as discussed in the “Impact on Drying Time” and “Impact on Microwave Energy Utilization” sections.

The findings in Fig. 7 suggest that the favorable influence of higher Tmax on drying time reduction outweighs the associated increase in microwave energy demand. This can be seen from the overall observed significant decrease in total energy demand with increasing Tmax, an interesting observation, as existing publications lack an evaluation of maximum drying temperature (Tmax) on total energy demand of MWFD. It is important to note that this evaluation exclusively focuses on energy considerations. However, careful deliberation is crucial when contemplating increments in Tmax, as they may potentially have adverse effects on the final product’s quality, as highlighted by Wang et al. (2009). Therefore, thorough assessments are warranted for decisions regarding raising Tmax for energy benefits, particularly considering the product’s sensitivity to temperature and the effects of Tmax adjustment on uniformity of MWFD, as will be discussed in the subsequent “Inhomogeneity of MWFD” section.

Inhomogeneity of MWFD

The inhomogeneity of MWFD was assessed based on product temperature oscillation and ITC-induced color intensity patterns. The initial focus was on evaluating the effect of increasing Tmax on the temperature distribution’s inhomogeneity in MWFD. Figure 8 showcases an illustrative drying process representing temperature and moisture ratio over time for various Tmax settings (40 °C (A), 50 °C (C), 60 °C (E), and 70 °C (G) given on the left of Fig. 8. The corresponding ITC-induced color intensity patterns (Fig. 8B, D, F, and H) are displayed on the right, reporting the maximum temperature distribution by means of irreversible, thermochromic color intensity pattern detected at the end of drying. The oscillation in observed product temperature (seen in Fig. 8A, C, E, G) stems from continuously measuring surface temperature outside the sample’s rotational axis using an integrated, stationary pyrometer. This leads to temperature data oscillation over one rotation of the turntable, caused by variations in sample temperatures along the circular path of the measurement spot during that rotation, as detailed in the “Process Temperature and Temperature Span” section and Fig. 3. The oscillation span indicates inhomogeneity of temperature distribution at each point in time (Kalinke et al., 2022; Kalinke & Kulozik, 2023; Kubbutat et al., 2020; Szadzińska & Mierzwa, 2021).

Fig. 8
figure 8

Inhomogeneity of one exemplary drying repetition depicted by the oscillation of product temperature along drying for different setting of maximum drying temperature, i.e., Tmax = 40 °C (A), Tmax = 50 °C (C), Tmax = 60 °C (E), and Tmax = 70 °C (G) at Pset = 220 W; inhomogeneity of the respective drying repetition depicted by the ITC-induced color intensity pattern of the sample for Tmax = 40 °C (B), Tmax = 50 °C (D), Tmax = 60 °C (F), and Tmax = 70 °C (H) measured at the end of drying at Pset = 220 W

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Inhomogeneity During MWFD

In Fig. 8A, C, E, and G, a noticeable increase in oscillation span accompanied rising product temperatures, peaking around a moisture ratio (MR) of 2% at approximately 80 min. Subsequently to this peak in oscillation span, inhomogeneity steadily decreased towards the end of drying.

Interestingly, the temperature oscillation span consistently peaked during the second stage of pulsed microwave input, despite a reduced mean microwave input during this stage. This surprises because during this stage, the mean microwave input decreases due to the pulsed power input, allowing hot and cold spots in the sample more time to equilibrate. The peaking of inhomogeneity versus the end of drying aligns with Jiang et al. (2013b) observations in MWFD without a maximum setting for product temperature (meaning no Tmax setting). The authors reported that inhomogeneity peaked during the transition from sublimation to desorption drying. They suggested this surge in inhomogeneity stemmed from melting ice crystals due to high surrounding temperatures, creating a so-called thermal runaway effect. This effect implies that areas with higher temperatures absorb more microwave energy, accentuating temperature inhomogeneities due to varying dielectric properties in hot and cold spots. In the authors’ scenario, thermal runaway would arise from sudden free liquid water presence compared to the commonly present fully frozen free water or non-frozen bound (liquid) water in MWFD. Free liquid water (Kaatze & Uhlendorf, 1981) has significantly higher dielectric properties than frozen (Matzler & Wegmuller, 1987) or sample bound water in MWFD (Sickert et al., 2023b). Consequently, dielectric properties surge in segments with melting ice, speeding up microwave energy absorption and magnifying already present temperature differences. However, proving this local, individual ice melting, as postulated by Jiang et al. (2013b), remains challenging due to spatially variable water content and temperature, accompanied by potentially occurring changes in water’s aggregate state. A spatially resolved measurement of these variables throughout the entire drying process—without influencing the drying itself—appears hardly feasible (Kalinke et al., 2022).

