Pressure Antinode Research Articles

Revised model for the radiation force exerted by standing surface acoustic waves on a rigid cylinder.

In this paper, a model for the radiation force exerted by standing surface acoustic waves (SSAWs) on a rigid cylinder in inviscid fluids is extended to account for the dependence on the Rayleigh angle. The conventional model for the radiation force used in the SSAW-based applications is developed in plane standing waves, which fails to predict the movement of the cylinder in the SSAW. Our revised model reveals that, in the direction normal to the piezoelectric substrate on which the SSAW is generated, acoustic radiation force can be large enough to drive the cylinder even in the long-wavelength limit. Furthermore, the force in this direction can not only push the cylinder away, but also pull it back toward the substrate. In the direction parallel to the substrate, the equilibrium positions for particles can be actively tuned by changing Rayleigh angle. As an example considered in the paper, with the reduction of Rayleigh angle the equilibrium positions for steel cylinders in water change from pressure nodes to pressure antinodes. The model can thus be used in the design of SSAWs for particle manipulations.

Binary particle separation in droplet microfluidics using acoustophoresis

We show a method for separation of two particle species with different acoustic contrasts originally encapsulated in the same droplet in a continuous two-phase system. This was realized by using bulk acoustic standing waves in a 380 μm wide silicon-glass microfluidic channel. Polystyrene particles (positive acoustic contrast particles) and in-house synthesized polydimethylsiloxane (PDMS) particles (negative acoustic contrast particles) were encapsulated inside water-in-oil droplets either individually or in a mixture. At acoustic actuation of the system at the fundamental resonance frequency, the polystyrene particles were moved to the center of the droplet (pressure node), while the PDMS particles were moved to the sides of the droplet (pressure anti-nodes). The acoustic particle manipulation step was combined in series with a trifurcation droplet splitter, and as the original droplet passed through the splitter and was divided into three daughter droplets, the polystyrene particles were directed into the center daughter droplet, while the PDMS particles were directed into the two side daughter droplets. The presented method expands the droplet microfluidics tool-box and offers new possibilities to perform binary particle separation in droplet microfluidic systems.

Acoustic radiation force on a compressible cylinder in the standing surface acoustic wave (SSAW)

In this work, the radiation force exerted by the standing surface acoustic wave (SSAW) on a compressible cylinder in inviscid fluids is derived. The formula obtained in plane standing waves fails to calculate the radiation force on the cylinder in the SSAW. The Rayleigh angle is introduced to extend the prior formula. According to our expressions, the radiation force can not only repel the cylinder but also attract it in the direction perpendicular to the piezoelectric substrate. The Rayleigh angle can be used to actively tune the equilibrium positions (pressure nodes or antinodes) in the SSAW. Additionally, it can also be used to manipulate bubbles. Thus, our expressions have great potential in the SSAW-based applications.

Measurement of distribution of broadband noise and sound pressures in sonochemical reactor

Cross-sectional area distribution of broadband noise in a sonochemical reactor was measured to estimate reaction fields. A needle-type hydrophone scanned the sonochemical reactor in horizontal and vertical directions at one-millimeter interval. To show an absolute value of broadband noise, average of broadband sound pressure was defined. The distribution of sound pressures at the fundamental and second harmonic frequencies were also measured. In the case of driving frequency at 130 kHz, sonochemical reaction fields were observed in several ellipse shapes. The reaction fields in upper part of the reactor was high because cavitation bubbles moved upper part due to radiation force. The sound pressure distribution at the fundamental frequency showed existence of standing wave and reaction fields were weak at pressure antinode because cavitation bubbles were repelled by primary Bjerknes force. The sound pressure distribution at the second harmonic frequency indicated that the pattern of bubbles distribution resembled to that of reaction fields closely. In the case at 43 kHz, distributions of reaction fields and sound pressures were complex due to coupled vibration. The reaction fields were relatively weak in areas which had very high sound pressures at the fundamental frequency.

