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1 Simon, G. and Andrade, M. A. B. and Roolvink, D. and Cormack, P. A. G. and Riehle, M. O. and Bernaau, A. L. (6) A determinitic method for particle orting by dynamic acoutic field. In: 6 IEEE International Ultraonic Sympoium (IUS). IEEE International Ultraonic Sympoium. Proceeding. IEEE, Picataway, NJ. ISBN , Thi verion i available at Strathprint i deigned to allow uer to acce the reearch output of the Univerity of Strathclyde. Unle otherwie explicitly tated on the manucript, Copyright and Moral Right for the paper on thi ite are retained by the individual author and/or other copyright owner. Pleae check the manucript for detail of any other licence that may have been applied. You may not engage in further ditribution of the material for any profitmaking activitie or any commercial gain. You may freely ditribute both the url ( and the content of thi paper for reearch or private tudy, educational, or not-for-profit purpoe without prior permiion or charge. Any correpondence concerning thi ervice hould be ent to the Strathprint adminitrator: trathprint@trath.ac.uk The Strathprint intitutional repoitory ( i a digital archive of Univerity of Strathclyde reearch output. It ha been developed to dieminate open acce reearch output, expoe data about thoe output, and enable the management and peritent acce to Strathclyde' intellectual output.

2 A Determinitic Method for Particle Sorting by Dynamic Acoutic Field G. Simon, M. A. B. Andrade, D. Roolvink 3, P. A. G. Cormack 3, M. O. Riehle, A. L. Bernaau * School of Engineering and Phyical Science, Heriot-Watt Univerity, Edinburgh, United Kingdom Intitute of Phyic, Univerity of São Paulo, Brazil 3 WetCHEM, Department of Pure and Applied Chemitry, Univerity of Strathclyde, Thoma Graham Building, 9 Cathedral Street, Glagow, G XL, United Kingdom Centre for Cell Engineering, Intitute for Molecular, Cell and Sytem Biology, CMVLS, Univerity of Glagow, Glagow, United Kingdom Abtract Thi paper invetigate the dynamic acoutic orting method from a theoretical perpective. Analytical equation of motion and numerical imulation have been ued to optimize parameter for orting variou particle mixture. The effect of change in field parameter a frequency or voltage on efficient orting ha been invetigated. Experiment have been carried out to verify theoretical finding. Keyword acoutic particle orting; acoutic particle manipulation; dynamic acoutic field; acoutic tweezing; acoutic radiation force; phae modulation I. INTRODUCTION Cell eparation i crucial in many reearch area including clinical ample preparation, regenerative medicine, tem cell reearch and improved food afety []. The applicable method for cell eparation comprie electric, dielectric, magnetic, hydrodynamic and acoutic technique [-]; however acoutic technique have an advantage a they offer contactle and calable orting with negligible advere effect on particle []. A wide range of approache which exploit difference in particle migration time ha been preented previouly. Thee comprie a half-wavelength reonator tructure, a frequency weeping device, and the dynamic acoutic field approach (DAF) [6]. The feaibility of our DAF method ha been invetigated earlier for orting particle by ize. In thi paper, a detailed and predictive theoretical background for the DAF method i preented. The effect of denity, compreibility of media and excitation frequency on the eparation efficiency and purity of the orted ample are invetigated. denity () and compreibility () of particle (ubcript p) and media (ubcript m) a p / m p / p m m () Therefore the acoutic radiation force cale with the cube of the radiu of the particle, and alo ha a weak dependence on the denity. Baed on the particle parameter they can either have negative or poitive acoutic contrat factor. Particle with poitive contrat factor are puhed toward the preure node by the acoutic radiation force, while particle with negative contrat factor agglomerate along the antinode. Thi can be readily utilized for binary fractionation []. When the acoutic energy denity i appropriately choen for the flow rate in the microchannel, eparation due to the difference in mobility of particle can be achieved. Thee free flow fractionation device have alo been extenively invetigated in the literature [3, ]. II. METHOD When two oppoing ultraonic tranducer are activated by the ame inuoidal ignal an acoutic tanding wave pattern i formed. The pherical particle upended in the fluid media between tranducer catter the acoutic field and give rie to the primary acoutic radiation force: F V ke in kx () r r ac where V r, k, E ac and are the volume of the particle, wavenumber, acoutic energy denity and acoutic contrat factor, repectively. The acoutic contrat factor depend on the Fig.. The dynamic acoutic field method. The top graph how the phae hift pattern, the bottom graph how the induced particle diplacement Our method for orting particle utilize a dynamic acoutic field (DAF), where the phae of one of the tranducer i hifted *correponding author, A.Bernaau@hw.ac.uk

