{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T04:32:48Z","timestamp":1774499568515,"version":"3.50.1"},"reference-count":54,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2016,10,5]],"date-time":"2016-10-05T00:00:00Z","timestamp":1475625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>We present a \ufb01nite-element method modeling of acoustophoretic devices consisting of a single, long, straight, water-\ufb01lled microchannel surrounded by an elastic wall of either borosilicate glass (pyrex) or the elastomer polydimethylsiloxane (PDMS) and placed on top of a piezoelectric transducer that actuates the device by surface acoustic waves (SAW). We compare the resulting acoustic \ufb01elds in these full solid-\ufb02uid models with those obtained in reduced \ufb02uid models comprising of only a water domain with simpli\ufb01ed, approximate boundary conditions representing the surrounding solids. The reduced models are found to only approximate the acoustically hard pyrex systems to a limited degree for large wall thicknesses and but not very well for acoustically soft PDMS systems shorter than the PDMS damping length of 3 mm.<\/jats:p>","DOI":"10.3390\/mi7100182","type":"journal-article","created":{"date-parts":[[2016,10,5]],"date-time":"2016-10-05T10:18:55Z","timestamp":1475662735000},"page":"182","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Modeling of Microdevices for SAW-Based Acoustophoresis \u2014 A Study of Boundary Conditions"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6822-2094","authenticated-orcid":false,"given":"Nils","family":"Skov","sequence":"first","affiliation":[{"name":"Department of Physics, Technical University of Denmark, DTU Physics Building 309, DK-2800 Kongens Lyngby, Denmark"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5827-2939","authenticated-orcid":false,"given":"Henrik","family":"Bruus","sequence":"additional","affiliation":[{"name":"Department of Physics, Technical University of Denmark, DTU Physics Building 309, DK-2800 Kongens Lyngby, Denmark"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5117","DOI":"10.1021\/ac070444e","article-title":"Free flow acoustophoresis: Microfluidic-based mode of particle and cell separation","volume":"79","author":"Petersson","year":"2007","journal-title":"Anal. Chem."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2739","DOI":"10.1039\/c4lc00128a","article-title":"Inertial microfluidic physics","volume":"14","author":"Amini","year":"2014","journal-title":"Lab Chip"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3354","DOI":"10.1039\/b915113c","article-title":"Continuous particle separation in a microfluidic channel via standing surface acoustic waves (SSAW)","volume":"9","author":"Shi","year":"2009","journal-title":"Lab Chip"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1039\/c1lc20042a","article-title":"Three-dimensional continuous particle focusing in a microfluidic channel via standing surface acoustic waves (SSAW)","volume":"11","author":"Shi","year":"2011","journal-title":"Lab Chip"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1039\/C3LC51139A","article-title":"Standing surface acoustic wave (SSAW)-based microfluidic cytometer","volume":"14","author":"Chen","year":"2014","journal-title":"Lab Chip"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2321","DOI":"10.1021\/nn506538f","article-title":"Acoustic purification of extracellular microvesicles","volume":"9","author":"Lee","year":"2015","journal-title":"ACS Nano"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2388","DOI":"10.1039\/C5LC00240K","article-title":"Exosome isolation: A microfluidic road-map","volume":"15","author":"Liga","year":"2015","journal-title":"Lab Chip"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1644","DOI":"10.1039\/b712784g","article-title":"Continuous flow separations in microfluidic devices","volume":"7","author":"Pamme","year":"2007","journal-title":"Lab Chip"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1039\/B512049G","article-title":"Microfluidic diffusive filter for apheresis (leukapheresis)","volume":"6","author":"Sethu","year":"2006","journal-title":"Lab Chip"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1021\/ac061542n","article-title":"Gravity-driven microfluidic particle sorting device with hydrodynamic separation amplification","volume":"79","author":"Huh","year":"2007","journal-title":"Anal. Chem."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1039\/C3AY40971F","article-title":"Simple density-based particle separation in a microfluidic chip","volume":"6","author":"Sugiyama","year":"2014","journal-title":"Anal. Methods"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1039\/C5LC01159K","article-title":"Fundamentals and applications of inertial microfluidics: A review","volume":"16","author":"Zhang","year":"2016","journal-title":"Lab Chip"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"974","DOI":"10.1039\/b604542a","article-title":"Continuous sorting of magnetic cells via on-chip free-flow magnetophoresis","volume":"6","author":"Pamme","year":"2006","journal-title":"Lab Chip"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"905","DOI":"10.3390\/s120100905","article-title":"Sheathless size-based acoustic particle separation","volume":"12","author":"Guldiken","year":"2012","journal-title":"Sensors"},{"key":"ref_15","first-page":"e50524","article-title":"Fabrication, Operation and flow visualization in surface-acoustic-wave-driven acoustic-counterflow microfluidics","volume":"78","author":"Travagliati","year":"2013","journal-title":"J. Vis. Exp."