The mismatch between experimental and computational fluid dynamics analyses for magnetic surface microrollers

www.nature.com/scientificreports OPEN The mismatch between experimental and computational fluid dynamics analyses for magnetic surface microrollers Ugur Bozuyuk 1,2, Hakancan Ozturk 1 & Metin Sitti 1,2,3* Magnetically actuated Janus surface microrollers are promising microrobotic platform with numerous potential biomedical engineering applications. While the locomotion models based on a "rotating sphere on a nearby wall" can be adapted to surface microrollers, real-world dynamics may differ from the proposed theories/simulations. In this study, we examine the locomotion efficiency of surface microrollers with diameters of 5, 10, 25, and 50 µm and demonstrate that computational fluid dynamics simulations cannot accurately capture locomotion characteristics for different sizes of microrollers. Specifically, we observe a significant mismatch between lift forces predicted by simulations and opposite balancing forces, particularly for smaller microrollers. We propose the existence of an unaccounted force component in the direction of lift, which is not included in the computational fluid dynamics simulations. Overall, our findings provide a deeper understanding of the physical mechanisms underlying surface microroller locomotion and have important implications for future applications in biomedical engineering. Magnetic surface microrollers have shown great potential for various biomedical applications, such as navigation in blood flow for cargo delivery and potential lab-on-a-chip applications1–14. The translational motion of the microrollers is achieved by the rotation of the particle body on a nearby wall, by applying external uniform rotating fields15–18. The locomotion direction can also be precisely controlled by changing the orientation of the rotational field1–4. To better understand the locomotion characteristics of surface microrollers and improve their practical applications, proposed theories of "rotating sphere on a nearby wall" can be e mployed15,16,18. Such theories provide a valuable framework for studying the behavior of these microrollers and optimizing their performance. Asymptotic solutions of the Stokes equations15 are proposed to explain the locomotion of the rotating sphere on a nearby wall in the low Reynolds number regime, which also has been used for surface-rolling microrobots1–3,6,19–21. The theory explains the force balance on the x-axis, that the sphere’s rotation creates a propulsion force, FP, which is balanced out by a drag force, FD, due to the translational motion of the sphere (Fig. 1) 15. On the other hand, the extent of these forces also depends on the lubrication distance, δ, which is the result of the force balance on the z-axis (Fig. 1). Unlike the forces in the x-axis, there are forces with nonhydrodynamic origins, such as Frep and FG, in the z-axis (Fig. 1). Frep is the chemical repulsion force between the sphere and the w all22, and FG is gravitational over buoyancy, a permanent non-contact force depending on the material properties23. On the other hand, the lift force, FL, has a hydrodynamic origin, which explains the hydrodynamic repulsion of the sphere due to flows created by the nearby wall (Fig. 1) 24–26. To capture the forces with a hydrodynamic origin, we developed a computational fluid dynamics (CFD) simulation in three dimensions for the rotating and translating sphere c ase2 that converged the same results from Goldman et al. 2,15. Therefore, we can study the nature of these forces for different environments and sizes for different conditions. In this work, we demonstrated how experimental results were mismatched with the CFD simulation results for surface microrollers. We performed basic experimental analysis on the spherical microrollers of different 1 Physical Intelligence Department, Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany. 2Institute for Biomedical Engineering, ETH Zurich, 8092 Zurich, Switzerland. 3School of Medicine and School of Engineering, Koç University, Istanbul 34450, Turkey. *email: Scientific Reports | (2023) 13:10196 | https://doi.org/10.1038/s41598-023-37332-5 1 Vol.:(0123456789) www.nature.com/scientificreports/ Figure 1.  The basic force balance on a microroller near a wall. A microroller, rotating with an angular velocity of Ω, with a distance of δ from the nearby wall, creates a propulsion force, FP, balanced out the drag force, FD, on the x-axis. The lift force, FL, and repulsion force, Frep, are balanced by the gravitational over-buoyancy force, FG. The origin of the forces was marked with the color code. diameters, 5, 10, 25, and 50 µm. We analyzed their translational speeds (V) in a static and semi-infinite environment for increasing rotational speeds (Ω). Our investigation revealed a non-linear relationship between microroller size and locomotion efficiency, defined as the microroller’s ability to convert rotational motion into translational motion. The microroller with a diameter of 50 µm demonstrated the highest efficiency among the different sizes tested, while the 10 µm microroller was found to be the least efficient. The overall ranking of the microrollers from most to least efficient was as follows: 50 µm > 5 µm > 25 µm > 10 µm. To understand this relationship, we conducted computational fluid dynamics (CFD) analyses. However, the analyses failed to explain the irregular relationship observed in the experimental results. In fact, the CFD analyses significantly overestimated the forces involved, with FG dominating over FL and Frep. This discrepancy indicated that the force balance on the z-axis was not satisfied. Overall, the main aim of this study is to analyze this discrepancy and discuss the reasons behind it. Results The basic speed analyses of microrollers with different diameters. We characterized the speeds of magnetic surface microrollers for different sizes (Fig. 2). The fabrication of surface microrollers is summarized in Fig. 2a. The silica particles with different sizes were monolayered on a glass substrate, and then the particles were sputter-coated with Ni and Au. To obtain ≈5 μm microroller, 4 μm silica particles are sputter coated with 1000 nm Ni and 50 nm Au; the ≈10 μm microroller also has 1000 nm Ni and 50 nm Au on top of 10 μm particles (Fig. 2b). The ≈25 and ≈50 μm microrollers contain 1800 nm Ni and 50 nm Au on top of 25 and 50 μm silica particles, respectively (Fig. 2b). Then, we characterized their steady-state translational speeds for increasing rotational frequencies until f = 80 Hz since it was the highest actuation frequency for 50 μm (Figure S1); therefore, f = 80 Hz was selected for the highest limit for all groups for a concise comparison. The other microrollers did not also step-out until f = 80 Hz as their translational speed never decreased with increasing rotation frequency (Fig. 2c). The 50 μm microrollers performed best with the highest body length per second (Fig. 2c), and 5 μm microrollers had the second rank (...truncated)