Reducing WBC background in cancer cell separation products by negative acoustic contrast particle immuno-acoustophoresis

Cancer cells display acoustic properties enabling acoustophoretic separation from white blood cells (WBCs) with 2–3 log suppression of the WBC background. However, a subset of WBCs has overlapping acoustic properties with cancer cells, which is why label-free acoustophoretic cancer cell isolation needs additional purification prior to analysis. This paper reports for the first time a proof of concept for continuous flow acoustophoretic negative selection of WBCs from cancer cells using negative acoustic contrast elastomeric particles (EPs) activated with CD45-antibodies that specifically bind to WBCs. The EP/WBC complexes align at the acoustic pressure anti-nodes along the channel walls while unbound cancer cells focus to the pressure node in the channel center, enabling continuous flow based depletion of WBC background in a cancer cell product. The method does not provide a single process solution for the CTC separation challenge, but provides an elegant part to a multi-step process by further reducing the WBC background in cancer cell separation products derived from an initial step of label-free acoustophoresis. We report the recorded performance of the negative selection immuno-acoustophoretic WBC depletion and cancer cell recovery. To eliminate the negative impact of the separation due to the known problems of aggregation of negative acoustic contrast particles along the sidewalls of the acoustophoresis channel and to enable continuous separation of EP/WBC complexes from cancer cells, a new acoustic actuation method has been implemented where the ultrasound frequency is scanned (1.991MHz ± 100 kHz, scan rate 200 kHz ms−1). Using this frequency scanning strategy EP/WBC complexes were acoustophoretically separated from mixtures of WBCs spiked with breast and prostate cancer cells (DU145 and MCF-7). An 86-fold (MCF-7) and 52-fold (DU145) reduction of WBCs in the cancer cell fractions were recorded with separation efficiencies of 98.6% (MCF-7) and 99.7% (DU145) and cancer cell recoveries of 89.8% (MCF-7) and 85.0% (DU145).

Estimation of acoustic forces on submicron aerosol particles in a standing wave field

ABSTRACTThe net acoustic force acting on submicron particles suspended in a gas and exposed to a standing wave field is investigated as a function of particle size, by measuring both the aerosol number density and size distribution in a flow-through resonator. By taking into account all contributions relevant to the net force, this experimental study provides a first estimate for the acoustic radiation force in a size range where molecular effects are expected to be significant. The experiment consists of an electrostatic transducer generating a standing wave in the 50–80 kHz frequency range, with the submicron aerosol particles concentrated at pressure antinodes located across the height of a rectangular channel. A section of the flow is sampled isokinetically and analyzed using a Scanning Mobility Particle Sizer (SMPS), while the nodal patterns are visualized simultaneously using light scattering. The net acoustic force is calculated from their measured displacement along the axis of the 1D standing wav...

Impact of Ceramic Substrates Geometry on the Performance of Simple Thermo-Acoustic Engines

This work experimentally examines the influence of the stack geometry and position on the performance of thermo-acoustic engines (TAE). Twenty cordierite honeycomb ceramic stacks with square pores and five different lengths (7, 13, 17, 22 and 25 mm) were considered. Measurements were taken at seven different locations of the stack hot ends from the pressure antinode (closed end), namely 52, 72, 92,112, 132, 152 and 172 mm respectively. The temperature difference across the stack and radiated sound pressure level at steady state are considered indicators of the performance of the device. The results obtained with a simple standing wave thermo-acoustic engine used in this experiment reveals that the relationships between the length, the stack pores sizes and the input power are non-linear. In addition, the effect of the viscous resistance and the thermal losses were confirmed to be strong enough when the input heating power is low.

