Nonlinear dynamics of diamagnetically levitating resonators.

The ultimate isolation offered by levitation provides new opportunities for studying fundamental science and realizing ultra-sensitive floating sensors. Among different levitation schemes, diamagnetic levitation is attractive because it allows stable levitation at room temperature without a continuous power supply. While the dynamics of diamagnetically levitating objects in the linear regime are well studied, their nonlinear dynamics have received little attention. Here, we experimentally and theoretically study the nonlinear dynamic response of graphite resonators that levitate in permanent magnetic traps. By large amplitude actuation, we drive the resonators into nonlinear regime and measure their motion using laser Doppler interferometry. Unlike other magnetic levitation systems, here we observe a resonance frequency reduction with amplitude in a diamagnetic levitation system that we attribute to the softening effect of the magnetic force. We then analyze the asymmetric magnetic potential and construct a model that captures the experimental nonlinear dynamic behavior over a wide range of excitation forces. We also investigate the linearity of the damping forces on the levitating resonator, and show that although eddy current damping remains linear over a large range, gas damping opens a route for tuning nonlinear damping forces via the squeeze-film effect. Supplementary Information: The online version contains supplementary material available at 10.1007/s11071-024-10018-x.

Pyrolytic Graphite for an In-Plane Force Study of Diamagnetic Levitation: A Potential Microdetector of Cracks in Magnetic Material.

The diamagnetic levitation technique can be applied in non-destructive testing for identifying cracks and defects in magnetic materials. Pyrolytic graphite is a material that can be leveraged in micromachines due to its no-power diamagnetic levitation on a permanent magnet (PM) array. However, the damping force applied to pyrolytic graphite prevents it from maintaining continuous motion along the PM array. This study investigated the diamagnetic levitation process of pyrolytic graphite on a permanent magnet array from various aspects and drew several important conclusions. Firstly, the intersection points on the permanent magnet array had the lowest potential energy and validated the stable levitation of pyrolytic graphite on these points. Secondly, the force exerted on the pyrolytic graphite during in-plane motion was at the micronewton level. The magnitude of the in-plane force and the stable time of the pyrolytic graphite were related to the size ratio between it and the PM. During the fixed-axis rotation process, the friction coefficient and friction force decreased as the rotational speed decreased. Smaller-sized pyrolytic graphite can be used for magnetic detection, precise positioning and other microdevices. The diamagnetic levitation of pyrolytic graphite can also be used for detecting cracks and defects in magnetic materials. We hope this technique will be used in crack detection, magnetic detection and other micromachines.

Diamagnetic Composites for High-Q Levitating Resonators.

Levitation offers extreme isolation of mechanical systems from their environment, while enabling unconstrained high-precision translation and rotation of objects. Diamagnetic levitation is one of the most attractive levitation schemes because it allows stable levitation at room temperature without the need for a continuous power supply. However, dissipation by eddy currents in conventional diamagnetic materials significantly limits the application potential of diamagnetically levitating systems. Here, a route toward high-Q macroscopic levitating resonators by substantially reducing eddy current damping using graphite particle based diamagnetic composites is presented. Resonators that feature quality factors Q above 450 000 and vibration lifetimes beyond one hour are demonstrated, while levitating above permanent magnets in high vacuum at room temperature. The composite resonators have a Q that is >400 times higher than that of diamagnetic graphite plates. By tuning the composite particle size and density, the dissipation reduction mechanism is investigated, and the Q of the levitating resonators is enhanced. Since their estimated acceleration noise is as low as some of the best superconducting levitating accelerometers at cryogenic temperatures, the high Q and large mass of the presented composite resonators positions them as one of the most promising technologies for next generation ultra-sensitive room temperature accelerometers.

Spatial Manipulation of Particles and Cells at Micro- and Nanoscale via Magnetic Forces.

The importance of magnetic micro- and nanoparticles for applications in biomedical technology is widely recognised. Many of these applications, including tissue engineering, cell sorting, biosensors, drug delivery, and lab-on-chip devices, require remote manipulation of magnetic objects. High-gradient magnetic fields generated by micromagnets in the range of 103-105 T/m are sufficient for magnetic forces to overcome other forces caused by viscosity, gravity, and thermal fluctuations. In this paper, various magnetic systems capable of generating magnetic fields with required spatial gradients are analysed. Starting from simple systems of individual magnets and methods of field computation, more advanced magnetic microarrays obtained by lithography patterning of permanent magnets are introduced. More flexible field configurations can be formed with the use of soft magnetic materials magnetised by an external field, which allows control over both temporal and spatial field distributions. As an example, soft magnetic microwires are considered. A very attractive method of field generation is utilising tuneable domain configurations. In this review, we discuss the force requirements and constraints for different areas of application, emphasising the current challenges and how to overcome them.

Lab-on-a-Chip Technologies for Microgravity Simulation and Space Applications.

