Micromanipulation of Small Particles with Ultrasound Doctoral exam 26 th August 24 Albrecht Haake Advisor: Prof. J. Dual Co-examiner: Prof. A. Stemmer Swiss Federal Institute of Technology Zurich (ETHZ), Institute of Mechanical Systems - Mechanics Telephone: +41/ 1/ 632 31 82, Fax: +41/ 1/ 632 11 45 E-mail: albrecht.haake@imes.mavt.ethz.ch A. Haake Doctoral exam, 26 th August 24 I
OVEVIEW clamp glass plate (vibrating) piezo transducers fluid arbitrary surface particles, arranged by the sound field Particles are manipulated by acoustical forces. These forces appear in a sound field that is excited between a vibrating glass plate and a rigid surface. A. Haake Doctoral exam, 26 th August 24 II CONTENTS Contents I Introduction 1 II Sound Field in the Fluid Layer 3 III Sound Field in the Fluid Gap 4 IV Dispersion elation of a Plate with Fluid Loading 8 V Technical Setup 13 VI Experimental esults 16 VII Conclusions 25 A. Haake Doctoral exam, 26 th August 24 III
Introduction Motivation IINTODUCTION I.1 MOTIVATION Aim: manipulation of small particles with ultrasound. easons to consider the manipulation with ultrasound: Handling of small particles with solid instruments is problematic (sticking, damage). Ultrasonic manipulation is a complementary method to existing techniques of non-contact manipulation (e.g. optical tweezers, Dielectrophoresis [DEP]). I.2 SPECIFICATION FO THE ULTASONIC MICOMANIPULATION Contactless (not contact to solid bodies) manipulation, Single or multiple particles (mechanical parts, biological cells, etc.), Size of the particles lies between 1m and 1m. A. Haake Doctoral exam, 26 th August 24 1/ 25 Introduction Historical Development I.3 HISTOICAL DEVELOPMENT first description of the effect of acoustical forces by first description 1886 Kundt 1) force on a rigid sphere in a plane standing wave calculation of the force 1934 2) idea for a device that uses ultrasound to coagulate first idea of an application 194 dust and smoke 3) force on a compressible sphere in a plane standing calculation of the force 1955 wave 4) force on a compressible sphere in an arbitrary sound calculation of the force 1961 field 5) ideas and devices to remove particles from a liquid by acoustic filters 198 -... an ultrasound field 6) ideas to manipulate particles with ultrasound acoustic manipulation 199-... ideas to manipulate particles with ultrasound with acoustic micromanipulation 2 -... micro-meter accuracy 1) Kundt A.; Ueber eine neue Art akustischer Staubfiguren und über die Anwendung derselben zur Bestimmung der Schallgeschwindikeit in festen Körpern und Gasen.; Annalen der Physik und Chemie 1866; Vol. 127, Iss. 4, pp 496-523. 2) King L. V.; On the Acoustic adiation Pressure on Spheres; Proc. o. t.. Soc. of London. Ser A, Math. and phys. sc. 1934; Vol. 147, 3) US 2,215,484; St Clair H. W.; Sonic Flocculator and Method of Flocculating Smoke or the Like (194-9-24). 4) Yosioka K. and. Kawasima Y.; Acoustic adiation Pressure on a Compressible Sphere; Acustica 1955; Vol. 5, Iss. pp 167-173. 5) Gorkov L. P.; Forces Acting on a Small Particle in an Acoustic Field within an Ideal Fluid; Doklady Akademii Nauk Sssr 1961; Vol. 14, Iss. 1, pp 88-. 6) Gröschl M.; Ultrasonic Separation of Suspended Particles - Part I: Fundamentals; Acustica 1998; Vol. 84, Iss. 3, pp 432-447. A. Haake Doctoral exam, 26 th August 24 2/ 25
Sound Field in the Fluid Layer How can particles be manipulated by a sound field? II SOUND FIELD IN THE FLUID LAYE II.1 HOW CAN PATICLES BE MANIPULATED BY A SOUND FIELD? When a particle is placed in a sound field, it experiences a force. resulting sound wave after particle is placed in fluid force on the particle due to sound wave single particle sound wave in fluid incident sound wave scattered sound wave sound wave in particle The magnitude of the force depends on the frequency, the radius of the particle and the material parameters. A. Haake Doctoral exam, 26 th August 24 3/ 25 Sound Field in the Fluid Gap How can particles be manipulated by a sound field? III SOUND FIELD IN THE FLUID GAP The sound field is emitted by a vibrating surface