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1522","DOI":"10.1073\/pnas.1524813113","article-title":"Three-dimensional manipulation of single cells using surface acoustic waves","volume":"113","author":"Guo","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3579","DOI":"10.1039\/c1lc90058g","article-title":"Forthcoming lab on a chip tutorial series on acoustofluidics: Acoustofluidics-exploiting ultrasonic standing wave forces and acoustic streaming in microfluidic systems for cell and particle manipulation","volume":"11","author":"Bruus","year":"2011","journal-title":"Lab Chip"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2588","DOI":"10.1039\/C5LC00290G","article-title":"Non-contact acoustic capture of microparticles from small plasma volumes","volume":"15","author":"Evander","year":"2015","journal-title":"Lab Chip"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2018","DOI":"10.1039\/c2lc40201g","article-title":"Acoustofluidics 12: Biocompatibility and cell viability in microfluidic acoustic resonators","volume":"12","author":"Wiklund","year":"2012","journal-title":"Lab Chip"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"8686","DOI":"10.1038\/ncomms9686","article-title":"Two-dimensional single-cell patterning with one cell per well driven by surface acoustic waves","volume":"6","author":"Collins","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"11085","DOI":"10.1038\/ncomms11085","article-title":"Rotational manipulation of single cells and organisms using acoustic waves","volume":"7","author":"Ahmed","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"11556","DOI":"10.1038\/ncomms11556","article-title":"Iso-acoustic focusing of cells for size-insensitive acousto-mechanical phenotyping","volume":"7","author":"Augustsson","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4296","DOI":"10.1039\/c2lc40697g","article-title":"Seed particle enabled acoustic trapping of bacteria and nanoparticles in continuous flow systems","volume":"12","author":"Laurell","year":"2012","journal-title":"Lab Chip"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3830","DOI":"10.1039\/C4LC00577E","article-title":"A thin-reflector microfluidic resonator for continuous-flow concentration of microorganisms: A new approach to water quality analysis using acoustofluidics","volume":"14","author":"Carugo","year":"2014","journal-title":"Lab Chip"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1038\/nmeth.3183","article-title":"Acoustic force spectroscopy","volume":"12","author":"Sitters","year":"2015","journal-title":"Nat. Meth."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"7954","DOI":"10.1021\/ac301723s","article-title":"Microfluidic, label-Free enrichment of prostate cancer cells in blood based on acoustophoresis","volume":"84","author":"Augustsson","year":"2012","journal-title":"Anal. Chem."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4970","DOI":"10.1073\/pnas.1504484112","article-title":"Acoustic separation of circulating tumor cells","volume":"112","author":"Li","year":"2015","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"10560","DOI":"10.1021\/ac502020f","article-title":"Acoustic trapping for bacteria identification in positive blood cultures with MALDI-TOF MS","volume":"86","author":"Nilson","year":"2014","journal-title":"Anal. Chem."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4617","DOI":"10.1039\/c2lc40612h","article-title":"A numerical study of microparticle acoustophoresis driven by acoustic radiation forces and streaming-induced drag forces","volume":"12","author":"Muller","year":"2012","journal-title":"Lab Chip"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1039\/C3LC51109J","article-title":"Impedance matched channel walls in acoustofluidic systems","volume":"14","author":"Leibacher","year":"2014","journal-title":"Lab Chip"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"063018","DOI":"10.1103\/PhysRevE.92.063018","article-title":"Theoretical study of time-dependent, ultrasound-induced acoustic streaming in microchannels","volume":"92","author":"Muller","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/0022-5096(93)90013-6","article-title":"A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials","volume":"41","author":"Arruda","year":"1993","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/j.jcis.2008.12.054","article-title":"Deformation of PDMS membrane and microcantilever by a water droplet: Comparison between Mooney\u2013Rivlin and linear elastic constitutive models","volume":"332","author":"Yu","year":"2009","journal-title":"J. Colloid Interface Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.egypro.2013.07.026","article-title":"Mechanical behavior of polymeric membrane: Comparison between PDMS and PMMA for micro fluidic application","volume":"36","author":"Bourbaba","year":"2013","journal-title":"Energy Procedia"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2701","DOI":"10.1039\/C6LC00390G","article-title":"Computation of the pressure field