A study of acoustic radiation force on fluid interface and suspended particles in micro fluidic devices

A STUDY OF ACOUSTIC RADIATION FORCE ON FLUID INTERFACE AND SUSPENDED PARTICLES IN MICRO-FLUIDIC DEVICES LIU YANG NATIONAL UNIVERSITY OF SINGAPORE 2009 A STUDY OF ACOUSTIC RADIATION FORCE ON FLUID INTERFACE AND SUSPENDED PARTICLES IN MICRO-FLUIDIC DEVICES LIU YANG (B.ENG., M.ENG. HIT) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2009 Acknowledgements Acknowledgements First of all, I would like to give my heartfelt gratitude to my supervisor A/Professor. Lim Kian Meng, for his invaluable guidance, support and encouragement throughout this entire research. His profound knowledge in mechanical dynamics and serious attitude towards academic research will benefit my whole life. I would like to thank Ms. Zhu Liang, Dr. Cui Haihang, and Dr. Wang Zhenfeng for the interesting and insightful discussion about vibration system. Special thanks to Professor Lim Siak Piang for his sincere help and advises in my research. I would also like to thank Zhuang Han, Li Huaxiang, Li Hailong, He Xuefei, my best friends in Singapore, for the unforgettable happiness and hardship shared with me. During the four years of my research, their care and support deserve a lifetime memory. Finally, I would like to express my deepest gratitude and love to my parents and wife for their self-giving and continuous understanding and support. I Table of Contents Table of Contents Acknowledgements I Table of Contents . II Summary . V List of Figures .VIII List of Tables . XII 1. Introduction 1.1 Acoustic radiation force used in cell separation in microfluidic devices 1.2 Micro-cell/particle separation in bi-fluid system . 1.3 Objective and scope . 10 1.4 Original contributions 12 1.5 Thesis organization 13 2. Literature Review 15 2.1 Acoustic radiation force . 15 2.2 Particle separation using the acoustic radiation force 17 2.3 Bi-fluid flow in micro systems 20 3. Particle Separation in a Single Fluid using Acoustic Radiation Force . 28 3.1 Theoretical model for particle separation in a single micro fluid 28 3.1.1 Flow in a microchannel . 29 3.1.2 Forces acting on particles 29 3.2 Simulation of particle motion in a single fluid medium 32 3.2.1 Problem description . 32 3.2.2 Particle convergence trace . 34 3.3 Experiments of particle separation in one micro fluid . 39 3.3.1 Materials and methods . 39 3.3.2 Experimental results 43 II Table of Contents 3.4 Discussion 47 4. Bi-fluid Flow in a Micro Channel . 49 4.1 Numerical simulation using BEM model 50 4.1.1 Problem description . 50 4.1.2 Formulation of boundary element method 51 4.1.3 Iteration for equilibrium interface . 55 4.1.4 Convergence of the simulation 57 4.1.5 Simulation results 61 4.2 Experiments on bi-fluid flow in a micro channel 65 4.2.1 System setup and materials . 65 4.2.2 Methods . 65 4.2.3 Comparison of experimental and simulation results . 68 5. Particle Transport across Two-Fluid Flows (Similar Fluids) 73 5.1 Methodology of particle transport between two similar-fluid flows . 75 5.1.1 Interface and particle motion across the interface . 75 5.1.2 Outlet pressure difference and transported particle collection 78 5.2 Experiment method and material . 83 5.3 Results and discussions 84 6. Particle Transport between Two-Fluid Flows (Dissimilar Fluids) 89 6.1 Node shift in dissimilar-fluid flow . 90 6.2 Particle transport between two dissimilar fluids 93 6.2.1 Particle convergence in bi-fluid flow 93 6.2.2 Methodology of particle transport . 94 6.2.3 Experimental results and discussions 96 6.3 Experimental studies on the effect of acoustic field on bi-fluid interface . 99 6.3.1 Interface deformation at different acoustic intensities 100 6.3.2 Interface deformation at different acoustic frequencies 103 6.3.3 Interface deformation and the direction of the acoustic radiation force . 