Experimental Validation of Acoustofluidic Theory and Simulations using an Optical Trapping Set-Up
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Date
2022
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Doctoral Thesis
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Abstract
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.
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Examiner: Dual, Jürg
Examiner : Ahmed, Daniel
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ETH Zurich
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Subject
Acoustofluidics; Microfluidic; Optical tweezers; Optical Trapping; Acoustics
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03307 - Dual, Jürg (emeritus) / Dual, Jürg (emeritus)