with the displacement u Sf and reflected by a rigid surface. x y λ Sf y vibrating surface h x 3 2 1 4 fluid y rigid surface The sound field is modelled as a superposition of four plane waves ( 1, 2, 3 and 4 ). The resulting velocity potential is given by F 4 m m = 1 F u Sf = u Sf cosxk Sf y = h = e it,.....spatial coordinates, Fy.wave numbers k.....displacement amplitude......velocity potential.......angular frequency........time.......height of the fluid gap......wavelength of the surface k Sf u Sf. t h Sf = = i--------------------- cosxk Fx cosh + y Fy sin Fy k hk e it A. Haake Doctoral exam, 26 th August 24 4/ 25
Sound Field in the Fluid Gap The Force Field in the Fluid Gap III.1 THE FOCE FIELD IN THE FLUID GAP III.1.1 PIMAY FOCES The force field acting on the particles in the fluid F can be calculated from the force potential U: with F = U, 1 U 2r S3 F -- p2 q ---------- f 2 = 2 1 --------- f 2 3 F2 c F 2 1). p 2 q 2. c. r S,...... mean square fluctuations of the pressure and velocity,,........... densities and speeds of sound of the fluid and of the particle,................ radius of the particle. f 1 1 2 F c F 2 S c S ------------------- 2 S + F = ---------, f 2 2 S F = 1) L. P. Gorkov, Forces Acting on a Small Particle in an Acoustic Field within an Ideal Fluid, Doklady Akademii Nauk Sssr 14 (1961) A. Haake Doctoral exam, 26 th August 24 5/ 25 Sound Field in the Fluid Gap The Force Field in the Fluid Gap Two-dimensional case The particles are concentrated at the minima of the force potential. Force field in the fluid gap.5 1 x/λ Sf Plane for which the force field is displayed y z x -.25 y λ Fy h =.75λ Fy -.75 force vectors lines of constant force potential saddle point of the force potential points where particles are collected It depends on the material combination where these minima lie. With a quasi one-dimensional plate wave the sound field is two-dimensional and the particles will be arranged in lines. A. Haake Doctoral exam, 26 th August 24 6/ 25
Sound Field in the Fluid Gap The Force Field in the Fluid Gap Three-dimensional case When the plate wave propagates in two perpendicular directions, the sound field is three- dimensional and it is possible to concentrate single particles in points. A large quantity of particles will be arranged in ellipse shaped areas (according to the isolines of potential of forces). 1 /2 1 /4 Force field in the fluid gap at the reflecting surface 1 z /λ Fz 1 /4 1 /2 x/λ Fx 1 points where single particles are collected lines of constant force potential force vectors z Plane for which the force field is displayed y x A. Haake Doctoral exam, 26 th August 24 7/ 25 Dispersion elation of a Plate with Fluid Loading Characteristic Equation IV DISPESION ELATION OF A PLATE WITH FLUID LOADING IV.1 CHAACTEISTIC EQUATION The plate has a thickness of d. y Geometrical alignment of plate and fluid The fluid is on one side, at y = h, in contact with a rigid surface and on the other side, at y =, in contact with the vibrating plate. x plate fluid h d For the calculation of the dispersion relation of the plate/fluid combination the displacement potentials in the plate are assumed to be P s coshqy + a sinhqye i t = xk P P a coshsy + s sinhsye i t xk P = F F = i--------------------- cosxk Fx cosh + y Fy sin Fy k hk e it A. Haake Doctoral exam, 26 th August 24 8/ 25
Dispersion elation of a Plate with Fluid Loading Characteristic Equation The solution of this system of equation leads to the characteristic equation of the plate/fluid combination 16k P4 q 2 s 2 2 d k P + s 2 4 4qs d d d tanh--s coth--q + tanh--q coth--s 2 = + kp2 k 2 2 2 2 P + s 2 2 ----- 2 k P + s 2 2 2 2 cothdq 4qsk P cothdsk t2 k P s 2 coshk Fy ---- q F P k Fy + k P k l................ wave number in the plate,, k t............. wave numbers corresponding to the longitudinal and transversal waves,,. 