104 III Table of Contents 6.3.4 Output flowrate changes at different acoustic intensities 106 6.4 Acoustic radiation force on the interface . 109 6.4.1 2-D acoustic model of the micro-system . 110 6.4.2 Acoustic radiation stress at the interface . 118 6.5 Model for shift in interface 120 6.6 Diffusion between bi-fluid flows . 124 7. Conclusions . 126 References 130 Appendix 139 Publications . 145 IV Summary Summary Previous studies on cellular particle separation using acoustic radiation force have mainly focused on separation within a single fluid that needs a subsequent procedure to re-dilute separated particles into other media for cellular analysis. In this thesis, a new bi-fluid micro-flow methodology is proposed to combine the particle separation and re-dilution, also known as solvent exchange process, using the acoustic radiation force. The prototype experimental results show successful particle transport from its original solvent to the other solvent and particle collection at the outlet. This particle transport methodology extends the previous acoustic particle separation methods, most of which were performed within a single fluid. The transport process simplifies the cell preparation, resulting in less complex lab-on-chip systems. A 2-D viscous hydrodynamic model governed by Stokes equations was firstly developed and solved by the boundary element method (BEM). The flow of two fluids in parallel in a micro-channel was studied by this model and verified by the experimental results. This 2-D model shows that the fluid viscosities, input flow rates and outlet pressures are the three major factors which affect the location of the fluid interface in the micro-channel. By changing these three factors, the fluid interface location can be controlled. V Summary A methodology has been employed to transport particles between two parallel flows. In this methodology, the shift of the acoustic pressure node due to the different acoustic properties of the two fluids was studied. The fully developed fluid interface was designed to be offset from the shifted acoustic pressure node by adjusting the input flow rates. This offset between the interface and the pressure node enables particle transport from one fluid to the other using the acoustic radiation force. The experimental results obtained by the prototype micro-flow system proved that, for both the similar-fluid case (the pressure node is not shifted) and the dissimilar-fluid case (the pressure node is shifted significantly), this methodology could separate micro particles from one aquatic dilution, and simultaneously transport them into another one. The transported particles suspended in the second fluid flow could be collected downstream. Since the acoustic radiation force is a non-contact force which is based on the densities and compressibilities of the particles and fluids, this methodology provides a wide application potential, especially for cell separation integrated in lab-on-chip systems where aquatic dilutions are commonly used. Finally, the deformation of the fully developed fluid interface due to the acoustic field was studied. The experimental results show that the directions of both the interface deformation and the acoustic radiation force agree with each other. The experimental results also indicate the frequency sensitivity of the interface deformation. Besides the experimental studies, a 2-D numerical model including the piezo-ceramic transducer, the microchannel structure and the bi-fluid flow was built to simulate the acoustic radiation force acting the interface. The analysis obtained indicates that the acoustic radiation force has caused the interface to be deformed VI Summary from its original location. This estimation of the interface deformation is critical for the particle transportation. VII List of Figures List of Figures Figure 2.1 Polystyrene particle manipulation in a standing acoustic wave 18 Figure 2.2 Schematic diagram of Yasuda’s apparatus for blood concentration, adapted from [39] 18 Figure 2.3 Petersoon’s experimental setup and results, adapted from [8]. . 