Anke Klingner

Self-excited oscillatory dynamics of capillary bridges in electric fields

We studied the stability of capillary bridges between flat, parallel, and dielectrically coated electrodes as a function of the voltage applied between them. The stability limits of the capillary bridge state and the state consisting of two separated droplets are shifted with respect to ordinary capillary hysteresis at zero voltage. Surprisingly, we found that the system can oscillate periodically between the two states within a certain range of applied voltage and electrode separation. These oscillations could be applied to promote mixing in electrowetting-based microfluidic devices. We present a model based on the balance between interfacial and electrostatic energies, which explains the experimental findings quantitatively.

Magnetic propulsion of robotic sperms at low-Reynolds number

We investigate the microswimming behaviour of robotic sperms in viscous fluids. These robotic sperms are fabricated from polystyrene dissolved in dimethyl formamide and iron-oxide nanoparticles. This composition allows the nanoparticles to be concentrated within the bead of the robotic sperm and provide magnetic dipole, whereas the flexibility of the ultra-thin tail enables flagellated locomotion using magnetic fields in millitesla range. We show that these robotic sperms have similar morphology and swimming behaviour to those of sperm cells. Moreover, we show experimentally that our robotic sperms swim controllably at an average speed of approximately one body length per second (around 125 μm s−1), and they are relatively faster than the microswimmers that depend on planar wave propulsion in low-Reynolds number fluids.

Propulsion and steering of helical magnetic microrobots using two synchronized rotating dipole fields in three-dimensional space

We control the motion of helical microrobots with average diameter of 500 μm in two-dimensional (2D) and three-dimensional (3D) spaces using two synchronized rotating dipole fields. The utilization of the two synchronized dipole fields not only increases the magnetic torque exerted on the magnetic dipole of the helical microrobot but also eliminates the magnetic field gradients along its lateral directions. Our finite element simulations and experimental results show that the utilization of two rotating dipole fields increases the magnetic field by 100%, as opposed to single rotating magnetic field. In addition, we show that the magnetic field gradient within the workspace of the microrobot is eliminated. Therefore, the lateral oscillations of the helical microrobot are mitigated within the center of two rotating dipole fields, and hence the motion of the microrobot is stabilized inside tubes with relatively large inner diameters, as opposed to the diameter of the helical microrobot. This strategy allows the microrobot to compensate for gravity and swim in 3D space inside water reservoirs at an average speed of 0.25 body lengths per second. In addition, closed-loop motion control of the helical microrobot is achieved in 2D space at an average speed of 2 mm/s and maximum steady-state error of 100 μm.

Non-Contact manipulation of microbeads via pushing and pulling using magnetically controlled clusters of paramagnetic microparticles

In contact micromanipulation, the adhesive forces between manipulators and microobjects decrease the chances of achieving successful releases at the desired positions. We study a non-contact micromanipulation technique of microbeads (300 μm in average diameter) using clusters of paramagnetic microparticles (100 μm in average diameter). This non-contact micromanipulation is done using the hydrodynamic forces instead of the interaction forces in contact manipulation, and hence eliminates the adhesive forces that decrease the chances of achieving successful releases. Motion of the cluster of microparticles results in a pressure gradient (within the vicinity of the microbead in a fluid) that derives and steers the microbeads without contact. The microparticles are moved under the influence of controlled magnetic field gradient to push or pull the microbeads towards reference positions. We achieve non-contact manipulation via pushing and pulling at average speeds of 219 μm/s and 258 μm/s for the microbead, respectively (using cluster of 10 microparticles). The noncontact pushing and pulling localize the microbeads within the vicinity of reference positions with average steady-state errors of 177 μm and 100 μm, respectively. Moreover, we experimentally demonstrate non-contact microassembly of 3 microbeads into an L-shape at a task completion time of 25 seconds.

Magnetic-based motion control of a helical robot using two synchronized rotating dipole fields

This work addresses the magnetic-based control of a helical robot and the mitigation of the magnetic forces on its dipole moment during radial steering using rotating permanent magnets. A magnetic system with two synchronized permanent magnets that rotate quasistatically is used to move the helical robot (length and diameter of 12.5 mm and 4 mm, respectively). We experimentally demonstrate that using two synchronized permanent magnets for radial steering of a helical robot achieves higher motion stability, as opposed to propulsion using single rotating dipole field. The two synchronized dipole fields decrease the lateral oscillation (average peak-to-peak amplitude) of the helical robot by 37%, compared to the radial steering using a single dipole field at angular velocity of 31 rad/s. We also show that driving the helical robot using two synchronized rotating magnets achieves average swimming speed of 2.1 mm/s, whereas the single rotating dipole field achieves average swimming speed of 0.4 mm/s at angular velocity of 31 rad/s for the rotating permanent magnets. The proposed configuration of the helical propulsion allows us to decrease the magnetic forces that could cause tissue damage or potential trauma for in vivo applications.