In light of this proposed explanation of peaking inhomogeneity during the transition of sublimation to desorption drying, further considerations arise:

Uneven heating in MWFD causes faster drying in hot spots than in neighboring cold spots within a sample. This is due to uneven field distribution, with cold spots located in product regions of lower field strength and hot spots located in areas of higher field strength. In cold spots, where less energy is absorbed due to lower field strength, the available limited energy supports relatively faster drying rates than in neighboring hot spots, where despite there is more energy absorption, lower drying rates persist due to ongoing desorption drying. This is because sublimation is characterized by higher drying rates and gradual temperature increase, whereas desorption drying involves lower drying rates causing exponential temperature rise, as discussed in more detail for MWFD in Ambros et al. (2018) and Duan et al. (2010). Hence, during the transition from sublimation to desorption drying, hot spots experience exponential temperature increase and low drying rates, while nearby cold spots remain in sublimation drying with slow temperature rise due to sustained high sublimation rates. This in essence means, regardless of a potential thermal runaway effect due to unwanted ice melting as proposed by Jiang et al. (2013b), spatially varying drying rates induce exponential temperature growth in hot spots and slow temperature elevation in cold spots, especially during the transition from sublimation to desorption drying. This aspect alone can explain the sudden inhomogeneity increase towards the end of MWFD, during the transition between desorption and sublimation drying.

The transition between both drying stages is often determined by the exponential increase in temperature or a decrease in drying rate. The latter criterion is not feasible in our case because the pulsed microwave input also leads to a flattening of the drying rate. Nevertheless, it is evident that the onset of exponential temperature rise coincides with the initial increase in temperature oscillation span. This supports the notion that the growing and eventually peaking inhomogeneity results from the coexistence of cold spots in the sublimation drying stage (associated with a slight temperature increase) and hot spots in the desorption drying stage (characterized by an exponential temperature rise).

Following the inhomogeneity peak, there is a convergence of water content in both hot and cold spots. Cold spots also enter the desorption drying stage. This coincides with a reduction in microwave input during the later stages of MWFD (i.e., during pulsed microwave input). Consequently, there is a subsequent decrease in inhomogeneity as the desorption drying stage advances uniformly across the entire sample.

Impact of Tmax

This section aimed to assess the impact of increasing Tmax on the inhomogeneous distribution of temperatures in the MWFD process. Figure 8A, C, E, and G illustrates a noticeable rise in the maximum oscillation span as Tmax increases. This increasing inhomogeneity in temperature distribution with higher Tmax agrees with the ITC coloration patterns in Fig. 8B, D, F, and H. Each color level represents a span of 1.0 of a*, serving as an indicator for the range of a*-values on the sample surface. A broader range of a*-values indicates more uneven coloration, and the number of excited color levels reflects the inhomogeneity of the MWFD process (Kalinke & Kulozik, 2023).

At a Tmax of 40 °C (Fig. 8B), a minor variation in the a*-values was observed, with only two distinct color levels excited in the contour plot. However, at Tmax = 50 °C, three color levels were spanned, and at Tmax = 60 °C, it covered four. Interestingly, at Tmax = 70 °C, the a*-value spanned only three color levels, suggesting a smaller range of a*-values compared to Tmax = 60 °C. However, this is most likely due to reaching the maximum achievable a*-value, inhibiting further color differentiation at Tmax = 70 °C (Kalinke & Kulozik, 2023). Hence, a clear trend of increased inhomogeneity with higher Tmax was evident in the color intensity patterns shown in Fig. 8.