2 2 2 2 q = k P k l s = k P k t The first term (blue, in square brackets) is the product of the characteristic equations of the symmetrical and antisymmetrical mode of a free plate. The symmetrical and antisymmetrical mode are coupled by the second term of the equation (red, in curly brackets). A. Haake Doctoral exam, 26 th August 24 9/ 25 Dispersion elation of a Plate with Fluid Loading Two Cases of Plate/Fluid Combinations IV.2 TWO CASES OF PLATE/FLUID COMBINATIONS IV.2.1 DOMINATING PLATE (EXAMPLE: 1mmGLASS PLATE,.1 mm WATE LAYE) Fluid layer is thin with respect to the vertical wave length in the fluid hk Fy 1, the coupling term has a constant influence on the plate dispersion. There is no wave propagation below the speed of sound in the fluid. 7 c P m/s 5 4 c 3 2 c F 1 Dispersion diagram for the case of a dominating plate A S dispersion in plate without fluid dispersion in plate with fluid 1 2 3 4 5 f / MHz 7 A. Haake Doctoral exam, 26 th August 24 1/ 25
Dispersion elation of a Plate with Fluid Loading Two Cases of Plate/Fluid Combinations IV.2.2 COUPLING OF FLUID AND PLATE (EXAMPLE: 1mm GLASS PLATE, 1mm WATE LAYE) Dispersion diagram for a plate with a layer The fluid layer is so thick that coshk Fy has many zero points in the regarded frequency range; such a zero point represents resonance in the fluid layer. There is decoupling when coshk Fy =, as the coupling term vanishes. 7 c P m/s 5 4 c 3 2 c F 1 A S dispersion in plate without fluid dispersion in plate with fluid decoupling 1 2 3 4 5 f / MHz 7 A. Haake Doctoral exam, 26 th August 24 11/ 25 Dispersion elation of a Plate with Fluid Loading Two Cases of Plate/Fluid Combinations IV.2.3 CONCLUSIONS OF THE INVESTIGATION OF THE PLATE/FLUID DISPESION The first antisymmetrical mode fits the requirements best: It has the smallest wave length, It is easy to excite. For a rough estimate it is sufficient to calculate the wavelength of the plate without fluid loading, because its influence is not very strong. A. Haake Doctoral exam, 26 th August 24 12/ 25
Technical Setup Design of the Device V TECHNICAL SETUP V.1 DESIGN OF THE DEVICE The device consists of a glass plate and transducers, held in a clamp and a fluid and a rigid surface (does not necessarily belong to the setup). The glass plate and the piezo transducers are only held by the tension in the clamp. top view dimetric section view glass plate 14 clamp h1 piezo bar observation direction power supply clamp 12.5 piezo bar 56 glass plate fluid gap reflecting surface 6 A. Haake Doctoral exam, 26 th August 24 13/ 25 Technical Setup Design of the Device For later experiments the glass plate with the piezo transducers are glued without tension into a holder. Top view glass plate 14 piezo bar 25 holder glass plate piezo transducer wire.5 Bottom view holder 12 75 insulation Advantages compared to the old clamp easier to handle, electrodes of the piezo transducer can be insulated, better results in the experiments (straighter lines, better repeatability). A. Haake Doctoral exam, 26 th August 24 14/ 25
Technical Setup Experimental Setup V.2 EXPEIMENTAL SETUP CCD camera The experimental setup is placed on a vibration insulation table; monitor for the microscope camera microscope positioning system It consists of a microscope with camera and monitor, a light source with fiber optic, a vertical translation stage, a positioning system. fiber optic light source glass- piezounit basin translation stage A. Haake Doctoral exam, 26 th August 24 15/ 25 Experimental esults Concentration of particles in Lines and Points VI EXPEIMENTAL ESULTS VI.1 CONCENTATION OF PATICLES IN LINES AND POINTS VI.1.1 CONCENTATION HL6-CELLS IN LINES, f = 1.2MHz (see Two-dimensional case ) Top view through the vibrating glass plate Top view through the vibrating glass plate (magnified) A. Haake Doctoral exam, 26 th August 24 16/ 25
Experimental esults Concentration of particles in Lines and Points VI.1.2 CONCENTATION HL6-CELLS IN POINTS f = 1.2MHz (see Three-dimensional case ) Top view through the vibrating glass plate Top view through the vibrating glass plate (magnified) A. Haake Doctoral exam, 26 th August 24 17/ 25 Experimental esults Concentration of particles in Lines and Points VI.1.3 VETICAL POSITION OF PATICLES Particles can also levitate in the fluid, (see Two-dimensional case ). Side view into the fluid gap Lifting of particles from the object slide; it is possible to lift a particle from the a surface, the force at the reflecting surface is zero but the sphere is r S above this surface. A. Haake Doctoral exam, 26 th August 24 18/ 25
