Sensors & TransducersVolume 3Special IssueDecember 2008www.sensorsportal.comISSN 1726-5479Editor-in-Chief: professor Sergey Y. Yurish, phone: 34 696067716, fax: 34 93 4011989, e-mail: [email protected] Editors: Dr. Elena Gaura and Dr. James P. BruseyEditors for Western EuropeMeijer, Gerard C.M., Delft University of Technology, The NetherlandsFerrari, Vittorio, Universitá di Brescia, ItalyEditor South AmericaCosta-Felix, Rodrigo, Inmetro, BrazilEditor for Eastern EuropeSachenko, Anatoly, Ternopil State Economic University, UkraineEditors for North AmericaDatskos, Panos G., Oak Ridge National Laboratory, USAFabien, J. Josse, Marquette University, USAKatz, Evgeny, Clarkson University, USAEditor for AsiaOhyama, Shinji, Tokyo Institute of Technology, JapanEditorial Advisory BoardAbdul Rahim, Ruzairi, Universiti Teknologi, MalaysiaAhmad, Mohd Noor, Nothern University of Engineering, MalaysiaAnnamalai, Karthigeyan, National Institute of Advanced Industrial Scienceand Technology, JapanArcega, Francisco, University of Zaragoza, SpainArguel, Philippe, CNRS, FranceAhn, Jae-Pyoung, Korea Institute of Science and Technology, KoreaArndt, Michael, Robert Bosch GmbH, GermanyAscoli, Giorgio, George Mason University, USAAtalay, Selcuk, Inonu University, TurkeyAtghiaee, Ahmad, University of Tehran, IranAugutis, Vygantas, Kaunas University of Technology, LithuaniaAvachit, Patil Lalchand, North Maharashtra University, IndiaAyesh, Aladdin, De Montfort University, UKBahreyni, Behraad, University of Manitoba, CanadaBaoxian, Ye, Zhengzhou University, ChinaBarford, Lee, Agilent Laboratories, USABarlingay, Ravindra, RF Arrays Systems, IndiaBasu, Sukumar, Jadavpur University, IndiaBeck, Stephen, University of Sheffield, UKBen Bouzid, Sihem, Institut National de Recherche Scientifique, TunisiaBenachaiba, Chellali, Universitaire de Bechar, AlgeriaBinnie, T. David, Napier University, UKBischoff, Gerlinde, Inst. Analytical Chemistry, GermanyBodas, Dhananjay, IMTEK, GermanyBorges Carval, Nuno, Universidade de Aveiro, PortugalBousbia-Salah, Mounir, University of Annaba, AlgeriaBouvet, Marcel, CNRS – UPMC, FranceBrudzewski, Kazimierz, Warsaw University of Technology, PolandCai, Chenxin, Nanjing Normal University, ChinaCai, Qingyun, Hunan University, ChinaCampanella, Luigi, University La Sapienza, ItalyCarvalho, Vitor, Minho University, PortugalCecelja, Franjo, Brunel University, London, UKCerda Belmonte, Judith, Imperial College London, UKChakrabarty, Chandan Kumar, Universiti Tenaga Nasional, MalaysiaChakravorty, Dipankar, Association for the Cultivation of Science, IndiaChanghai, Ru, Harbin Engineering University, ChinaChaudhari, Gajanan, Shri Shivaji Science College, IndiaChen, Jiming, Zhejiang University, ChinaChen, Rongshun, National Tsing Hua University, TaiwanCheng, Kuo-Sheng, National Cheng Kung University, TaiwanChiriac, Horia, National Institute of Research and Development, RomaniaChowdhuri, Arijit, University of Delhi, IndiaChung, Wen-Yaw, Chung Yuan Christian University, TaiwanCorres, Jesus, Universidad Publica de Navarra, SpainCortes, Camilo A., Universidad Nacional de Colombia, ColombiaCourtois, Christian, Universite de Valenciennes, FranceCusano, Andrea, University of Sannio, ItalyD'Amico, Arnaldo, Università di Tor Vergata, ItalyDe