Performance Study of Acoustophoretic Microfluidic Silicon-Glass Devices by Characterization of Material- and Geometry-Dependent Frequency Spectra

The mechanical and electrical response of acoustophoretic microfluidic devices attached to an ac-voltage-driven piezoelectric transducer is studied by means of numerical simulations. The governing equations are formulated in a variational framework that, introducing Lagrangian and Hamiltonian densities, is used to derive the weak form for the finite element discretization of the equations and to characterize the device response in terms of frequency-dependent figures of merit or indicators. The effectiveness of the device in focusing microparticles is quantified by two mechanical indicators: the average direction of the pressure gradient and the amount of acoustic energy localized in the microchannel. Further, we derive the relations between the Lagrangian, the Hamiltonian and three electrical indicators: the resonance Q-value, the impedance and the electric power. The frequency response of the hard-to-measure mechanical indicators is correlated to that of the easy-to-measure electrical indicators, and by introducing optimality criteria, it is clarified to which extent the latter suffices to identify optimal driving frequencies as the geometric configuration and the material parameters vary.Comment: 15 pages, 10 figures, Supplementary Materia

Optimal Design of Silicon-based Chips for Piezo-induced Ultrasound Resonances in Embedded Microchannels

AbstractWe present a variational formulation of the governing equations and introduce global indicators to describe the behavior of acoustofluidic devices driven at resonance frequencies by means of a piezoelectric transducer. The individuation of the correct Lagrangian densities for the different parts constituting the device (the piezo transducer, the silicon walls, the fluid-filled microchannel, and the glass lid) allows for the introduction of the weak formulation used in the finite element discretization of the equations describing the system in its oscillatory regime. Additionally, the knowledge of the Lagrangian density leads to the derivation of the correct structure of the Hamiltonian density, i.e. the energy density, which is important for the quantification of the energy content of the whole system and its individual parts. Specifically, the energy content of the embedded microchannel is quantified by means of the acoustofluidic yield η defined as the ratio between the energy in the channel and the total energy. From the standpoint of acoustophoretic application, the introduction of the acoustophoretic mean orientation allows us to identify the frequencies for which an acoustophoretic effect, i.e. the lateral motion of particle dragged by the axial main flow, is particularly strong. Finally, the connection between the mechanical and electrical degrees of freedom of the system is addressed. This is important for proper determination of the dissipated power, and it may lead to the detection of resonance states by means of purely electrical measurements. Numerical simulations and preliminary experimental results show some features of the model introduced

Theory of pressure acoustics with boundary layers and streaming in curved elastic cavities

The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic wavelength, which makes direct numerical simulations challenging. Based on this separation in length scales, we extend the classical theory of pressure acoustics by deriving a boundary condition for the acoustic pressure that takes boundary-layer effects fully into account. Using the same length-scale separation for the steady second-order streaming, and combining it with time-averaged short-range products of first-order fields, we replace the usual limiting-velocity theory with an analytical slip-velocity condition on the long-range streaming field at the wall. The derived boundary conditions are valid for oscillating cavities of arbitrary shape and wall motion as long as the wall curvature and displacement amplitude are both sufficiently small. Finally, we validate our theory by comparison with direct numerical simulation in two examples of two-dimensional water-filled cavities: The well-studied rectangular cavity with prescribed wall actuation, and the more generic elliptical cavity embedded in an externally actuated rectangular elastic glass block.Comment: 18 pages, 5 figures, pdfLatex, RevTe

Ultrasound-induced acoustophoretic motion of microparticles in three dimensions

We derive analytical expressions for the three-dimensional (3D) acoustophoretic motion of spherical microparticles in rectangular microchannels. The motion is generated by the acoustic radiation force and the acoustic streaming-induced drag force. In contrast to the classical theory of Rayleigh streaming in shallow, infinite, parallel-plate channels, our theory does include the effect of the microchannel side walls. The resulting predictions agree well with numerics and experimental measurements of the acoustophoretic motion of polystyrene spheres with nominal diameters of 0.537 um and 5.33 um. The 3D particle motion was recorded using astigmatism particle tracking velocimetry under controlled thermal and acoustic conditions in a long, straight, rectangular microchannel actuated in one of its transverse standing ultrasound-wave resonance modes with one or two half-wavelengths. The acoustic energy density is calibrated in situ based on measurements of the radiation dominated motion of large 5-um-diam particles, allowing for quantitative comparison between theoretical predictions and measurements of the streaming induced motion of small 0.5-um-diam particles.Comment: 13 pages, 8 figures, Revtex 4.

Acoustic radiation- and streaming-induced microparticle velocities determined by micro-PIV in an ultrasound symmetry plane

We present micro-PIV measurements of suspended microparticles of diameters from 0.6 um to 10 um undergoing acoustophoresis in an ultrasound symmetry plane in a microchannel. The motion of the smallest particles are dominated by the Stokes drag from the induced acoustic streaming flow, while the motion of the largest particles are dominated by the acoustic radiation force. For all particle sizes we predict theoretically how much of the particle velocity is due to radiation and streaming, respectively. These predictions include corrections for particle-wall interactions and ultrasonic thermoviscous effects, and they match our measurements within the experimental uncertainty. Finally, we predict theoretically and confirm experimentally that the ratio between the acoustic radiation- and streaming-induced particle velocities is proportional to the square of the particle size, the actuation frequency and the acoustic contrast factor, while it is inversely proportional to the kinematic viscosity.Comment: 11 pages, 9 figures, RevTex 4-

Correction of RT–qPCR data for genomic DNA-derived signals with ValidPrime

Genomic DNA (gDNA) contamination is an inherent problem during RNA purification that can lead to non-specific amplification and aberrant results in reverse transcription quantitative PCR (RT—qPCR). Currently, there is no alternative to RT(−) controls to evaluate the impact of the gDNA background on RT–PCR data. We propose a novel method (ValidPrime) that is more accurate than traditional RT(−) controls to test qPCR assays with respect to their sensitivity toward gDNA. ValidPrime measures the gDNA contribution using an optimized gDNA-specific ValidPrime assay (VPA) and gDNA reference sample(s). The VPA, targeting a non-transcribed locus, is used to measure the gDNA contents in RT(+) samples and the gDNA reference is used to normalize for GOI-specific differences in gDNA sensitivity. We demonstrate that the RNA-derived component of the signal can be accurately estimated and deduced from the total signal. ValidPrime corrects with high precision for both exogenous (spiked) and endogenous gDNA, contributing ∼60% of the total signal, whereas substantially reducing the number of required qPCR control reactions. In conclusion, ValidPrime offers a cost-efficient alternative to RT(−) controls and accurately corrects for signals derived from gDNA in RT–qPCR