# Optimized Analytical-Numerical Procedure for Ultrasonic Sludge Treatment for Agricultural Use
###### Abstract
The use of ultrasound promotes further solubilization of the compounds and reduces the viscosity of the sludge [37; 38]. There is no lack of significant studies on the combined use of microwaves (as a heat source), which can increase the permeability of cell membranes, with ultrasound, which, by causing cavitation, destroys cellular structures and significantly biodegrades sludge [39]. Recently, the combination of ultrasonic techniques with electrocoagulation has been successfully used to remove heavy metals from sludge. Electrical charges destabilize suspended particles, while sonication breaks down cellular structures, facilitating sedimentation of the sludge [40]. These studies strongly suggest that a major line of research must be based on using sonication in combination with chemical or physical treatments to improve sludge quality and manageability significantly. Indeed, combined sonication methods show superior results compared to single treatments, positively impacting process efficiency. Research in this field constantly evolves, with the intent to develop increasingly efficient, sustainable, and environmentally friendly conditioning techniques. This work introduces an innovative approach that combines sonication with thermal treatment, proposing an advanced physical-mathematical model that couples the thermal and ultrasonic aspects. Such a model allows the reconstruction of detailed maps of temperature, humidity, and pressure on the walls of the treatment tank, providing an accurate and predictive view of system behavior throughout the sludge processing. Integrating this information enables optimized and scientifically based treatment management, reducing operating time and costs. The design of the apparatus was preceded by a detailed numerical simulation using the finite element method (FEM), which allowed the functional characteristics of the tank to be developed and verified virtually, ensuring efficient management of thermal and water variables [41]. The entire apparatus was built and tested only after this software validation, demonstrating complete adherence to regulatory standards for sludge use in agriculture. The proposed system, through integrated sensor monitoring and optimization of operating parameters, has shown the ability to reduce heavy metal content and improve the organic composition of sludge, making it fully compatible with current environmental requirements. The combined drying and sonication technique also enables particle size reduction of up to 50%, contributing to the sustainability and reuse of materials within a circular economy model [42]. This approach emerges as a practical and innovative model of sustainable sewage sludge management, with results that improve environmental and energy efficiency and demonstrate the possibility of valorizing sludge as a safe and certified agricultural resource. For completeness, with the aim to provide the reader with a comprehensive overview of related work to the present research, we refer to some scientific studies on innovative sludge treatment and valorization techniques, focusing on sustainable methods, advanced technologies, and energy and nutrient recovery processes. Prominent among them are: (a) work on C recovery for bioenergy and N and P recovery for nutrients [43]; (b) on resource recovery for biogas production and P extraction for agricultural reuse [44];(c) Anaerobic digestion combined with phosphorus recovery from sludge [45]; (d) Chemical/electrochemical methods for removal of heavy metals [46]; (e) Use of thermolysis and sonication for biogas production [47]; (f) on biochar production and C sequestration [48]; (g) on the use of electrodehydration to improve water removal [49]; (h) on the use of phytoremediation to remove heavy metals [50]; (i) the joint use of microwaves and chemical treatments to reduce pathogens in sludge and recover P and N [51]; (l) waste-to-energy for energy resources [52]; (m) hydrothermal carbonization for biofuel production, nutrient recovery, and energy enhancement [53].