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Wójcik J, Żołek N. Derivation of acoustical streaming equations for nonlinear and dispersive fluids. ULTRASONICS 2023; 132:107000. [PMID: 37062103 DOI: 10.1016/j.ultras.2023.107000] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Revised: 02/24/2023] [Accepted: 03/24/2023] [Indexed: 05/29/2023]
Abstract
The equations of streaming generated by an acoustic mod propagating in a nonlinear dispersive medium (exhibiting absorption and dispersion of phase sound speed) are derived with an arbitrarily shaped incident acoustical field assumed. This field may be periodic or non-periodic. A general dispersion model represented by a convolution operator taking into account relaxation effects was taken into account. Making the assumption of a periodic acoustic field from the general streaming equation. The quasi-stationary flow is driven by a force given by the average value of the dispersion operator with respect to the velocity and acoustic pressure fields. In the spectral representation, it is given by the weighted spectral power density distribution of the acoustic field. The weight of the distribution is the dispersion coefficient - the eigenvalue of the dispersion operator. A new result also reveals the effect of the refractive index deviation on the driving force of streaming. The possibility of generalizing the description of streaming in the simplest case of a non-Newtonian fluid was analyzed. The Reiner-Revlin model of a simple liquid was assumed. It was also noted that the streaming model in the Maxwell liquid is analytically solvable. It was found that asymptotic states of streaming in this model and the Navier-Stokes model are identical. The derivations use new methods different from those used so far. They are based on the separation of nonlinear modes in the momentum transport equation and on the properties of the Gauss-Weierstrass function for the Fick diffusion operator. So far, the method of successive approximations has been used. The consistency of the obtained equations with the assumptions was checked. The obtained formulas generalize the known descriptions of the form of forces driving streaming and extend their application to the case of nonlinear propagation.
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Affiliation(s)
- Janusz Wójcik
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland.
| | - Norbert Żołek
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland
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Orosco J, Friend J. Modeling fast acoustic streaming: Steady-state and transient flow solutions. Phys Rev E 2022; 106:045101. [PMID: 36397528 DOI: 10.1103/physreve.106.045101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2022] [Accepted: 09/09/2022] [Indexed: 06/16/2023]
Abstract
Traditionally, acoustic streaming is assumed to be a steady-state, relatively slow fluid response to passing acoustic waves. This assumption, the so-called slow streaming assumption, was made over a century ago by Lord Rayleigh. It produces a tractable asymptotic perturbation analysis from the nonlinear governing equations, separating the acoustic field from the acoustic streaming that it generates. Unfortunately, this assumption is often invalid in the modern microacoustofluidics context, where the fluid flow and acoustic particle velocities are comparable. Despite this issue, the assumption is still widely used today, as there is no suitable alternative. We describe a mathematical method to supplant the classic approach and properly treat the spatiotemporal scale disparities present between the acoustics and remaining fluid dynamics. The method is applied in this work to well-known problems of semi-infinite extent defined by the Navier-Stokes equations, and preserves unsteady fluid behavior driven by the acoustic wave. The separation of the governing equations between the fast (acoustic) and slow (hydrodynamic) spatiotemporal scales are shown to naturally arise from the intrinsic properties of the fluid under forcing, not by arbitrary assumption beforehand. Solution of the unsteady streaming field equations provides physical insight into observed temporal evolution of bulk streaming flows that, to date, have not been modeled. A Burgers equation is derived from our method to represent unsteady flow. By then assuming steady flow, a Riccati equation is found to represent it. Solving these equations produces direct, concise insight into the nonlinearity of the acoustic streaming phenomenon alongside an absolute, universal upper bound of 50% for the energy efficiency in transducing acoustic energy input to the acoustic streaming energy output. Rigorous validation with respect to experimental and theoretical results from the classic literature is presented to connect this work to past efforts by many authors.
