Millimeter-Scale Lagrangian Sensor Spheres for Local State Monitoring in SMART Reactors: Towards Energy-Autonomous Operation

Abstract Flow-following sensor particles are a promising route to obtaining spatially resolved measurements in (bio)chemical reactors. However, their practical deployment is limited by miniaturization, power supply, and packaging. This work presents a millimeter-scale Lagrangian sensor-node platform that integrates an inertial measurement unit (IMU) and a low-power microcontroller unit (MCU) on a high-density interconnect (HDI) printed circuit board (PCB), illustrating the evolution from a first demonstrator (V1) toward a reduced-footprint design (V2) intended for spherical encapsulation. The main contribution is a quantitative system-level feasibility boundary that links miniaturized sensor-node design, duty-cycled energy demand, candidate energy-input routes, and spherical packaging constraints at the targeted millimeter scale. We analyze the baseline power demand of the current duty-cycled implementation, including a cycle-based charge and energy budget, and relate this demand to two experimentally investigated energy-input routes: photovoltaic harvesting under controlled optical illumination and resonant inductive power transfer at 13.56 MHz. The harvesting experiments are performed on dedicated evaluation platforms and are used to quantify candidate energy-input routes. A closed energy-autonomous sensor-in-flow demonstration is not yet claimed. The results show that the platform concept, compact HDI integration, low-power duty cycling, optical data transmission, and a glass-based encapsulation route are technically feasible at the targeted size. At the same time, neither harvesting route yet closes the gap to robust energy-autonomous operation under realistic reactor conditions. Photovoltaic powering appears strongly constrained by alignment, optical access, and geometric coupling. Inductive transfer is more promising but remains highly sensitive to orientation, field distribution, and RF-to-DC conversion efficiency. The presented measurements therefore define both the current feasibility range and the remaining engineering requirements for future energy-autonomous sensor spheres.