In addition, the color intensity patterns in Fig. 8 show similar maximum temperature distributions; namely, one edge of the sample exhibited more coloration, indicating exposure to higher temperatures. The specific location of this noticeable lateral coloration is not defined since the samples rotated during drying. Therefore, the orientation in Fig. 8 does not imply a fixed sample orientation during drying but rather signifies increased temperatures on one side of the sample throughout the process. Thereby, the higher temperatures observed at both the edge and partially the center of the sample align with existing literature noting similar heating patterns in cylindrical samples during microwave treatment with turntable rotation (Kalinke & Kulozik, 2023; Schubert et al., 1991; Taghian Dinani et al., 2021).

In summary, Fig. 8 shows in both, exemplarily given drying curves and color intensity patterns, an increasing inhomogeneity with raising Tmax. To emphasize this effect, the maximum oscillation spans were extracted from the temperature curves of each MWFD process and compared. The corresponding data is presented in Fig. 9, indicating the influence of Tmax at different Pset on the maximum oscillation span of temperature data during drying. The results show a significant increase in maximum temperature oscillation spans with higher Tmax, while the effect of Pset was not found to be significant (ANOVA, p < 0.05).

Fig. 9
figure 9

Maximum temperature oscillation spans (Tspan) displaying the maximum inhomogeneity of MWFD. Values of Tspan were extracted from the temperature curves of each MWFD process for different settings of Tmax (40, 50, 60, 70 °C) and Pset (180 W, 200 W, 220 W); the dashed line shows the significant increasing trend of Tspan with increasing Tmax irrespective of Pset setting; Whereat, the effect of different Pset on Tspan was not significant, the effect of Tmax was significant

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These findings demonstrate that the trend of heightened inhomogeneity with higher Tmax settings was observable in both temperature plots (i.e., temperature oscillation spans in Figs. 8 and 9) and ITC color intensity patterns (in Fig. 8), affirming our initial hypothesis. We anticipated that higher Tmax settings would result in greater inhomogeneity owing to the prolonged duration of continuous microwave power application and thus reduced equilibration time. Although the peak of oscillation span occurred during the pulsed microwave power input stage, this hypothesis remained valid. Analysis of the temperature curves in Fig. 8 suggests that higher Tmax results in a higher oscillation span upon entering the second stage of pulsed microwave power input. Furthermore, due to more progressed drying at the onset of this second (pulsed) power stage, the point of peaking inhomogeneity (i.e., the transition from sublimation to desorption drying) approaches the first stage of constant microwave input with higher Tmax. As a result, there was less time for temperature peaks to equilibrate in the pulsed microwave input stage at higher Tmax levels. Consequently, the equilibration time in the pulsed microwave power stage was reduced and the initial inhomogeneity upon entering this stage was heightened for higher Tmax. This explains an overall higher inhomogeneity in MWFD at higher Tmax.

Impact of Pset

While increasing Tmax evidently impacted the uniformity of the process, elevating Pset did not significantly affect the inhomogeneity of MWFD. This became apparent upon analyzing the maximum temperature oscillation spans in Fig. 9. Maximum temperature oscillation spans were slightly higher for 220 W than those for Pset = 200 W, with 180 W displaying the smallest spans. However, this trend lacked both statistical significance and consistency, as the oscillation spans at Tmax = 60 °C contradicted this trend (Fig. 9).