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Affiliation(s)
- Jeremy Orosco
- Medically Advanced Devices Laboratory, Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, and Department of Surgery, School of Medicine, University of California San Diego, 9500 Gilman Dr., MC0411, La Jolla, California 92093, USA
| | - James Friend
- Medically Advanced Devices Laboratory, Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, and Department of Surgery, School of Medicine, University of California San Diego, 9500 Gilman Dr., MC0411, La Jolla, California 92093, USA
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Qu G, Wang Y, Zhong Z, Li M, Zhou M, Liu D, Xu Z, Lin W, Liu X, Han J. Formation mechanism of the nanostructure in laser streaming phenomenon. OPTICS EXPRESS 2020; 28:30586-30596. [PMID: 33115056 DOI: 10.1364/oe.401909] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Accepted: 09/16/2020] [Indexed: 06/11/2023]
Abstract
Laser streaming is a phenomenon in which liquid streaming is driven directly from the laser through an in situ fabricated nanostructure. In this study, liquid streaming of a gold nanoparticle suspension driven by a pulsed laser was studied using a high-speed camera. The laser streaming formation time, streaming velocity, and relative energy conversion efficiency of laser streaming was measured for different nanoparticle concentrations, focal lens position, laser powers, and laser repetition rates. In addition to the laser intensity, which played a significant role in the formation process of laser streaming, the optical gradient force was found to be an important approach involved in the transport and provision of nanoparticles during the formation of laser streaming. This finding facilitated a better understanding of the formation mechanism of laser streaming and demonstrated the possibilities of a new potential laser etching technique based on nanosecond lasers and nanoparticle suspensions. This result can also expand the application of laser streaming in microfluids and other fields that require lasers to move macroscopic objects at relatively high speeds.
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Gold-implanted plasmonic quartz plate as a launch pad for laser-driven photoacoustic microfluidic pumps. Proc Natl Acad Sci U S A 2019; 116:6580-6585. [PMID: 30872482 PMCID: PMC6452654 DOI: 10.1073/pnas.1818911116] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
A revolutionary microfluidic pump is demonstrated; it has no moving parts and no electrical contacts. It consists of a quartz plate implanted by Au particles where every point on the plate can function as a micropump. The pump is driven by a laser beam and is based on the discovered principle of photoacoustic laser streaming. When a pulsed laser hits the plate, it is absorbed by Au nanoparticles that generate an ultrasound wave, which then drives the fluid via acoustic streaming. Because laser beams can be arbitrarily patterned and timed, the fluid can be controlled by laser in a fashion similar to musical water fountains. Such a laser-driven photoacoustic micropump will find wide applications in microfluidics and optofluidics. Enabled initially by the development of microelectromechanical systems, current microfluidic pumps still require advanced microfabrication techniques to create a variety of fluid-driving mechanisms. Here we report a generation of micropumps that involve no moving parts and microstructures. This micropump is based on a principle of photoacoustic laser streaming and is simply made of an Au-implanted plasmonic quartz plate. Under a pulsed laser excitation, any point on the plate can generate a directional long-lasting ultrasound wave which drives the fluid via acoustic streaming. Manipulating and programming laser beams can easily create a single pump, a moving pump, and multiple pumps. The underlying pumping mechanism of photoacoustic streaming is verified by high-speed imaging of the fluid motion after a single laser pulse. As many light-absorbing materials have been identified for efficient photoacoustic generation, photoacoustic micropumps can have diversity in their implementation. These laser-driven fabrication-free micropumps open up a generation of pumping technology and opportunities for easy integration and versatile microfluidic applications.
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Wang Y, Zhang Q, Zhu Z, Lin F, Deng J, Ku G, Dong S, Song S, Alam MK, Liu D, Wang Z, Bao J. Laser streaming: Turning a laser beam into a flow of liquid. SCIENCE ADVANCES 2017; 3:e1700555. [PMID: 28959726 PMCID: PMC5617372 DOI: 10.1126/sciadv.1700555] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2017] [Accepted: 09/05/2017] [Indexed: 05/07/2023]
Abstract
Transforming a laser beam into a mass flow has been a challenge both scientifically and technologically. We report the discovery of a new optofluidic principle and demonstrate the generation of a steady-state water flow by a pulsed laser beam through a glass window. To generate a flow or stream in the same path as the refracted laser beam in pure water from an arbitrary spot on the window, we first fill a glass cuvette with an aqueous solution of Au nanoparticles. A flow will emerge from the focused laser spot on the window after the laser is turned on for a few to tens of minutes; the flow remains after the colloidal solution is completely replaced by pure water. Microscopically, this transformation is made possible by an underlying plasmonic nanoparticle-decorated cavity, which is self-fabricated on the glass by nanoparticle-assisted laser etching and exhibits size and shape uniquely tailored to the incident beam profile. Hydrophone signals indicate that the flow is driven via acoustic streaming by a long-lasting ultrasound wave that is resonantly generated by the laser and the cavity through the photoacoustic effect. The principle of this light-driven flow via ultrasound, that is, photoacoustic streaming by coupling photoacoustics to acoustic streaming, is general and can be applied to any liquid, opening up new research and applications in optofluidics as well as traditional photoacoustics and acoustic streaming.
