The manipulation of cells and microparticles within microfluidic systems using external forces is valuable for many microscale analytical and bioanalytical applications. Acoustofluidics is the ultrasound-based external forcing of microparticles with microfluidic systems. It has gained much interest because it allows for the simple label-free separation of microparticles based on their mechanical properties without affecting the microparticles themselves.
Microscale Acoustofluidics provides an introduction to the field providing the background to the fundamental physics including chapters on governing equations in microfluidics and perturbation theory and ultrasound resonances, acoustic radiation force on small particles, continuum mechanics for ultrasonic particle manipulation, and piezoelectricity and application to the excitation of acoustic fields for ultrasonic particle manipulation. The book also provides information on the design and characterization of ultrasonic particle manipulation devices as well as applications in acoustic trapping and immunoassays.
Written by leading experts in the field, the book will appeal to postgraduate students and researchers interested in microfluidics and lab-on-a-chip applications.
Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.
The manipulation of cells and microparticles within microfluidic systems using external forces is valuable for many microscale analytical and bioanalytical applications. Acoustofluidics is the ultrasound-based external forcing of microparticles with microfluidic systems. It has gained much interest because it allows for the simple label-free separation of microparticles based on their mechanical properties without affecting the microparticles themselves.
Microscale Acoustofluidics provides an introduction to the field providing the background to the fundamental physics including chapters on governing equations in microfluidics and perturbation theory and ultrasound resonances, acoustic radiation force on small particles, continuum mechanics for ultrasonic particle manipulation, and piezoelectricity and application to the excitation of acoustic fields for ultrasonic particle manipulation. The book also provides information on the design and characterization of ultrasonic particle manipulation devices as well as applications in acoustic trapping and immunoassays.
Written by leading experts in the field, the book will appeal to postgraduate students and researchers interested in microfluidics and lab-on-a-chip applications.
The manipulation of cells and microparticles within microfluidic systems using external forces is valuable for many microscale analytical and bioanalytical applications. Acoustofluidics is the ultrasound-based external forcing of microparticles with microfluidic systems. It has gained much interest because it allows for the simple label-free separation of microparticles based on their mechanical properties without affecting the microparticles themselves.
Microscale Acoustofluidics provides an introduction to the field providing the background to the fundamental physics including chapters on governing equations in microfluidics and perturbation theory and ultrasound resonances, acoustic radiation force on small particles, continuum mechanics for ultrasonic particle manipulation, and piezoelectricity and application to the excitation of acoustic fields for ultrasonic particle manipulation. The book also provides information on the design and characterization of ultrasonic particle manipulation devices as well as applications in acoustic trapping and immunoassays.
Written by leading experts in the field, the book will appeal to postgraduate students and researchers interested in microfluidics and lab-on-a-chip applications.
Chapter 1 Governing Equations in Microfluidics Henrik Bruus, 1,
Chapter 2 Perturbation Theory and Ultrasound Resonances Henrik Bruus, 29,
Chapter 3 Continuum Mechanics for Ultrasonic Particle Manipulation Jürg Dual and Thomas Schwarz, 46,
Chapter 4 Acoustic Radiation Force on Small Particles Henrik Bruus, 65,
Chapter 5 Piezoelectricity and Application to the Excitation of Acoustic Fields for Ultrasonic Particle Manipulation Jürg Dual and Dirk Möller, 81,
Chapter 6 Building Microfluidic Acoustic Resonators Andreas Lenshof, Mikael Evander, Thomas Laurell, and Johan Nilsson, 100,
Chapter 7 Modelling and Applications of Planar Resonant Devices for Acoustic Particle Manipulation Peter Glynne-Jones, Rosemary J. Boltryk, and Martyn Hill, 127,
Chapter 8 Applications in Continuous Flow Acoustophoresis Andreas Lenshof, Per Augustsson, and Thomas Laurell, 148,
Chapter 9 Applications in Acoustic Trapping Mikael Evander and Johan Nilsson, 189,
Chapter 10 Ultrasonic Microrobotics in Cavities: Devices and Numerical Simulation Jürg Dual, Philipp Hahn, Andreas Lamprecht, Ivo Leibacher, Dirk Möller, Thomas Schwarz, and Jingtao Wang, 212,
Chapter 11 Acoustic Manipulation Combined with Other Force Fields Peter Glynne-Jones and Martyn Hill, 242,
Chapter 12 Analysis of Acoustic Streaming by Perturbation Methods Satwindar Singh Sadhal, 256,
Chapter 13 Applications of Acoustic Streaming Roy Green, Mathias Ohlin, and Martin Wiklund, 312,
Chapter 14 Theory of Surface Acoustic Wave Devices for Particle Manipulation Michael Gedge and Martyn Hill, 337,
