Christoph Goering


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Goering

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Christoph

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0000-0003-0451-2997

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2020 - 20227
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Publications 1 - 7 of 7
  • Rotational speed measurements of small spherical particles driven by acoustic viscous torques utilizing an optical trap
    Item type: Journal Article
    Lamprecht, Andreas; Goering, Christoph; Schaap, Iwan A.T.; et al. (2021)
    Journal of Micromechanics and Microengineering
    Two orthogonal standing acoustic waves, generated by piezoelectric excitation, can form a two-dimensional pressure field in microfluidic devices. A phase difference of the excitation waves can be employed to rotate spherical µm-sized silica particles by a torque mediated through the viscous boundary δ around the particle. The measurement of the rotational rate is, so far, limited to high-speed cameras and their frame rate, and gets increasingly difficult when the sphere gets smaller. We report here a new method for measuring the rotational rate of µm sized spherical particles. We utilize an optical trap with high-speed position detection to overcome the frame rate limitation of wide field image recording. The power spectrum of an optically trapped, rotating particle reveals additional peaks corresponding to the rotational frequencies—compared to a non-rotating particle. We validate our method at low rotational rates against high-speed video observation. To demonstrate the potential of this method we addressed a recent controversy about the rotation of particles with a relatively large viscous boundary layer δ. We measured steady-state rotational rates up to 229 Hz (13.8 × 103 rpm) for a particle with a radius R ≈ δ. Recent numerical research suggests that in this regime the existing theoretical approach (valid for $R\gg\delta$) overpredicts the steady-state rotational rate by a factor of 10. With our new method we also confirm the numerical results experimentally. © 2021 IOP Publishing
  • Direct Measurement of Small Spherical Particle Rotation driven by the Acoustic Viscous Torque
    Item type: Other Conference Item
    Goering, Christoph; Lamprecht, Andreas; Schaap, Iwan; et al. (2020)
    The Journal of the Acoustical Society of America
  • OSAFT Library: An Open-Source Python Library for Acoustofluidics
    Item type: Journal Article
    Fankhauser, Jonas; Goering, Christoph; Dual, Jürg (2022)
    Frontiers in Physics
    In this article, we present the Open-Source AcoustoFluidics Theories (OSAFT) library (version 0.9.14), a Python library for acoustofluidics. The focus of the library is the classical problem of a particle suspended in a fluid and subjected to an incident acoustic wave. The Python code provides easy access to a number of theories describing acoustic scattering, acoustic streaming, and most importantly the acoustic radiation force exerted on the particle. At the time of submission of this article, six different theoretical models and various limiting cases thereof are available. All are treating the problem of a single, spherical particle in an infinite 3D-domain subjected to an incident plane standing or plane traveling wave. The implementations of further theories are currently under development. Our code is designed to be extensible. A library of fluid and solid material models facilitates the implementation of new theories. A unified application programming interface (API), which is used across all models, makes comparisons between different theories straightforward. Such comparisons can be made directly by the user or through the plotting capabilities of our library. The code is distributed through Python’s standard software repository PyPi. Illustrative examples on the project’s website serve as a starting point for learning the library’s API. For a more in-depth understanding of the code, complete documentation of the codebase, directed at users as well as future collaborators, is available online. In an effort to make the library as extensive as possible, the authors of this article are looking for collaborators on the project.
  • Measuring the temporal difference in build up between the acoustic radiation force and acoustic streaming with an optical tweezer
    Item type: Other Conference Item
    Goering, Christoph; Dual, Jürg (2021)
    Acoustofluidic 2021: Abstract Book
  • Measuring the effects of a pulsed excitation on the buildup of acoustic streaming and the acoustic radiation force utilizing an optical tweezer
    Item type: Journal Article
    Goering, Christoph; Dual, Jürg (2022)
    Physical Review E
    Pulsed excitations of piezoelectric transducers affect during the buildup the force contributions from acoustic streaming (AS) and the acoustic radiation force (ARF) to the total force in a standing pressure wave differently. We find with an optical tweezer as measuring instrument that during the first 120 000 excitation periods and across different pulsing frequencies, the AS-induced displacement is on average less than 20% of its nonpulsed value for a duty cycle of 50%, whereas the ARF-induced displacement is around 50%. These findings show that a pulsed excitation can be a tool for reducing AS compared to the ARF.
  • Experimental Validation of Acoustofluidic Theory and Simulations using an Optical Trapping Set-Up
    Item type: Doctoral Thesis
    Goering, Christoph (2022)