At Tmax = 70 °C, the extent of inhomogeneity and the differences in oscillation spans between different Pset values were most pronounced, as reported in Fig. 9. However, differences in the respective color intensity patterns for different Pset levels at Tmax = 70 °C were still small. This observation was derived from the respective color intensity patterns given in Fig. 10, displaying similar color intensity patterns for all Pset settings, with a*-values spanning two to three distinct color levels. It seemed that the inhomogeneity for 220 W might be somewhat more pronounced than for 200 W and 180 W. This impression stemmed from the presence of three distinct color levels in Fig. 10C and a lower a*-value in the cold spot position, hinting at a higher temperature inhomogeneity for 220 W (Fig. 10C) compared to 180 W (Fig. 10A) and 200 W (Fig. 10B) at the same setting of Tmax (i.e., 70 °C). When temperature inhomogeneity increases at a constant maximum drying temperature setting, this implies colder cold spot temperatures and increased hot spot temperatures. However, as previously described in the “Impact of Tmax” section, further color differentiation for Tmax = 70 °C was already limited by reaching the maximum achievable a*-value at these high Tmax settings. This explains why a further increase in hot spot temperatures could not be observed in the color intensity patterns.

Fig. 10
figure 10

Inhomogeneity of one exemplary drying repetition depicted by the ITC-induced color intensity pattern of the sample for Pset = 180 W (A), Pset = 200 W (B), and Pset = 220 W (C) measured at the end of drying for Tmax = 70 °C

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Overall, neither oscillation temperature spans nor color intensity patterns can be considered clear indicators of increased inhomogeneity with higher Pset, as anticipated in our initial hypothesis. Consequently, our findings did not confirm the hypothesis that higher Pset would lead to increased inhomogeneity. This hypothesis stemmed from the assumption that faster drying processes reduce the equilibration time for peak temperatures, thereby heightening the inhomogeneity of MWFD. However, previous results have already indicated that Pset did not significantly accelerate temperature-controlled MWFD. In addition to this, peaking oscillation spans occurred roughly 7 min after entering the pulsed microwave input stage for all Pset at Tmax = 70 °C. The initial inhomogeneity upon entering this pulsed stage remained relatively consistent across all Pset values at approximately 25 °C (data not shown). Consequently, both the equilibration times and the initial inhomogeneity did not vary with different Pset values. This likely accounts for the absence of a clear correlation between inhomogeneity and Pset.

Conclusion

In conclusion, our study sheds light on the pivotal role of the maximum drying temperature (Tmax) in influencing drying time, energy consumption, and the inhomogeneity of microwave freeze drying (MWFD). Our findings strongly support the hypothesis that shorter equilibration times, linked to higher Tmax resulting from prolonged input of constant microwave power, notably amplify the inhomogeneity of temperature distribution.

Contrary to our initial expectations, the examination of microwave input power (Pset) did not yield statistically significant differences in drying time, energy consumption, or MWFD inhomogeneity, despite a noticeable trend towards shorter drying times and increased inhomogeneity with rising Pset. The limited range of explored Pset values, coupled with the temperature-controlled nature of the drying process, may have rendered a potential influence of Pset in this study negligible. Due to the pulsed microwave input stage of temperature-controlled MWFD, characterized by alternating activated and inactivated microwave input pulses, the mean input power significantly deviates from the nominal value of Pset. Therefore, moving forward, a more comprehensive examination of MWFD with continuous microwave power input could enhance our understanding of how microwave input power levels impact these parameters, particularly the inhomogeneity of MWFD.

Notably, this study underscores the critical importance of temperature control in MWFD. At Tmax = 70 °C, pronounced temperature inhomogeneities were observed, peaking at a considerable temperature span of approximately 55.8 °C. Without reliable temperature tracking or temperature-controlled processing, as commonly reported in the literature, inhomogeneities could be even more substantial, potentially going undetected and presenting significant challenges in achieving high-quality dry products.

The pursuit of gentle and uniform processing remains a fundamental goal, especially in applications where freeze drying is the preferred drying technology. Our study emphasizes the need for targeted approaches to ensure more uniform processing and encourages further exploration into energy-efficient, uniform MWFD. As the pioneering study elucidating the impact of processing parameters in temperature-controlled MWFD on processing uniformity, this research significantly contributes to advancing the understanding of optimal processing in MWFD.