Chapter 15 Lab-on-a-chip Technologies Enabled by Surface Acoustic Waves Xiaoyun Ding, Peng Li, Sz-Chin Steven Lin, Zackary S. Stratton, Nitesh Nama, Feng Guo, Daniel Slotcavage, Xiaole Mao, Jinjie Shi, Francesco Costanzo, Thomas Franke, Achim Wixforth, and Tony Jun Huang, 354,
Chapter 16 Surface Acoustic Wave Based Microfluidics and Droplet Applications Thomas Franke, Thomas Frommelt, Lothar Schmid, Susanne Braunmüller, Tony Jun Huang, and Achim Wixforth, 399,
Chapter 17 Ultrasound-Enhanced Immunoassays and Particle Sensors Martin Wiklund, Stefan Radel, and Jeremy Hawkes, 420,
Chapter 18 Multi-Wavelength Resonators, Applications and Considerations Jeremy J. Hawkes and Stefan Radel, 452,
Chapter 19 Microscopy for Acoustofluidic Micro-Devices Martin Wiklund, Hjalmar Brismar, and Björn Önfelt, 493,
Chapter 20 Experimental Characterization of Ultrasonic Particle Manipulation Devices Jürg Dual, Philipp Hahn, Ivo Leibacher, Dirk Möller, and Thomas Schwarz, 520,
Chapter 21 Biocompatibility and Cell Viability in Acoustofluidic Resonators Martin Wiklund, 545,
Subject Index, 566,
Governing Equations in Microfluidics
HENRIK BRUUS
Department of Physics, Technical University of Denmark, Lyngby, Denmark E-mail: bruus@fysik.dtu.dk
1.1 Introduction
Microfluidics deals with the flow of fluids and suspensions in channels of sub-millimetre-sized cross-sections under the influence of external forces. Here, viscosity dominates over inertia, ensuring the absence of turbulence and the appearance of regular and predictable laminar flow streams, which implies an exceptional spatial and temporal control of solutes. The combination of laminar flow streams and precise control of external forces acting on particles in solution, has resulted in particle handling methods useful for analytical chemistry and bioanalysis, based on different physical mechanisms including inertia, electrokinetics, dielectrophoretics, magneto-phoretics, as well as mechanical contact forces.
Acoustofluidics, i.e. ultrasound-based external forcing of microparticles in microfluidics, has attracted particular attention because it allows gentle, label-free separation based on purely mechanical properties: size, shape, density, and compressibility. The early acoustophoretic microparticle filters were soon developed into the first successful on-chip acoustophoretic separation devices. Many different biotechnical applications of acoustophoresis have subsequently emerged including cell trapping, plasmapheresis, forensic analysis, food analysis, cell sorting using surface acoustic waves, cell synchronization, and cell differentiation.
Furthermore, substantial advancements in understanding the fundamental physics of microsystems acoustophoresis have been achieved through full-chip imaging of acoustic resonances, surface acoustic wave generation of standing waves, multi-resonance chips, advanced frequency control, on-chip integration with magnetic separators, acoustics-assisted micro-grippers, in situ force calibration, automated systems, and full 3D characterization of acoustophoresis.
In this chapter, adapted from Bruus, we study the governing equations in microfluidics formulated in terms of the classical continuum field description of velocity v, pressure p, and density ρ. We also present some of the basic flow solutions, equivalent circuit modeling useful for predicting the flow rates in networks of microfluidic channels, and scaling laws for various microfluidic phenomena.
1.2 The Basic Continuum Fields
In the following we use the so-called Eulerian picture of the continuum fields, where we observe how the fields evolve in time at each fixed spatial position r. Consequently, the position r and the time t are independent variables. The Eulerian picture is illustrated by the velocity field in Figure 1.1. In general, the value of any field variable F(r, t) is defined as the average value <(Fmol(r', t')> of the corresponding molecular quantity for all the molecules contained in some liquid particle of volume ΔV(r) around r at time t
[MATHEMATICAL EXPRESSION OMITTED] (1.1)
If we, for brevity, let mi and vi be the mass and the velocity of molecule i, respectively, and furthermore let i]member of]ΔV stand for all molecules i present inside the volume ΔV(r) at time t, then the definition of the density ρ(r, t) and the velocity field v(r,t) can be written as
[MATHEMATICAL EXPRESSION OMITTED] (1.2a)
[MATHEMATICAL EXPRESSION OMITTED] (1.2b)
Here, we have introduced the symbol "[equivalent to]" to mean "equal-to-by-definition". Notice how the velocity is defined through the more fundamental concept of momentum.
The dependent field variables in microfluidics can be scalars (such as density ρ, viscosity η, pressure p, temperature T, and free energy Φ), vectors (such as velocity v, current density J, pressure gradient [nabla]p, force density f, and electric fields E), and tensors (such as stress tensor σ and velocity gradient [nabla]v).
1.3 Mathematical Notation
The mathematical treatment of microfluidic problems is complicated due to the presence of several scalar, vector and tensor fields and the non-linear partial differential equations that govern them. To facilitate the treatment, some simplifying notation is called for, and here we follow Bruus. First, a suitable co-ordinate system must be chosen. We shall mainly work with...
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