19 Figure 2.4 Particle switching between two fluids using ultrasound, adapted from [25] . 19 Figure 2.5 Interface between two fluids . 21 Figure 2.6 Interface between two immiscible fluids . 23 Figure 2.7 Diffusion layer between two miscible fluids (modified from[64]) . 25 Figure 3.1 Contours of the fully developed Poiseuille flow . 29 Figure 3.2 Sketch of standing wave and particles concentrated at either node or anti-node . 31 Figure 3.3 Schematic diagram of microchannel and standing wave 33 Figure 3.4 Velocity profile along x-direction . 35 Figure 3.5 Simulation results of polystyrene particle position in a single fluid . 35 Figure 3.6 Simulation results of silicone oil droplets concentration in a single fluid . 36 Figure 3.7 Convergence times for different velocities along x direction. 37 Figure 3.8 Convergence distance and time for different velocities along x direction. . 37 Figure 3.9 Convergence distance and time for different contrast factors. 38 Figure 3.10 Experiment setup . 40 Figure 3.11 Sketch of the micro-device part . 41 Figure 3.12 Sketch of microchannel . 42 VIII References References [1] J. 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These field quantities are related by the fundamental equations: T =C du dϕ +e , dx dx (A.1) D=e du dϕ −ε . dx dx (A.2) where, x is the location vector, C is the elastic stiffness constant, e is the piezoelectric constant, and ε is the dielectric constant. As a consequence of the restriction to a single displacement direction (z), all material, which are tensor quantities in general case, are reduced to the scalar quantities that apply to the direction of the sound propagation. For a single homogeneous layer, from the Newton’s second law, we have ρ ∂ u ∂T = ∂x . ∂t (A.3) Since there are no free electric charges in the dielectric layers, the divergence of the electric displacement is zero, ∇⋅D = (A.4) 139 Appendix Substitute Eqs.A.1 and A.2 into Equations. A.3 and A.4, the motion equations and the piezoelectric equation can be shown as ∂ 2u ∂ 2u ∂ 2ϕ ρ =C +e , ∂t ∂z ∂z e ∂ 2u ∂ 2ϕ ε − = 0. ∂z ∂z (A.5) (A.6) Integration of Eq.A.6 gives the expression of electric potential, e ϕ = u + φ1 z + φ , ε (A.7) where, φ0 and φ1 are integration constants. Substituting Eq.A.6 into Eq.A.5, we get ρ where C = C + e2 ε ∂ 2u ∂ 2u C = . ∂t ∂z (A.8) is the piezoelectrically stiffened elastic constant in the usual wave. Thus, Eq. A.8 becomes ρ ∂ 2u ∂ 2u C = . ∂t ∂z (A.9) The general steady state solution of Eq. A.8, u ( x , t ) = u ( z )e − jωt , has the form u ( z ) = A cos(kz ) + B sin(kz ) , where k = ω ρ C (A.10) ; A and B are constants. Substituting equation A.10 and A.7 into the fundamental Eqs.A1,A2, we have the expression of the stress and electric displacement in z direction, T ( z ) = C (− Ak sin(kz ) + Bk cos(kz )) + eφ1 (A.11) D( z ) = −εφ1 (A.12) 140 Appendix Thus, Total integration constants ( A, B, φ , φ1 ) need to be determined from boundary conditions. Assuming the boundary conditions at z=0 as T (0) , D(0) , ϕ (0) , u (0) , we can compute the four integration constants, A = u (0) , B= Ck (A.13) e ⎡ ⎤ ⎢⎣T (0) + ε D(0)⎥⎦ , e φ = ϕ (0) − u (0) , ε φ1 = − D(0) ε (A.14) (A.15) . (A.16) Transfer matrix of a ceramic layer By substituting the integration constants, as given in Equations A.13-A.16, into Equations. A.7 and A.10, we get a solution of the differential equations system of Equations. A.5 and A.6 for all values of z depending linearly on the boundary values at z = . Supposing the thickness of the ceramic layer is l p , the unknowns of a plate exiting between z = and z = l p , can be expressed as follows ⎛ ⎜ cos(kz ) ⎛ u( z) ⎞ ⎜ ⎟ ⎜ ⎜ T ( z ) ⎟ ⎜ − C k sin( kz ) ⎜ ϕ ( z) ⎟ = ⎜ e ⎟ ⎜ ⎜ ⎜ D( z ) ⎟ ⎜ [cos(kz ) − 1] ⎠ ⎜ ⎝ ε ⎜ ⎝ sin( kz ) Ck cos(kz ) sin(kz ) e Ck ε ⎞ ⎟ ⎟⎛ u (0) ⎞ e ⎟⎜ T ⎟ [cos(kz ) − 1] ⎜ (0) ⎟ ε ⎟⎜ ⎟. sin(kz ) e z ⎟⎜ ϕ (0) ⎟ ⎟ − ⎟⎜ C k ε ε ⎟⎝ D(0) ⎠ ⎟ ⎠ sin( kz ) e Ck ε (A.17) When z = l p , the relation between the four variables on both sides of the ceramic layer is, 141 Appendix ⎛ ⎜ cos(k l p ) ⎛ u (l p ) ⎞ ⎜ ⎟ ⎜ ⎜ T (l p ) ⎟ ⎜ − C k sin(k l p ) ⎜ ϕ (l ) ⎟ = ⎜ p ⎟ ⎜ ⎜ e ⎜ D(l ) ⎟ ⎜ cos(k l p ) − p ⎠ ⎝ ε ⎜ ⎜ ⎝ [ sin(k l p ) Ck cos(k l p ) sin( k l p ) e Ck ε ] sin( k l p ) e Ck ε 0 [cos(k l p ]εe ) −1 sin( k l p ) e l p − Ck ε ε ⎞ ⎟ ⎟⎛⎜ u (0) ⎞⎟ ⎟⎜ T (0) ⎟ ⎟⎜ . (A.18) ⎟⎜ ϕ (0) ⎟⎟ ⎟⎜ D(0) ⎟ ⎠ ⎟⎝ ⎟ ⎠ The transfer matrix of this ceramic layer is ⎛ M uu p ⎜ Tu ⎜M M p = ⎜ ϕpu ⎜M p ⎜ ⎝ M uT p M Tp M ϕpT ⎞ M uD p ⎟ M TD p ⎟ ϕD ⎟ Mp ⎟ ⎟⎠ sin(kz l ) Ck ⎛ ⎜ cos(kz l ) ⎜ ⎜ − C k sin(kz ) l =⎜ ⎜ e ⎜ [cos(kz l ) − 1] ε ⎜⎜ ⎝ cos(kz l ) sin( kz l ) e Ck ε 0 sin(kz l ) e Ck ε [cos(kz l ) − 1] e ε sin( kz l ) e z l − Ck ε ε ⎞. ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟⎟ ⎠ (A.19) Simplification of the transducer Considering the simplified transducer shown in Figure 6.19, the boundary condition at z = is traction free, and the continuity boundary conditions are required at z = z l where the transducer is connected to the silicon channel. Thus, the traction is T (0) = . (A.20) Since we are free to determine the zero point of the electric potential, we can set the electric potential at the two surfaces ( ϕ1 and ϕ ) as, ϕ1 = −ϕ = U , (A.21) 142 Appendix where U is the voltage applied on the PZT transducer. From surface to surface 2, the electric potential inside the PZT ϕ p varies from ϕ1 to ϕ continuously. The electric displacement D p has the expression, Dp = U0 −U jωAR (A.22) Using the transfer matrix shown in Equation A.19, the relations between the variables at the two surfaces ( u1 , T1 , ϕ1 , D1 , and u , T2 , ϕ , D2 ) become, uD u1 = M uu p u2 + M p Dp , (A.23.a) TD T1 = M Tu p u2 + M p D p , (A.23.b) U ⎛ U⎞ = M ϕpu u + M ϕpD D p + ⎜ − ⎟ , ⎝ 2⎠ (A.23.c) U0 U − . jωAR jωAR Dp = (A.23.d) Further simplification of Equations A.23 shows, T1 = a u + b , (A.24) where the two parameters a and b are: a= b= ( + (M Tu TD ϕD ϕu jωAR M Tu p + Mp Mp −Mp Mp jωAR M uu p ( + (M uu p ϕD Mp −M uD p ϕu Mp ), ) )( ) ) jωAR + M (A.25) Tu TD ϕD ϕu − jωAR M uD jωAR M Tu p + Mp Mp −Mp Mp p jωAR M uu p uu p ϕu M ϕpD − M uD p Mp ϕD p + jωAR M TD p jωAR + M ϕpD U . (A.26) 143 Appendix U is the electric potential difference provided by the voltage source; R is the total equivalent resistance of the external circuit excluding the transducer; A is the effective area of the transducer; and ω is the time harmonic angular frequency. The parameter a is equivalent spring constant, and b is equivalent to the applied force due to the electric field. 144 Publications Publications Y. Liu, K.M. Lim, Particle transport across bi-fluid interface using acoustic radiation force. The third international symposium on physics of fluids, 15-18 June, 2009, Jiuzhaigou, China 145 [...]... performed in stationary fluids to demonstrate moving[32], trapping[33], fractionation[34] of rigid particles by the acoustic radiation force Subsequently, manipulation of the suspended particles was studied with the acoustic standing wave being applied in a laminar flow within a microchannel Yasuda and his colleagues applied the acoustic standing wave in a laminar flow within their microchannel[35]... the concentration was accomplished in a stationary fluid This manipulation method of micro cellular particles using the acoustic standing wave in stationary fluid was also widely studied for the microalgae concentration and detection Tessier, et al reported a portable device which couples a spectrometer with the acoustic standing wave field[20] The acoustic standing