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Affiliation(s)
- Yanan Wang
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
- Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204, USA
| | - Qiuhui Zhang
- Department of Electrical Information Engineering, Henan University of Engineering, Xinzheng, Henan 451191, China
- Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204, USA
| | - Zhuan Zhu
- Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204, USA
| | - Feng Lin
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
- Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204, USA
| | - Jiangdong Deng
- Center for Nanoscale Systems, Harvard University, Cambridge, MA 02138, USA
| | - Geng Ku
- Department of Mechanical Engineering, University of Kansas, Lawrence, KS 66045, USA
| | - Suchuan Dong
- Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
| | - Shuo Song
- Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204, USA
| | - Md Kamrul Alam
- Materials Science and Engineering, University of Houston, Houston, TX 77204, USA
| | - Dong Liu
- Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA
| | - Zhiming Wang
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
| | - Jiming Bao
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
- Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204, USA
- Materials Science and Engineering, University of Houston, Houston, TX 77204, USA
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Moudjed B, Botton V, Henry D, Millet S, Ben Hadid H. Y-shaped jets driven by an ultrasonic beam reflecting on a wall. ULTRASONICS 2016; 68:33-42. [PMID: 26907890 DOI: 10.1016/j.ultras.2016.02.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2015] [Revised: 12/29/2015] [Accepted: 02/01/2016] [Indexed: 06/05/2023]
Abstract
This paper presents an original experimental and numerical investigation of acoustic streaming driven by an acoustic beam reflecting on a wall. The water experiment features a 2 MHz acoustic beam totally reflecting on one of the tank glass walls. The velocity field in the plane containing the incident and reflected beam axes is investigated using Particle Image Velocimetry (PIV). It exhibits an original y-shaped structure: the impinging jet driven by the incident beam is continued by a wall jet, and a second jet is driven by the reflected beam, making an angle with the impinging jet. The flow is also numerically modeled as that of an incompressible fluid undergoing a volumetric acoustic force. This is a classical approach, but the complexity of the acoustic field in the reflection zone, however, makes it difficult to derive an exact force field in this area. Several approximations are thus tested; we show that the observed velocity field only weakly depends on the approximation used in this small region. The numerical model results are in good agreement with the experimental results. The spreading of the jets around their impingement points and the creeping of the wall jets along the walls are observed to allow the interaction of the flow with a large wall surface, which can even extend to the corners of the tank; this could be an interesting feature for applications requiring efficient heat and mass transfer at the wall. More fundamentally, the velocity field is shown to have both similarities and differences with the velocity field in a classical centered acoustic streaming jet. In particular its magnitude exhibits a fairly good agreement with a formerly derived scaling law based on the balance of the acoustic forcing with the inertia due to the flow acceleration along the beam axis.
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Affiliation(s)
- Brahim Moudjed
- Univ Lyon, Ecole Centrale de Lyon, Université Lyon 1, INSA de Lyon, CNRS, Laboratoire de Mécanique des Fluides et d'Acoustique, ECL, 36 avenue Guy de Collongue, F-69134, ECULLY Cedex, France; CEA, Laboratoire d'Instrumentation et d'Expérimentation en Mécanique des Fluides et Thermohydraulique, DEN/DANS/DM2S/STMF/LIEFT, CEA-Saclay, F-91191 Gif-sur-Yvette Cedex, France
| | - Valéry Botton
- Univ Lyon, Ecole Centrale de Lyon, Université Lyon 1, INSA de Lyon, CNRS, Laboratoire de Mécanique des Fluides et d'Acoustique, ECL, 36 avenue Guy de Collongue, F-69134, ECULLY Cedex, France.
| | - Daniel Henry
- Univ Lyon, Ecole Centrale de Lyon, Université Lyon 1, INSA de Lyon, CNRS, Laboratoire de Mécanique des Fluides et d'Acoustique, ECL, 36 avenue Guy de Collongue, F-69134, ECULLY Cedex, France
| | - Séverine Millet
- Univ Lyon, Ecole Centrale de Lyon, Université Lyon 1, INSA de Lyon, CNRS, Laboratoire de Mécanique des Fluides et d'Acoustique, ECL, 36 avenue Guy de Collongue, F-69134, ECULLY Cedex, France
| | - Hamda Ben Hadid
- Univ Lyon, Ecole Centrale de Lyon, Université Lyon 1, INSA de Lyon, CNRS, Laboratoire de Mécanique des Fluides et d'Acoustique, ECL, 36 avenue Guy de Collongue, F-69134, ECULLY Cedex, France
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