3 ideal t ramp () ret time () temporally reulting in a lateral diplacement of the acoutic pattern and preure node. When the movement of the node i low enough, the trapping force on particle i large enough to drag them with the pattern, however maller particle will not be able to follow. Thi difference in behavior allow for orting. The phae pattern conit of two region: firtly, it i linearly hifted from to 36, and the time required for thi i called the ramp time. Secondly the phae i kept teady to allow the particle to tabilize their poition (Fig. ). To be able to deign experiment and verify experimental reult an analytical olution for the differential equation of motion hall be preented for our dynamic orting method. A during the ramping the radiation force change patially, it ha a different form to (). Denoting the tart of phae hift a t, defining the rate of phae hift a (3) t ramp and i defined a before. Therefore, the poition of any particle can be determined theoretically uing thee equation. The validity of thee equation for particle trajectorie ha been verified by comparing reult obtained from direct numerical olution of the differential equation of motion. Both approache were implemented in MATLAB, the new method being ignificantly fater allowing for algorithm for parameter optimization. III. RESULTS AND DISCUSSION A. Parameter Optimiation with DAF For a given et of particle eparation can be achieved by chooing the appropriate t ramp and t ret time. Since the analytical equation for poition are complex, a numerical approximation can be ued intead for ideal parameter determination. An example i given for and m polytyrene particle in Fig.. and collecting all parameter of the radiation force into the ingle variable c rad, the force ha the form F c kx t t r rad in () Newton econd law for the force acting horizontally (the radiation force and the Stoke drag force) take the form µm 67.3 µm. µm 6.8 µm 369. µm 76.3 µm 83. µm 9.7 µm d x m F v Fr dt Neglecting the acceleration term ince in microfluidic inertial effect are minucule [7] we arrive at c vic dx dt rad c in kx t t (6) and ubtitution of the argument of the in with a new variable give the olution of the form x( t) t t Q tanc Q tq k i / tan k (7) where = kc rad/c vic, Q = ( - ) / and tan - () i the invere tangent function normalized to [, ). The contant c i can be determined from initial condition, and can be complex uch a Q. For the range where the phae i kept contant at 36, the equation preented in [7] ha been ued. The only difference i the preence of a minu ign due to the different definition of the origin: x( t) tan ci exp t k ramp time () Fig.. (color online) Difference in final poition of m and m polytyrene particle for variou t ramp and t ret value after four cycle. A MHz tranducer wa ued in water for imulation, therefore the maximum eparation i four time half the wavelength, 7 m. Red color correpond to no eparation and green denote full eparation. 6 8 imulation reult fitted invere-quare curve 6 8 f (MHz) Fig. 3. Ideal ramp time v frequency of tranducer. The anticipated invere quare dependence ha been verified by imulation. The effect of frequency, acoutic preure (tranducer voltage) and denity of media on ideal tramp time ha been alo invetigated. Since increaing the frequency the acoutic force

4 ideal t ramp () ideal t ramp () increae linearly and alo the ditance between node decreae in an inverely proportional manner, it wa expected that the ideal tramp time i inverely proportional to the quare of the tranducer frequency. Simulation reult revealed an almot perfect f dependence a we anticipated (Fig. 3). The acoutic radiation force ha a quadratic dependence on the preure amplitude, therefore again an inverely quadratic dependence of ideal t ramp on the preure amplitude wa expected and verified (Fig. ). Since the preure amplitude i directly proportional to the tranducer voltage, the ideal t ramp i alo proportional to V. imulation reult fitted invere-quare curve 6 8 p (kpa) Fig.. Ideal ramp time v the preure amplitude (or tranducer voltage). The anticipated invere-quare dependence ha been verified by imulation. B. Experimental Reult To verify the equation of motion for particle preented in the theoretical ection, two experiment have been carried out, one for ize-baed eparation and one for denity-baed eparation. For the experiment a previouly decribed octagon bulk acoutic wave device wa ued [6]. To quantify the eparation efficiency and purity we defined thee a the following: number of target particle orted Efficiency (9) number of all target particle number of target particle in orted outlet Purity () all particle in orted outlet For ize-baed eparation and m polytyrene particle have been upended in aqueou olution. The applied voltage on the two PZT tranducer wa Vpp, the frequency of the ignal wa MHz. The experiment howed mot effective eparation for. ramp time and ret time (Fig. 6). The recorded particle trace have been matched with theoretical reult, the only fitting parameter being the acoutic preure amplitude, p = 6 kpa. The theoretical and experimental reult how excellent match (Fig. 7). For thi experiment all of the large particle have been eparated, reulting in % efficiency, and ince ome of the mall particle alo have been moved, the purity of the eparation wa 7%. Finally, the radiation force ha a weak dependence on the denity of the media, and therefore we predicted only a imilarly weak dependence of ideal t ramp on the denity which wa again validated by the imulation (Fig. ). imulation reult 9 3 denity of media (kg/m 3 ) Fig.. Ideal ramp time v the denity of the media. Only a weak dependence can be oberved. Thee obervation can help deigning a device for eparation of pecific target cell or particle. The imulation alo help chooing the appropriate field parameter for eparation. Fig. 6. (color online) Separation of m and m polytyrene particle. The image from left to right, top to bottom were recorded every 7. econd (one after each full cycle). The large particle hift gradually to the left (in green) while the maller one (in orange) tay in place.