Longitudinal Combustion Instability in a Rocket Engine with a Single Coaxial Injector

Longitudinal combustion instability in liquid-propellant rocket engines is investigated using an in-house axisymmetric, multispecies compressible flow solver. Turbulence is treated using a hybrid Reynolds-averaged Navier–Stokes/large-eddy simulation approach. The combustion–turbulence interactions are modeled using the flamelet/progress-variable approach. The computational time is at least an order of magnitude smaller than existing axisymmetric simulations with a more detailed chemistry mechanism. Three flow configurations with a choked nozzle are studied: unstable cases with 12 and 14 cm oxidizer post lengths, and a semiunstable case with a 9 cm oxidizer port length. Numerical results for oscillation frequencies and amplitudes agree with the continuously variable resonance combustor experiments conducted at Purdue University. Good agreements with existing computational results are also found. An additional open-end constant-pressure simulation with (otherwise) the same configuration as the continuously variable resonance combustor experiment with the 14 cm oxidizer post is performed, yielding minor acoustic oscillation. The open-end vortex-shedding frequency is found to be roughly one-half of the frequency of vortex shedding calculated in the continuously variable resonance combustor configuration. The flame region compacts as the combustion chamber becomes more unstable. The choked nozzle allows large-amplitude oscillation, thereby enhancing mixing and leading to more complete combustion near the pressure antinode (combustion chamber entrance) as compared to the open-end chamber. Pulse timing in the unstable case is identified as a major factor for the instability mechanism. Oscillatory behaviors for all three instability domains are described.

Effective cell trapping using PDMS microspheres in an acoustofluidic chip

We present a facile particle-based cell manipulation method using acoustic radiation forces. In this work, we selected several representative particles including poly(lactic-co-glycolic acid) (PLGA) microspheres, silica-coated magnetic microbeads, polydimethylsiloxane (PDMS) microspheres and investigated the responses of these particle systems to ultrasonic standing waves (USWs) in a microfluidic chip. We show that depending on the nature (positive or negative acoustic contrast factors) of the particles, these particle systems display different alignment behaviors along the microfluidic channel under USWs. Specifically, PLGA microspheres and silica-coated magnetic microbeads are able to be aligned in the middle of the microfluidic channel, while PDMS microspheres are translocated to the side walls of the channel, which is beneficial for cell trapping and manipulation. Further results demonstrate that the functional PDMS microspheres with a negative acoustic contrast factor can be used to trap cells to the pressure antinodes in the acoustofluidic chip. Cell viability tests reveal that the ultrasonic manipulation does not exert any harmful effect to the cells. This acoustic-based particle and cell manipulation technique may hold a great promise for the development of rapid, noninvasive, continuous assays for detecting of cells and separation of biological samples.

MicroBubble activated acoustic cell sorting

Acoustophoresis, the ability to acoustically manipulate particles and cells inside a microfluidic channel, is a critical enabling technology for cell-sorting applications. However, one of the major impediments for routine use of acoustophoresis at clinical laboratory has been the reliance on the inherent physical properties of cells for separation. Here, we present a microfluidic-based microBubble-Activated Acoustic Cell Sorting (BAACS) method that rely on the specific binding of target cells to microbubbles conjugated with specific antibodies on their surface for continuous cell separation using ultrasonic standing wave. In acoustophoresis, cells being positive acoustic contrast particles migrate to pressure nodes. On the contrary, air-filled polymer-shelled microbubbles being strong negative acoustic contrast particles migrate to pressure antinodes and can be used to selectively migrate target cells. As a proof of principle, we demonstrate the separation of cancer cell line in a suspension with better than 75% efficiency. Moreover, 100% of the microbubble-cell conjugates migrated to the anti-node. Hence a better upstream affinity-capture has the potential to provide higher sorting efficiency. The BAACS technique expands the acoustic cell manipulation possibilities and offers cell-sorting solutions suited for applications at point of care.