Experimental esults Displacement of Particles VI.2 DISPLACEMENT OF PATICLES Three possible principles of horizontal displacement were demonstrated experimentally: Displacement of the glass-piezo-unit Changing the excitation frequency and consequently the wavelength Superposition of two standing waves with different amplitude generator glass plate piezo element clamp f u u 1 particle fluid f 1 f f 1 u 2 u 3 A. Haake Doctoral exam, 26 th August 24 19/ 25 Experimental esults Displacement of Particles VI.2.1 DISPLACEMENT OF THE GLASS-PIEZO-UNIT At the initial position the sound field is turned on, so that the particles align according to the sound field. Then the full glass-piezo-unit is displaced, the particles follow that movement Displacement of particle by a small distance (micrometers) Displacement of particle by a large distance (millimeters) A. Haake Doctoral exam, 26 th August 24 2/ 25
Experimental esults Displacement of Particles VI.2.2 CHANGING THE EXCITATION FEQUENCY The wavelength of the plate wave depends on the excitation frequency (see section IV.2.1). When the frequency is increased, the wavelength decreases. f f 1 f f 1 One-dimensional positioning (polystyrene bread) Two-dimensional positioning (HL6-cells) A. Haake Doctoral exam, 26 th August 24 21/ 25 Experimental esults Displacement of Particles VI.2.3 SUPEPOSITION OF TWO STANDING WAVES WITH DIFFEENT AMPLITUDES If two standing waves with a fixed phase and varying amplitudes u 1 = sin 1 + k P x and u 2 = 1 sin 2 + k P x are superimposed u sp = sin 1 + xk P + 1 sin 2 + xk P, the resulting wave has the same wavelength and a varying phase. u u 1 u 2 u 3 Displacement of the nodes of the superimposed wave u sp for 1 ( 2 1 = 2 ) A. Haake Doctoral exam, 26 th August 24 22/ 25
Experimental esults Displacement of Particles The signal of the amplifier is split by a voltage divider. Two opposite piezo transducer are connected to the connectors e 1 and e 2. By turning the switch, the amplitudes of the voltage at the two transducers can be changed discretely. u u 1 u 2 u 3 One-dimensional positioning (polystyrene beads) Voltage divider U ampl 3 21 4 5 6 P 1 3 21 4 5 6 S 1 S e 2 1 e2 U 1 U 2 P2 gr A. Haake Doctoral exam, 26 th August 24 23/ 25 Experimental esults Displacement of Particles VI.2.4 COMPAISON OF THE THEE DISPLACEMENT PINCIPLES Displacement of the glass-piezo-unit Changing the excitation frequency Superposition of two standing waves f u u 1 f 1 f f 1 u 2 u 3 + easy to implement + electronic parameters stay constant external positioning unit necessary might cause fluid flow suitable for large and small displacement ranges for systems where the glass-piezo-unit can be displaced + geometry stays constant frequency has to be changed displacement is not continuously suitable for large displacement ranges for systems with low accuracy demands (prior to higher accuracy positioning) + geometry stays constant + electronic parameter stay constant + simple voltage divider low displacement amplitudes suitable for small displacement ranges for systems with high accuracy demands A. Haake Doctoral exam, 26 th August 24 24/ 25
Conclusions Displacement of Particles VII CONCLUSIONS Introduction of a method for contactless positioning of small particles. Theoretical derivation of the sound field in a fluid gap which is excited by surface wave. Theoretical derivation of the dispersion relation of plate with fluid loading on one side. Introduction of a method and device for contactless positioning and displacement. The device can be placed opposite any plane surface to position particles on it. Possible application are in the field of micro-technology (assembling and aligning of components), bio-technology (handling of cells). Presentation of experimental results of one- and two-dimensional positioning and displacement. A. Haake Doctoral exam, 26 th August 24 25/ 25