Robust and Optimal Control of Magnetic Microparticles inside Fluidic Channels with Time-Varying Flow Rates

Targeted therapy using magnetic microparticles and nanoparticles has the potential to mitigate the negative side-effects associated with conventional medical treatment. Major technological challenges still need to be addressed in order to translate these particles into in vivo applications. For example, magnetic particles need to be navigated controllably in vessels against flowing streams of body fluid. This paper describes the motion control of paramagnetic microparticles in the flowing streams of fluidic channels with time-varying flow rates (maximum flow is 35 ml.hr−1). This control is designed using a magnetic-based proportional-derivative (PD) control system to compensate for the time-varying flow inside the channels (with width and depth of 2 mm and 1.5 mm, respectively). First, we achieve point-to-point motion control against and along flow rates of 4 ml.hr−1, 6 ml.hr−1, 17 ml.hr−1, and 35 ml.hr−1. The average speeds of single microparticle (with average diameter of 100 μm) against flow rates of 6 ml.hr−1 and 30 ml.hr−1 are calculated to be 45 μm.s−1 and 15 μm.s−1, respectively. Second, we implement PD control with disturbance estimation and compensation. This control decreases the steady-state error by 50%, 70%, 73%, and 78% at flow rates of 4 ml.hr−1, 6 ml.hr−1, 17 ml.hr−1, and 35 ml.hr−1, respectively. Finally, we consider the problem of finding the optimal path (minimal kinetic energy) between two points using calculus of variation, against the mentioned flow rates. Not only do we find that an optimal path between two collinear points with the direction of maximum flow (middle of the fluidic channel) decreases the rise time of the microparticles, but we also decrease the input current that is supplied to the electromagnetic coils by minimizing the kinetic energy of the microparticles, compared to a PD control with disturbance compensation.

Sperm-shaped magnetic microrobots: Fabrication using electrospinning, modeling, and characterization

We use electrospinning to fabricate sperm-shaped magnetic microrobots with a range of diameters from 50 μm to 500 μm. The variables of the electrospinning operation (voltage, concentration of the solution, dynamic viscosity, and distance between the syringe needle and collector) to achieve beading effect are determined. This beading effect allows us to fabricate microrobots with similar morphology to that of sperm cells. The bead and the ultra-fine fiber resemble the morphology of the head and tail of the sperm cell, respectively. We incorporate iron oxide nanoparticles to the head of the sperm-shaped microrobot to provide a magnetic dipole moment. This dipole enables directional control under the influence of external magnetic fields. We also apply weak (less than 2 mT) oscillating magnetic fields to exert a magnetic torque on the magnetic head, and generate planar flagellar waves and flagellated swim. The average speed of the sperm-shaped microrobot is calculated to be 0.5 body lengths per second and 1 body lengths per second at frequencies of 5 Hz and 10 Hz, respectively. We also develop a model of the microrobot using elastohydrodynamics approach and Timoshenko-Rayleigh beam theory, and find good agreement with the experimental results.

Targeting of cell mockups using sperm-shaped microrobots in vitro

Sperm-shaped microrobots are controlled under the influence of weak oscillating magnetic fields (milliTesla range) to selectively target cell mockups (i.e., gas bubbles with average diameter of 200 μm). The sperm-shaped microrobots are fabricated by electrospinning using a solution of polystyrene, dimethylformamide, and iron oxide nanoparticles. These nanoparticles are concentrated within the head of the microrobot, and hence enable directional control along external magnetic fields. The magnetic dipole moment of the microrobot is characterized (using the flip-time technique) to be 1.4×10-11 A.m2, at magnetic field of 28 mT. In addition, the morphology of the microrobot is characterized using Scanning Electron Microscopy images. The characterized parameters and morphology are used in the simulation of the locomotion mechanism of the microrobot to prove that its motion depends on breaking the time-reversal symmetry, rather than pulling with the magnetic field gradient. We experimentally demonstrate that the microrobot can controllably follow S-shaped, U-shaped, and square paths, and selectively target the cell mockups using image guidance and under the influence of the oscillating magnetic fields.

Swimming Back and Forth Using Planar Flagellar Propulsion at Low Reynolds Numbers

Abstract Peritrichously flagellated Escherichia coli swim back and forth by wrapping their flagella together in a helical bundle. However, other monotrichous bacteria cannot swim back and forth with a single flagellum and planar wave propagation. Quantifying this observation, a magnetically driven soft two‐tailed microrobot capable of reversing its swimming direction without making a U‐turn trajectory or actively modifying the direction of wave propagation is designed and developed. The microrobot contains magnetic microparticles within the polymer matrix of its head and consists of two collinear, unequal, and opposite ultrathin tails. It is driven and steered using a uniform magnetic field along the direction of motion with a sinusoidally varying orthogonal component. Distinct reversal frequencies that enable selective and independent excitation of the first or the second tail of the microrobot based on their tail length ratio are found. While the first tail provides a propulsive force below one of the reversal frequencies, the second is almost passive, and the net propulsive force achieves flagellated motion along one direction. On the other hand, the second tail achieves flagellated propulsion along the opposite direction above the reversal frequency.

Swimming in low reynolds numbers using planar and helical flagellar waves

In travelling towards the oviducts, sperm cells undergo transitions between planar to helical flagellar propulsion by a beating tail based on the viscosity of the environment. In this work, we aim to model and mimic this behaviour in low Reynolds number fluids using externally actuated soft robotic sperms. We numerically investigate the effects of transition between planar to helical flagellar propulsion on the swimming characteristics of the robotic sperm using a model based on resistive-force theory to study the role of viscous forces on its flexible tail. Experimental results are obtained using robots that contain magnetic particles within the polymer matrix of its head and an ultra-thin flexible tail. The planar and helical flagellar propulsion are achieved using in-plane and out-of-plane uniform fields with sinusoidally varying components, respectively. We experimentally show that the swimming speed of the robotic sperm increases by a factor of 1.4 (fluid viscosity 5 Pa.s) when it undergoes a controlled transition between planar to helical flagellar propulsion, at relatively low actuation frequencies.