Hydrodynamic interaction of weakly nonspherical gas bubbles in a liquid in the three-dimensional problem statement

The influence of the relative location of weakly nonspherical gas (air) bubbles in liquid (water) on their hydrodynamic interaction at the pressure antinode of an ultrasonic standing wave is studied. Three essentially different configurations of the mutual arrangement of the bubbles are considered: the linear, planar, and spatial ones. In the linear configuration, three bubbles are located on one straight line. In the planar configuration, five bubbles are situated on two mutually orthogonal straight lines. In the spatial configuration, seven bubbles are located on three mutually orthogonal straight lines. In all the cases, one of the bubbles is central, the others are equally-spaced from it on those lines. All the bubbles are initially spherical with a radius of 3 ?m. Room conditions are considered, the frequency of the wave is 20 kHz, its amplitude is 1.2 times the static liquid pressure. A mathematical model is used, in which the liquid is assumed weakly compressible, the bubbles being homobaric. It is shown that in each configuration of the bubbles the influence of their interaction on their radial dynamics is insignificant. In each configuration, the central bubble remains stationary, while the others move to it at a speed equal for a fixed configuration. At transition from a linear configuration to a planar one and from a planar configuration to a spatial one, the bubble motion speed increases. In all the cases, the deformations of the central stationary bubbles are smaller than those of the rest. Among the central bubbles, the bubble in a planar configuration is deformed most.

Deformation of a bubble formed by coalescence of cavitation inclusions and shock wave inside it at strong expansion and compression

Dynamics of a cavitation bubble is considered at its strong expansion and subsequent compression. The bubble is formed by merging of two identical spherical cavitation microcavities in the pressure antinode of the intensive ultrasonic standing wave in the half-wave phase with negative pressure. Deformations of bubble and deformations of radially converging shock waves occurring therein at bubble compression are studied depending on the size of microcavities forming the bubble. It is found that compression of the medium in the bubble by the converging shock wave is kept close to the spherical one only in the case, when the radius of merging microcavities is 1800 times smaller than the radius of the bubble formed by merging at the time of its maximal expansion.

Experimental Investigation of Ceramic Substrates in Standing Wave Thermoacoustic Refrigerator

This work experimentally investigates the performance of ceramic substrates used as stacks in standing wave thermoacoustic coolers. Thermoacoustic technology is proposed in this study as an alternative sustainable solution to current issues with vapour compression refrigerators because of its environmentally friendlier attributes. However, the main hindrance to the expansion of this technology is its current lack of efficiency. Hence, an experimental investigation was conducted in this study. The influence of the geometrical configuration of the stack, described as the heart of the device, is investigated. The device was equipped with different selected low-cost porous materials (ceramic substrates) for performance testing and studies. Porosity, length and position of the ceramic substrates are variables that are considered in order to investigate the performance of the cooler. Eight cordierite honeycomb ceramic substrates with square cross sections and of four different lengths (26mm, 48mm, 70mm and 100mm) were considered. Five different stack positions, measured from the hot ends of the stack to the pressure antinode in increments of 100mm, were investigated. Measurement of temperature difference at steady state was used to determine the performance of a particular configuration. Guidance on the design of this sustainable solution for refrigeration and selection of the best geometrical configuration of ceramic substrates are provided. In addition, clarity on the relation between the geometrical configurations and the frequencies of the sound wave is highlighted.

Experimental study of Rijke-type thermoacoustic instability by using Proper Orthogonal Decomposition method

A low-order modal description of the thermoacoustic instability in a both-end-open Rijke tube with an electrical heater was proposed based on an experimental study using 15 microphones implemented along the tube wall. The simultaneous pressure measurements were decomposed into fluctuations of different eigenmodes (spatial modes) and acoustic (temporal) modes using the Proper Orthogonal Decomposition technique. Three types of pressure fluctuations, which contributed 99% of the total pressure fluctuations, were identified from the reconstructed pressure. The types I and III fluctuations resembled the spatial Fourier modes 1 and 2, respectively, in a unheated tube with slight differences caused by the local inhomogeneity near heater. The type I fluctuation appeared to cause a second type of fluctuation (type II) featured in-phased pressure near the two ends of the tube. The amount of contribution from each type of fluctuation varied with the heater position and the type I appeared to play a dominant role which contributed 85–95% to the total fluctuation. The contribution of type I increased when the heater position approached the midpoint between the pressure node and antinode of the spatial Fourier mode 1, at the same time the contribution of types II increased and the contribution of type III decreased. The phase lag between types I and III changed when the heater position varied, while the phase lag between types I and II remained constant.