    A typical channel within a micro-scale acoustofluidic (MSAF) device has a small cross-section where the height is usually less than 200 μm and the width less than 5 mm; the length can be up to several cm, however, often is not of big interest. Direct measurement of, e.g., the pressure produced by the acoustic excitation is impossible due to the smallness of the region of interest. Additionally, the acoustic driving frequencies are generally above 100kHz such that the time resolution of measurements must be even at least twice as high if one is also interested in the transient behaviour and build up of, e.g., the acoustic pressure field and not only the steady-state. At the moment, the most common and straightforward way to approxi- mate the acoustic pressure within the channel is to optically measure the velocity of several objects of known size and material properties and then calculate back which pressure would have led to this velocity. The va- lidity and correctness of the pressure approximation depends on several uncertainties. Besides the object dimensions and the material parameters of the object and the fluid, the biggest uncertainty is the validity of the underlying theory of the acoustic radiation force (ARF) that is used for the calculation. There exist many MSAF models for the calculation of the acoustic forces which differ mainly in the assumptions regarding the physical model for the fluid and the immersed object. Each theory has its parameter space where it is superior to the others because it includes, e.g., the effect of visco-elasticity of the fluid. Here, an optical trapping (OT) apparatus is utilized to investigate two phenomena where controversies exist in the MSAF community: 1) the transient build up of the ARF and the drag force from acoustic streaming (AS) for a continuous and pulsed acoustic excitation; 2) the quantification of the steady-state rotational velocity of a spherical particle driven by the acoustic viscous torque where the viscous boundary layer (VBL) thickness is comparable to the particle radius itself. So far, OTs have mainly been used as force sensors on single particles within MSAF devices. For the measurements of both phenomena we take advantage of the fine spatial and temporal resolution that the OT offers, as well as the OT property that single particle measurements are possible. In order to measure the build up of the ARF and AS, an acoustic exci- tation frequency and measurement location within the standing pressure wave was used where the two forces were orthogonal to each other. The orthogonality as well as the division into ARF and drag force from AS was measured and validated by force measurements with the OT throughout the fluid channel with differently sized particles. The results of a continuous excitation showed that the ARF starts to build up almost instantaneously after the acoustic excitation was switched on, whereas the AS takes significantly longer. Interestingly, the fast ARF build up was expected from theoretical considerations, but the slow AS build up was underestimated by a factor of about 4. The pulsed excita- tion experiments revealed that depending on the specific pulse parame- ters the build up of AS can be suppressed substantially while the ARF is not affected as much as AS. Therefore, smaller particles can still be mainly manipulated by the ARF because the relative importance of AS decreases for a pulsed excitation faster than for the ARF. Our measure- ments strengthen experimental findings for a pulsed excitation that could not yet be explained theoretically. For the steady-state rotational speed measurement, a high viscosity mix- ture of water with glycerol (7 to 3) was created such that the formed VBL around the particle was about the same as the particle radius. The phase difference between two acoustic excitation sources spatially orthogonal to each other led to a time-averaged acoustic streaming field in the VBL of the particle along its circumference. This streaming field creates a driving viscous torque that causes a rotation with the rotational velocity at which the driving viscous torque equals the counteracting viscous drag torque. A theoretical formula overestimates the steady-state rotational speed for the experimental parameters by more than one order of magnitude. This was expected because, up to now, there are no theories that are valid for the regime where the radius is the same size or smaller than the VBL. However, a numerical study investigated exactly this regime and proposed a calculation for the final rotational velocity including the effects of the VBL. The rotational velocities measured with the OT confirmed two points: 1) the expected invalidity of the simplified theory in the regime of high viscosity (VBL in the same order of magnitude as the particle dimension) and, hence, the necessity of its inclusion in the calculations; 2) the correctness of the numerical results.
  • Dynamic measurement of the acoustic streaming time constant utilizing an optical tweezer
    Item type: Journal Article
    Goering, Christoph; Dual, Jürg (2021)
    Physical Review E
    The combination of a bulk acoustic wave device and an optical trap allows for studying the buildup time of the respective acoustic forces. In particular, we are interested in the time it takes to build up the acoustic radiation force and acoustic streaming. For that, we measure the trajectory of a spherical particle in an acoustic field over time. The shape of the trajectory is determined by the acoustic radiation force and by acoustic streaming, both acting on different time scales. For that, we utilize the high temporal resolution (Δt=0.8μs) of an optical trapping setup. With our experimental parameters the acoustic radiation force on the particle and the acoustic streaming field theoretically have characteristic buildup times of 1.4μs and 1.44ms, respectively. By choosing a resonance mode and a measurement position where the acoustic radiation force and acoustic streaming induced viscous drag force act in orthogonal directions, we can measure the evolution of these effects separately. Our results show that the particle is accelerated nearly instantaneously by the acoustic radiation force to a constant velocity, whereas the acceleration phase to a constant velocity by the acoustic streaming field takes significantly longer. We find that the acceleration to a constant velocity induced by streaming takes in average about 17 500 excitation periods (≈4.4ms) longer to develop than the one induced by the acoustic radiation force. This duration is about four times larger than the so-called momentum diffusion time which is used to estimate the streaming buildup. In addition, this rather large difference in time can explain why a pulsed acoustic excitation can indeed prevent acoustic streaming as it has been shown in some previous experiments.
Publications 1 - 7 of 7