generated by surface acoustic waves in microchannels","volume":"16","author":"Darinskii","year":"2016","journal-title":"Lab Chip"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2700","DOI":"10.1039\/C5LC00231A","article-title":"Numerical study of acoustophoretic motion of particles in a PDMS microchannel driven by surface acoustic waves","volume":"15","author":"Nama","year":"2015","journal-title":"Lab Chip"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1039\/C5LC00707K","article-title":"Experimental and numerical studies on standing surface acoustic wave microfluidics","volume":"16","author":"Mao","year":"2016","journal-title":"Lab Chip"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1039\/C1LC20770A","article-title":"Acoustofluidics 2: Perturbation theory and ultrasound resonance modes","volume":"12","author":"Bruus","year":"2012","journal-title":"Lab Chip"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/BF00614817","article-title":"Lithium niobate: Summary of physical properties and crystal structure","volume":"37","author":"Weis","year":"1985","journal-title":"Appl. Phys. A"},{"key":"ref_40","unstructured":"Narottam, P., Bansal, N.P., and Bansal, R.H.D. (1986). Handbook of Glass Properties, Elsevier LTD."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"062005","DOI":"10.1063\/1.4922986","article-title":"A numerically efficient damping model for acoustic resonances in microfluidic cavities","volume":"27","author":"Hahn","year":"2015","journal-title":"Phys. Fluids"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.1121\/1.390158","article-title":"Ultrasonic shear wave properties of soft tissues and tissuelike materials","volume":"74","author":"Madsen","year":"1983","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"N475","DOI":"10.1088\/0031-9155\/52\/20\/N02","article-title":"Acoustical properties of selected tissue phantom materials for ultrasound imaging","volume":"52","author":"Zell","year":"2007","journal-title":"Phys. Med. Biol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"043016","DOI":"10.1103\/PhysRevE.90.043016","article-title":"Numerical study of thermoviscous effects in ultrasound-induced acoustic streaming in microchannels","volume":"90","author":"Muller","year":"2014","journal-title":"Phys. Rev. E"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"18675","DOI":"10.1073\/pnas.0807476105","article-title":"Materials and noncoplanar mesh designs for integrated circuits with linear elastic responses to extreme mechanical deformations","volume":"105","author":"Kim","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"065008","DOI":"10.1088\/0960-1317\/18\/6\/065008","article-title":"Mechanical properties of silicones for MEMS","volume":"18","author":"Schneider","year":"2008","journal-title":"J. Micromech. Microeng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"7743","DOI":"10.1021\/la803413x","article-title":"Flexible microfluidic device for mechanical property characterization of soft viscoelastic solids Such as bacterial biofilms","volume":"25","author":"Hohne","year":"2009","journal-title":"Langmuir"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"094102","DOI":"10.1103\/PhysRevB.88.094102","article-title":"Soft silicone rubber in phononic structures: Correct elastic moduli","volume":"88","author":"Still","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"035017","DOI":"10.1088\/0960-1317\/24\/3\/035017","article-title":"Mechanical characterization of bulk Sylgard 184 for microfluidics and microengineering","volume":"24","author":"Johnston","year":"2014","journal-title":"J. Micromech. Microeng."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1109\/JMEMS.2009.2029166","article-title":"Viscoelastic characterization and modeling of polymer transducers for biological applications","volume":"18","author":"Lin","year":"2009","journal-title":"J. Microelectromechan. Syst."},{"key":"ref_51","unstructured":"COMSOL Multiphysics, Version 5.2. Available online: http:\/\/www.comsol.com."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2352","DOI":"10.1137\/060676623","article-title":"Numerical simulation of acoustic streaming on surface acoustic wave-driven biochips","volume":"29","year":"2007","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"023006","DOI":"10.1103\/PhysRevE.88.023006","article-title":"Ultrasound-induced acoustophoretic motion of microparticles in three dimensions","volume":"88","author":"Muller","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"11851","DOI":"10.1038\/srep11851","article-title":"Acoustothermal heating of polydimethylsiloxane microfluidic system","volume":"5","author":"Ha","year":"2015","journal-title":"Sci. Rep."}],"container-title":["Micromachines"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-666X\/7\/10\/182\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:32:27Z","timestamp":1760211147000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-666X\/7\/10\/182"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,5]]},"references-count":54,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2016,10]]}},"alternative-id":["mi7100182"],"URL":"https:\/\/doi.org\/10.3390\/mi7100182","relation":{},"ISSN":["2072-666X"],"issn-type":[{"value":"2072-666X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10,5]]}}}