A preliminary acoustic analysis of three-dimensional shape of the human nasal cavity and paranasal sinuses extracted from cone-beam CT

The shape of the nasal cavity and paranasal sinuses is complex and varies between individuals. Because the shape is almost stable during speech, the acoustic properties could constantly provide speaker specific information to speech sounds, that is, speaker individuality. In this preliminary analysis, the shape was extracted from cone-beam CT data for a subject using a machine learning technique and its acoustic properties were examined using finite-difference time-domain simulation. The transfer function from the glottis to the nostrils was calculated and the distribution pattern of the pressure anti-nodes was visualized at frequencies of major spectral peaks and dips. In addition, transfer functions were calculated when each of the paranasal sinuses other than the ethmoidal ones was occluded to identify which sinus caused which dip. As a result, the longitudinal resonance in the right or left half of the nasal cavity generated each peak, while the transverse resonance in the pharyngeal cavity caused the...

Vertical normal modes of human ears: Individual variation and frequency estimation from pinna anthropometry.

Beyond the first peak of head-related transfer functions or pinna-related transfer functions (PRTFs) human pinnae are known to have two normal modes with "vertical" resonance patterns, involving two or three pressure anti-nodes in cavum, cymba, and fossa. However, little is known about individual variations in these modes, and there is no established model for estimating their center-frequencies from anthropometry. Here, with geometries of 38 pinnae measured, PRTFs were calculated and vertical modes visualized by numerical simulation. Most pinnae were found to have both Cavum-Fossa and Cavum-Cymba modes, with opposite-phase anti-nodes in cavum and either fossa or cymba, respectively. Nevertheless in both modes, fossa involvement varied substantially across pinnae, dependent on scaphoid fossa depth and cymba shallowness. Linear regression models were evaluated in mode frequency estimation, with 3322 measures derived from 31 pinna landmarks. The Cavum-Fossa normal mode frequency was best estimated [correlation coefficient r = 0.89, mean absolute error (MAE) = 257 Hz or 4.4%] by the distance from canal entrance to helix rim, and cymba horizontal depth. The Cavum-Cymba normal mode frequency was best estimated (r = 0.92, MAE = 247 Hz or 3.2%) by the sagittal-plane distance from concha floor to cymba anterior wall, and cavum horizontal depth.

Study of flame response to transverse acoustic modes from the LES of a 42-injector rocket engine

The Large-Eddy Simulation of a reduced-scale rocket engine operated by DLR has been conducted. This configuration features 42 coaxial injectors fed with liquid oxygen and gaseous hydrogen. For a given set of injection conditions the combustor exhibits strong transverse thermo-acoustic oscillations that are retrieved by the numerical simulation. The spatial structure of the two main modes observed in the LES is investigated through 3D Fourier analysis during the limit cycle. They are respectively associated with the first transverse and first radial resonant acoustic modes of the combustion chamber. The contributions of each individual flame to the unsteady heat release rate and the Rayleigh index are reconstructed for each mode. These contributions are in both cases low in the vicinity of velocity anti-nodes and high near pressure anti-nodes. Moreover it is noticed that these pressure fluctuations lead to large velocity oscillations in the hydrogen stream. From these observations, a driving mechanism for the flame response is proposed and values for the gain and phase of the associated flame transfer function are evaluated from the LES.

