Abstract:
Microwave thermotherapy can be expected to prevent the citrus Huanglongbing (HLB) in recent years. Yet the excessively long experimental cycles can rely mainly on many seedlings during large-scale application. It is often required to accurately characterize the dynamic distribution in the internal temperature field of the citrus seedlings during microwave heating. In this study, an efficient simulation model was developed for microwave heat treatment. A dielectric inversion model was constructed and then validated for the microwave thermotherapy of citrus seedlings. Firstly, the morphological data were captured from the citrus seedlings. A parameterized three-dimensional (3D) geometric model of the seedlings was constructed using SolidWorks 2025, in order to accurately reproduce the structural features of the leaves, branches, and their topological connections. Subsequently, a coupled "microwave electromagnetic-solid heat transfer" physical field was established to simulate the microwave heating in COMSOL Multiphysics 6.3. The key dielectric properties of the citrus seedling components (leaves and branches) were determined to optimize the microwave energy absorption. The Interior Point OPTimizer (IPOPT) algorithm was also employed for the inverse optimization. The real and imaginary parts of the complex dielectric parameters were iteratively adjusted from the pre-set initial values. The better performance was achieved by minimizing the root mean square error (RMSE) between the simulated temperature curves and the experimentally measured ones. Single-component experiments also validated the reliability of the inverse optimization. In both leaves and branches, the coefficient of determination (R²) between the simulated temperatures and the measurements exceeded 98.4%, while the RMSE was below 3% of the average measured temperature, indicating a high degree of consistency between the simulation and the actual heating. The whole-plant experiments were conducted under different microwave power conditions (150, 250, 350, 450, and 550 W), in order to further verify the applicability of the model to intact citrus seedlings. Temperature monitoring points were arranged at the top, middle, and bottom of the seedlings. The dynamic temperature was then recorded during monitoring. The results showed that the high prediction accuracy was maintained in the power range of 150-450 W: the
R2 for all monitoring positions was ≥ 98.5%, and the RMSE was below 3% of the average measured temperature. The actual microwave heating of the whole citrus seedlings was accurately simulated in the power range. Thereby, the temperature range (48-54°C) was required for the HLB pathogen inactivation. Once the microwave power increased to 550 W, significant deviations were observed between the simulated and measured temperatures. There was a rapid rise in the internal temperature of the seedling tissues under high power. Specifically, the molecular thermal motion was intensified to shorten the polarization relaxation time, leading to the nonlinear variations in the real and imaginary parts of the dielectric constant in the current model. Fixed dielectric properties failed to fully capture during this time. The key findings were as follows: 1) The IPOPT inversion of the dielectric parameters exhibited excellent stability, with the relative variation less than 0.5% over three repeated experiments, indicating the reliable input parameters of the model. 2) The coupled multi-physics modeling significantly reduced the consumption of the experimental seedlings. Only 3 seedlings were required at the initial construction stage, where the seedling usage was reduced by more than 90%. The efficiency of parameter optimization was improved with the cost savings, compared with the conventional method. 3) A power-adaptive range (150–450 W) was defined to stably and accurately predict the temperature distribution of citrus seedlings. A precise operational window was provided for the practical application of microwave thermotherapy in HLB control. In summary, this simulation platform can accurately reproduce the dynamic microwave heating of the citrus seedlings. A resource-efficient and scalable tool can offer to optimize the parameters of HLB microwave thermotherapy. The dependency on physical seedlings can be effectively reduced to provide technical support for the green and large-scale promotion of HLB control technologies. Future research should focus on the nonlinear variation of dielectric properties under high power. The high applicability and prediction accuracy can also be required to consider the microstructural heterogeneity (e.g., vascular bundles in leaves and branches).