Microwave technology is a promising field of current research, especially in view of its potential to heat food fast and energy-efficient due to volumetric heating. However, its main drawback is the inhomogeneity of temperature distribution resulting from the inherent standing wave pattern within the microwave treatment chamber. Hence, the electromagnetic field is not homogeneously distributed and the product is thus exposed to variable energy levels, which is the main reason for temperature inhomogeneities in the product. As a result, hot and cold spots form at positions of high or low microwave field strength. With the recent introduction of innovative solid-state generators to microwave heating new operating parameters were introduced to microwave processing. These include the precise control of microwave frequency, phase and power, which offers the possibility of influencing the microwave field in the cavity in a targeted manner. This aspect can be considered to optimise microwave heating regarding uniformity or energy efficiency of microwave heating. In this context, different optimisation strategies by means of targeted frequency adjustment have been discussed in various works (Du et al., 2019; Taghian Dinani, Feldmann, & Kulozik, 2021; Yakovlev, 2018; Yang, Fathy, Morgan and Chen, 2022a, Yang, Fathy, Morgan and Chen, 2022b). These authors used the approach of changing the standing wave pattern during the microwave process by varying the excitation frequency in order to achieve more homogeneous heating. This is because, for different frequency settings the resulting standing wave pattern in the cavity and thus, also the heating pattern in the product differ significantly (Luan, Wang, Tang, & Jain, 2017; Monteiro, Costa, Valente, Santos, & Sousa, 2011; Taghian Dinani, Feldmann, & Kulozik, 2021). This effect has already been used to achieve more homogeneous heating patterns than by excitation at a single fixed frequency setting (FF strategy). Thereby, superposition of different heating patterns along the entire processing time leads, on average, to a more homogeneous heating pattern in the product (Antonio & Deam, 2005; Du et al., 2019; Taghian Dinani, Feldmann, & Kulozik, 2021; Yang et al., 2022a; Zhou et al., 2018). This superposition approach to achieve more homogeneous heating, showed good results regarding uniformity in the so-called equidistant frequency shifting strategy (EF strategy) (Du et al., 2019; Taghian Dinani, Feldmann, & Kulozik, 2021; Yakovlev, 2018; Yang et al., 2022a). In this strategy, a pre-defined loop of frequency steps is successively run through along the heating process. Thereby, different frequency step widths in a pre-defined frequency range (e.g. 2400–2500 MHz) and different holding times of each frequency setting can be chosen. It was reported that the number of individual frequency settings was the decisive factor for increasing process homogeneity (Du et al., 2019; Taghian Dinani, Feldmann, & Kulozik, 2021). The authors showed that the holding time of a single frequency step and, thus, the number of total passes of a frequency loop in one heating process had no significant effect on process homogeneity. Furthermore, these works reported that the setting with the smallest frequency step width and thus, with the highest number of different frequency settings resulted in the most homogeneous heating.

Further strategies to enhance uniformity of microwave processing consist of targeted selection of frequency settings that, e.g., result in complementary heating patterns in the product (Yang, Fathy, Morgan and Chen, 2022a, Yang, Fathy, Morgan and Chen, 2022b). This, however, requires a prior identification of the individual heating patterns in the respective product resulting from the potential frequency settings, as well as the respective online measurement equipment (i.e. thermographic camera) and evaluation software. This strategy seems to be limited regarding its transferability to other microwave processes, where the product parameters change significantly during the microwave process, such as microwave-assisted drying. This is because heating patterns are not only a result of the microwave frequency setting, but also of the dielectric properties of the product (Monteiro et al., 2011).

In contrast to the previously described optimisation strategies that are mainly targeting on uniformity, a more common approach in solid-state systems comprises of targeted frequency selection to increase energy efficiency (Atuonwu & Tassou, 2018; Sickert, Kalinke, Christoph, & Gaukel, 2023). In this context, energy efficiency relates to the proportion of input microwave energy absorbed by the product – in contrast to energy reflection back into the generator. It was shown that the level of energy efficiency differs with excitation frequency (Atuonwu & Tassou, 2018; Taghian Dinani, Feldmann, & Kulozik, 2021; Yakovlev, 2018; Yang et al., 2022a). Therefore, instead of shifting frequencies un-biased throughout the frequency range (i.e. for EF strategy), a pre-selection based on energy efficiency or heating rate of individual frequency settings can be applied to improve the overall process efficiency (Tang et al., 2018; Yakovlev, 2018; Yang et al., 2022a). In this context, Yakovlev (2018) achieved a high energy efficiency for a frequency shifting strategy with excitation at all resonant frequencies in the range of 2400–2500 MHz, the so-called resonant frequencies strategy (RFS strategy). Resonant frequencies are characterised by a maximum of absorbed microwave power compared to neighbouring frequencies (Sickert et al., 2023; Yakovlev, 2018). While the RFS strategy showed a good performance regarding energy efficiency compared to the reference EF strategy (targeting solely uniformity), its contribution to process uniformity compared to other optimisation strategies remains still unclear. In contrast to the EF strategy, RFS showed no significant beneficial effect on uniformity (Yakovlev, 2018). However, these investigations on RFS strategy, including the selection of resonant frequencies, are based on simulation results only and have not been validated experimentally. With regard to the recently shown discrepancy of simulation and experimental data in the investigation of resonant frequencies (Sickert et al., 2023), an experimentally derived selection procedure of the resonant frequencies appears as better feasible for future applicability and therefore, for wide industrial application.

In summary, knowledge on the performance of different optimisation strategies regarding both, energy efficiency and uniformity, is scarce - especially concerning a comprehensive comparative study in one experimental setup. This is an important knowledge gap, as current literature concludes that a trade-off exists between pure maximisation of uniformity and energy efficiency (Sickert et al., 2023). Therefore, the aim of this work was to evaluate the potential of different frequency-selection optimisation strategies in a systematic experimental study, focusing on simultaneous improvement of heating uniformity and energy efficiency. It is known, that in a cavity only a limited number of standing wave patterns, so-called resonant modes, are excited (Tang, 2015). Further, it is known, that superposition of different heating patterns results in more uniform heating. Different heating patterns for different excitation frequencies are the result of changes in the standing wave pattern in the cavity (Monteiro et al., 2011; Yakovlev, 2018; Zhou et al., 2018). Thus, we hypothesised that due to the limited number of possible standing wave patterns in the microwave cavity, only a limited number of distinctly different heating patterns in the product can occur. Only distinctly different heating patterns should contribute significantly to increasing homogeneity by superposition. Based on this, we hypothesised that a simultaneous increase of energy efficiency and uniformity should be achieved by choosing these distinctly different heating patterns at the highest achievable energy efficiency. Therefore, we first investigated the heating patterns occurring at different fixed frequencies (FF strategy) and then put them in relation to their energy efficiency. Based on these findings, we investigated and compared five different optimisation strategies in terms of achievable energy efficiency and homogeneity:

Overall resonant frequency selection (RF strategy),

RFS strategy,

A new, adapted RFS strategy derived from our experimental data (aRFS strategy),

EF strategy, and.

Random frequency variation (RND strategy).

This study could help to address the high demand for broad-based and easy-to-use optimisation strategies for microwave processes addressing new possibilities of microwave field control inherent to up-coming solid-state microwave generators.