wave was designed to concentrate microalgae,... forces acting on a rigid sphere (1934)[10] and disk (1936)[26] in an ideal fluid King established that the radiation force in the field of the standing acoustic wave is spatially periodic with a period equal to the half-wavelength of the acoustic wave Subsequently, Yoshioka and Kawasima[11] extended King’s theory and derived the acoustic radiation force acting on compressible spherical particles in an... make the theory capable of describing biological cells consisting of a central nucleus coated by a cytoplasmic layer and bioactive layered sphere In addition to the studies of spheres, the acoustic force acting on objects with other shapes in ideal fluids was also studied widely Awatani[28] studied the acoustic radiation force acting on a rigid cylinder in an ideal fluid Hasegawa et al extented Awatani’s... review of the theoretical studies of the acoustic radiation force and the application of this force in 13 Chapter 1 cellular particle manipulations Chapter 3 describes a microchannel system where the acoustic radiation force is applied to separate particles within a single fluid A model is developed to describe particle concentration under the acoustic radiation force A series of experiments in Chapter... density and compressibility between the object and the surrounding fluid The theory of the acoustic radiation force was first proposed by Lord Rayleigh[9] King derived an expression of the acoustic radiation force acting on a rigid sphere suspended in an ideal acoustic field[10] Yashioka and Kawasima extended King’s theory, and derived an expression to estimate the acoustic radiation force on compressible... controllable force is needed Magnetic force has been studied 8 Chapter 1 and used in bead separation in bi -fluid system by Nixa[23] In Nixa’s separation, super-paramagnetic beads and non-magnetic beads were suspended in albumin solution and flowed parallel to another fluid (PBS buffer) in a micro- channel With an electric-magnetic field set up in the micro- channel, a magnetic force acts on super-paramagnetic... of the 2-D microchannel model and boundary conditions 117 Figure 6.22 Averaged acoustic radiation traction on the interface 119 Figure 6.23 Identified interface from the experimental images 120 Figure 6.24 Comparison of the hydrodynamic traction jump and the acoustic radiation tractions (Vpp=3V) 122 Figure 6.25 Comparison of the hydrodynamic traction jump and the acoustic radiation. .. theoretical and numerical models for different particles (from spherical particles to cylinders) and different acoustic fields (from infinite plane travelling wave to enclosed standing wave) will be reviewed 1.1 Acoustic radiation force used in cell separation in microfluidic devices When an object is subjected to an acoustic field in a fluid, it experiences an acoustic radiation force due to the difference in. .. accomplished in a single fluid In 2004, Hawkes, et al., reported using an acoustic chamber and half-wave length acoustic standing wave within the chamber to move yeast cells from a de-gassed water stream to a parallel fluorescent water stream In 2005, Petersson, Nilsson, and their partners described a method to translate particles from one medium into another one utilizing the acoustic radiation force[ 25] . simulate the acoustic radiation force acting the interface. The analysis obtained indicates that the acoustic radiation force has caused the interface to be deformed Summary VII from its original. A STUDY OF ACOUSTIC RADIATION FORCE ON FLUID INTERFACE AND SUSPENDED PARTICLES IN MICRO-FLUIDIC DEVICES LIU YANG NATIONAL UNIVERSITY OF SINGAPORE 2009 A STUDY. the acoustic radiation force 17 2.3 Bi -fluid flow in micro systems 20 3. Particle Separation in a Single Fluid using Acoustic Radiation Force 28 3.1 Theoretical model for particle separation