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Item type:Publication, Access status: with files , Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations(Institute of Physics (IOP), 2026-10-27); ; ; The Maxey-Riley-Gatignol equations (MaRGE) model the motion of spherical inertial particles in a fluid. They contain the Basset force, an integral term which models history effects due to the formation of wakes and boundary layer effects. This causes the force that acts on a particle to depend on its past trajectory and complicates the numerical solution of MaRGE. Therefore, the Basset force is often neglected, despite substantial evidence that it has both quantitative and qualitative impact on the movement patterns of modelled particles. Using the concept of universal differential equations, we propose an approximation of the history term via neural networks which approximates MaRGE by a system of ordinary differential equations that can be solved with standard numerical solvers like Runge-Kutta methods. In particular, for long-term and high-resolution simulations of trajectories, where the number of required time-steps is large, the UDE approach can reduce time-to-solution.Publicationtype: Journal Article54 1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Tracking in-silico Lagrangian sensors in a lab-scale stirred tank reactor.(Elsevier, 2026-09-28); ; ; ; Lagrangian sensors have shown promise to improve operator awareness of conditions inside a chemical reactor but three-dimensional tracking remains a mostly unsolved challenge. We explore a setup where in-silico sensors, based on a recently proposed real-world design, are tracked using data from an accelerometer and magnetometer available from a built-in inertial measurement unit. Filtering algorithms, using a bespoke dynamical model, are used to process these readings into position estimates. We compare tracking performance of an extended Kalman filter, a particle filter and the unscented Kalman filter implemented in the pykalman library. Our numerical experiments track in-silico particles moving in an analytically given threedimensional vortex as well as in the experimentally measured flow-field of a lab-scale stirred tank reactor. Using the Maxey-Riley-Gatignol equations for the movement of inertial particles as ground-truth, we demonstrate that the extended Kalman filter and the particle filter reconstruct trajectories from noisy synthetic data with mean relative errors below 3%.Publicationtype: Journal Article51 26 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Millimeter-scale Lagrangian sensor spheres for local state monitoring in SMART reactors: towards energy-autonomous operation(American Chemical Society (ACS), 2026-09-18); ; ; ; 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.Publicationtype: Journal Article40 22 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Numerical modeling of inertial particles in three‐dimensional fluid flowThe motion of inertial particles in a fluid is modeled by the Maxey–Riley–Gatignol equation (MaRGE). The MaRGE contains an integral term that arises due to the viscous diffusion of vorticity in the fluid around the particle. Because it makes MaRGE difficult to solve numerically, the integral term is often neglected or approximated, despite its demonstrated importance for obtaining realistic trajectories. There are some studies that propose algorithms to solve the full MaRGE numerically for two dimensional flows fields. For simple flows like a vortex, analytical solutions exist that can serve as test cases to verify implementations. However, in most practical applications, fluids will be three dimensional. This article extends a multi‐step algorithm proposed by Daitche to the three‐dimensional case. Based on an approach by Candelier et al., it derives an analytical solution for a particle moving in a three‐dimensional vortex while being subject to gravity. Numerical examples compare empirical and theoretical convergence orders and demonstrate order reduction in particular for particles with non‐zero relative initial velocity.Publicationtype: Journal Article58 48