5 particle poition (µm) particle poition (µm) 37 8 experiment µm ize experiment µm ize imulation µm ize imulation µm ize 37 8 FeO experiment PS experiment FeO imulation PS imulation time () Fig. 7. Experimental and imulation reult for ize-baed eparation. An excellent fit can be oberved for both type of particle. For the denity-baed eparation m polytyrene ( =. g/cm 3 ) and iron oxide ( =.7 g/cm 3 ) particle have been ued. The tranducer voltage wa reduced to 7 Vpp, the ramp time wa 3 and the ret time wa.. Again a good fit between theoretical and experimental particle trace can be oberved (Fig. 7). For thi experiment the efficiency i % but the purity only 6%. 6 8 Fig. 9. Experimental and imulation reult for denity-baed eparation. An excellent fit can be oberved for both type of particle. IV. time () CONCLUSION The governing equation of the dynamic acoutic orting have been preented in thi paper. A numerical approach wa introduced for determining the bet field parameter for orting. The effect of changing tranducer voltage or frequency on orting ha been invetigated along with changing the denity of media. Experiment were carried out for ize and denity baed eparation, and the recorded particle trace were matched perfectly with imulation reult. The efficiency of eparation for both type of experiment wa %, but the purity of eparation wa lower for the denity-baed eparation. Thi i due to the weak dependence of radiation force on denity of particle. We hall invetigate in the future the ame principle of orting for continuou flow device. ACKNOWLEDGEMENT Part of thi work wa upported by Scottih Crucible and EPSRC From Molecule to Sytem grant. Fig. 8. (color online) Separation of m polytyrene and iron oxide particle. The image from left to right, top to bottom were recorded every. econd (one after each full cycle). The dener iron oxide particle hift gradually to the right (in green) while the le dene one (in orange) tay in place. REFERENCES [] C. W. T. Shield, C. D. Reye, and G. P. Lopez, "Microfluidic cell orting: a review of the advance in the eparation of cell from debulking to rare cell iolation," Lab Chip, vol., pp. 3-9, Mar 7. [] F. Peteron, A. Nilon, C. Holm, H. Jönon, and T. Laurell, "Continuou eparation of lipid particle from erythrocyte by mean of laminar flow and acoutic tanding wave force," Lab Chip, vol., pp. -,. [3] B. L. Gray, H. Becker, Y. Ai, and B. L. Marrone, "Separation of biological cell in a microfluidic device uing urface acoutic wave (SAW)," in Proc. SPIE 8976, Microfluidic, BioMEMS, and Medical Microytem XII, 8976O,. [] D. A. Johnon and D. L. Feke, "Methodology for fractionating upended particle uing ultraonic tanding wave and divided flow field," Separation Technology, vol., pp. -8, // 99. [] M. Wiklund, "Acoutofluidic : Biocompatibility and cell viability in microfluidic acoutic reonator," Lab Chip, vol., pp. 8-8, May 8. [6] G. D. Skoti, D. R. Cumming, J. N. Robert, M. O. Riehle, and A. L. Bernaau, "Dynamic acoutic field activated cell eparation (DAFACS)," Lab Chip, vol., pp. 8-, Feb 7. [7] H. Bruu, "Acoutofluidic 7: The acoutic radiation force on mall particle," Lab Chip, vol., pp. -, Mar.