Investigation of polymer-shelled microbubble motions in acoustophoresis

The objective of this paper is to explore the trajectory motion of microsize (typically smaller than a red blood cell) encapsulated polymer-shelled gas bubbles propelled by radiation force in an acoustic standing-wave field and to compare the corresponding movements of solid polymer microbeads. The experimental setup consists of a microfluidic chip coupled to a piezoelectric crystal (PZT) with a resonance frequency of about 2.8MHz. The microfluidic channel consists of a rectangular chamber with a width, w, corresponding to one wavelength of the ultrasound standing wave. It creates one full wave ultrasound of a standing-wave pattern with two pressure nodes at w/4 and 3w/4 and three antinodes at 0, w/2, and w. The peak-to-peak amplitude of the electrical potential over the PZT was varied between 1 and 10V. The study is limited to no-flow condition. From Gor’kov’s potential equation, the acoustic contrast factor, Φ, for the polymer-shelled microbubbles was calculated to about −60.7. Experimental results demonstrate that the polymer-shelled microbubbles are translated and accumulated at the pressure antinode planes. This trajectory motion of polymer-shelled microbubbles toward the pressure antinode plane is similar to what has been described for other acoustic contrast particles with a negative Φ. First, primary radiation forces dragged the polymer-shelled microbubbles into proximity with each other at the pressure antinode planes. Then, primary and secondary radiation forces caused them to quickly aggregate at different spots along the channel. The relocation time for polymer-shelled microbubbles was 40 times shorter than that for polymer microbeads, and in contrast to polymer microbeads, the polymer-shelled microbubbles were actuated even at driving voltages (proportional to radiation forces) as low as 1V. In short, the polymer-shelled microbubbles demonstrate the behavior attributed to the negative acoustic contrast factor particles and thus can be trapped at the antinode plane and thereby separated from particles having a positive acoustic contrast factor, such as for example solid particles and cells. This phenomenon could be utilized in exploring future applications, such as bioassay, bioaffinity, and cell interaction studies in vitro in a well-controlled environment.

Fabrication and Operation of Acoustofluidic Devices Supporting Bulk Acoustic Standing Waves for Sheathless Focusing of Particles.

Acoustophoresis refers to the displacement of suspended objects in response to directional forces from sound energy. Given that the suspended objects must be smaller than the incident wavelength of sound and the width of the fluidic channels are typically tens to hundreds of micrometers across, acoustofluidic devices typically use ultrasonic waves generated from a piezoelectric transducer pulsating at high frequencies (in the megahertz range). At characteristic frequencies that depend on the geometry of the device, it is possible to induce the formation of standing waves that can focus particles along desired fluidic streamlines within a bulk flow. Here, we describe a method for the fabrication of acoustophoretic devices from common materials and clean room equipment. We show representative results for the focusing of particles with positive or negative acoustic contrast factors, which move towards the pressure nodes or antinodes of the standing waves, respectively. These devices offer enormous practical utility for precisely positioning large numbers of microscopic entities (e.g., cells) in stationary or flowing fluids for applications ranging from cytometry to assembly.

Fabrication and Operation of Acoustofluidic Devices Supporting Bulk Acoustic Standing Waves for Sheathless Focusing of Particles

Acoustophoresis refers to the displacement of suspended objects in response to directional forces from sound energy. Given that the suspended objects must be smaller than the incident wavelength of sound and the width of the fluidic channels are typically tens to hundreds of micrometers across, acoustofluidic devices typically use ultrasonic waves generated from a piezoelectric transducer pulsating at high frequencies (in the megahertz range). At characteristic frequencies that depend on the geometry of the device, it is possible to induce the formation of standing waves that can focus particles along desired fluidic streamlines within a bulk flow. Here, we describe a method for the fabrication of acoustophoretic devices from common materials and clean room equipment. We show representative results for the focusing of particles with positive or negative acoustic contrast factors, which move towards the pressure nodes or antinodes of the standing waves, respectively. These devices offer enormous practical utility for precisely positioning large numbers of microscopic entities (e.g., cells) in stationary or flowing fluids for applications ranging from cytometry to assembly.