Gravity plays an important role in the development of life on earth. The effect of gravity on living organisms can be investigated by controlling the magnitude of gravity. Most reduced gravity experiments are conducted on the Lower Earth Orbit (LEO) in the International Space Station (ISS). However, running experiments in ISS face challenges such as high cost, extreme condition, lack of direct accessibility, and long waiting period. Therefore, researchers have developed various ground-based devices and methods to perform reduced gravity experiments. However, the advantage of space conditions for developing new drugs, vaccines, and chemical applications requires more attention and new research. Advancements in conventional methods and the development of new methods are necessary to fulfil these demands. The advantages of Lab-on-a-Chip (LOC) devices make them an attractive option for simulating microgravity. This paper briefly reviews the advancement of LOC technologies for simulating microgravity in an earth-based laboratory.

Micro-UFO (Untethered Floating Object): A Highly Accurate Microrobot Manipulation Technique.

A new microrobot manipulation technique with high precision (nano level) positional accuracy to move in a liquid environment with diamagnetic levitation is presented. Untethered manipulation of microrobots by means of externally applied magnetic forces has been emerging as a promising field of research, particularly due to its potential for medical and biological applications. The purpose of the presented method is to eliminate friction force between the surface of the substrate and microrobot. In an effort to achieve high accuracy motion, required magnetic force for the levitation of the microrobot was determined by finite element method (FEM) simulations in COMSOL (version 5.3, COMSOL Inc., Stockholm, Sweden) and verified by experimental results. According to position of the lifter magnet, the levitation height of the microrobot in the liquid was found analytically, and compared with the experimental results head-to-head. The stable working range of the microrobot is between 30 µm to 330 µm, and it was confirmed in both simulations and experimental results. It can follow the given trajectory with high accuracy (<1 µm error avg.) at varied speeds and levitation heights. Due to the nano-level positioning accuracy, desired locomotion can be achieved in pre-specified trajectories (sinusoidal or circular). During its locomotion, phase difference between lifter magnet and carrier magnet has been observed, and relation with drag force effect has been discussed. Without using strong electromagnets or bulky permanent magnets, our manipulation approach can move the microrobot in three dimensions in a liquid environment.

Stabilization of Microrobot Motion Characteristics in Liquid Media.

Magnetically actuated microrobot in a liquid media is faced with the problem of head-tilting reaction caused by its hydrodynamic structure and its speed while moving horizontally. When the instance microrobot starts a lateral motion, the drag force acting on it increases. Thus, the microrobot is unable to move parallel to the surface due to the existence of drag force that cannot be neglected, particularly at high speeds such as >5 mm/s. The effect of it scales exponentially at different speeds and the head-tilting angle of the microrobot changes relative to the reference surface. To the best of our knowledge, there is no prior study on this problem, and no solution has been proposed so far. In this study, we developed and experimented with 3 control models to stabilize microrobot motion characteristics in liquid media to achieve accurate lateral locomotion. The microrobot moves in an untethered manner, and its localization is carried out by a neodymium magnet (grade N48) placed inside its polymer body. This permanent magnet is called a carrier-magnet. The fabricated microrobot is levitated diamagnetically using a pyrolytic graphite placed under it and an external permanent magnet, called a lifter-magnet (grade N48), aligned above it. The lifter-magnet is attached to a servo motor mechanism which can control carrier-magnet orientation along with roll and pitch axes. Controlling the angle of this servo motor, together with the lifter-magnet, allowed us to cope with the head-tilting reaction instantly. Based on the finite element method (FEM), analyses that were designed according to this experimental setup, the equations giving the relation of microrobot speed with servo motor angle along with the microrobot head-tilting angle with servo motor angle, were derived. The control inputs were obtained by COMSOL® (version 5.3, COMSOL Inc., Stockholm, Sweden). Using these derived equations, the rule-based model, laser model, and hybrid model techniques were proposed in this study to decrease the head-tilting angle. Motion control algorithms were applied in di-ionized water medium. According to the results for these 3 control strategies, at higher speeds (>5 mm/s) and 5 mm horizontal motion trajectory, the average head-tilting angle was reduced to 2.7° with the ruled-based model, 1.1° with the laser model, and 0.7° with the hybrid model.

A quality comparison of protein crystals grown under containerless conditions generated by diamagnetic levitation, silicone oil and agarose gel.

High-quality crystals are key to obtaining accurate three-dimensional structures of proteins using X-ray diffraction techniques. However, obtaining such protein crystals is often a challenge. Several containerless crystallization techniques have been reported to have the ability to improve crystal quality, but it is unknown which is the most favourable way to grow high-quality protein crystals. In this paper, a quality comparison of protein crystals which were grown under three containerless conditions provided by diamagnetic levitation, silicone oil and agarose gel was conducted. A control experiment on a vessel wall was also simultaneously carried out. Seven different proteins were crystallized under the four conditions, and the crystal quality was assessed in terms of the resolution limit, the mosaicity and the Rmerge. It was found that the crystals grown under the three containerless conditions demonstrated better morphology than those of the control. X-ray diffraction data indicated that the quality of the crystals grown under the three containerless conditions was better than that of the control. Of the three containerless crystallization techniques, the diamagnetic levitation technique exhibited the best performance in enhancing crystal quality. This paper is to our knowledge the first report of improvement of crystal quality using a diamagnetic levitation technique. Crystals obtained from agarose gel demonstrated the second best improvement in crystal quality. The study indicated that the diamagnetic levitation technique is indeed a favourable method for growing high-quality protein crystals, and its utilization is thus potentially useful in practical efforts to obtain well diffracting protein crystals.