Stefano, Luca, Institute for Microelectronics and Microsystem, ItalyDeshmukh, Kiran, Shri Shivaji Mahavidyalaya, Barshi, IndiaDickert, Franz L., Vienna University, AustriaDieguez, Angel, University of Barcelona, SpainDimitropoulos, Panos, University of Thessaly, GreeceDing Jian, Ning, Jiangsu University, ChinaDjordjevich, Alexandar, City University of Hong Kong, Hong KongKo, Sang Choon, Electronics and Telecommunications Research Institute,Donato, Nicola, University of Messina, ItalyDonato, Patricio, Universidad de Mar del Plata, ArgentinaDong, Feng, Tianjin University, ChinaDrljaca, Predrag, Instersema Sensoric SA, SwitzerlandDubey, Venketesh, Bournemouth University, UKEnderle, Stefan, University of Ulm and KTB Mechatronics GmbH,GermanyErdem, Gursan K. Arzum, Ege University, TurkeyErkmen, Aydan M., Middle East Technical University, TurkeyEstelle, Patrice, Insa Rennes, FranceEstrada, Horacio, University of North Carolina, USAFaiz, Adil, INSA Lyon, FranceFericean, Sorin, Balluff GmbH, GermanyFernandes, Joana M., University of Porto, PortugalFrancioso, Luca, CNR-IMM Institute for Microelectronics andMicrosystems, ItalyFrancis, Laurent, University Catholique de Louvain, BelgiumFu, Weiling, South-Western Hospital, Chongqing, ChinaGaura, Elena, Coventry University, UKGeng, Yanfeng, China University of Petroleum, ChinaGole, James, Georgia Institute of Technology, USAGong, Hao, National University of Singapore, SingaporeGonzalez de la Rosa, Juan Jose, University of Cadiz, SpainGranel, Annette, Goteborg University, SwedenGraff, Mason, The University of Texas at Arlington, USAGuan, Shan, Eastman Kodak, USAGuillet, Bruno, University of Caen, FranceGuo, Zhen, New Jersey Institute of Technology, USAGupta, Narendra Kumar, Napier University, UKHadjiloucas, Sillas, The University of Reading, UKHashsham, Syed, Michigan State University, USAHernandez, Alvaro, University of Alcala, SpainHernandez, Wilmar, Universidad Politecnica de Madrid, SpainHomentcovschi, Dorel, SUNY Binghamton, USAHorstman, Tom, U.S. Automation Group, LLC, USAHsiai, Tzung (John), University of Southern California, USAHuang, Jeng-Sheng, Chung Yuan Christian University, TaiwanHuang, Star, National Tsing Hua University, TaiwanHuang, Wei, PSG Design Center, USAHui, David, University of New Orleans, USAJaffrezic-Renault, Nicole, Ecole Centrale de Lyon, FranceJaime Calvo-Galleg, Jaime, Universidad de Salamanca, SpainJames, Daniel, Griffith University, AustraliaJanting, Jakob, DELTA Danish Electronics, DenmarkJiang, Liudi, University of Southampton, UKJiang, Wei, University of Virginia, USAJiao, Zheng, Shanghai University, ChinaJohn, Joachim, IMEC, BelgiumKalach, Andrew, Voronezh Institute of Ministry of Interior, RussiaKang, Moonho, Sunmoon University, Korea SouthKaniusas, Eugenijus, Vienna University of Technology, AustriaKatake, Anup, Texas A&M University, USAKausel, Wilfried, University of Music, Vienna, AustriaKavasoglu, Nese, Mugla University, TurkeyKe, Cathy, Tyndall National Institute, IrelandKhan, Asif, Aligarh Muslim University, Aligarh, IndiaKim, Min Young, Koh Young Technology, Inc., Korea SouthSandacci, Serghei, Sensor Technology Ltd., UK
Korea SouthKockar, Hakan, Balikesir University, TurkeyKotulska, Malgorzata, Wroclaw University of Technology, PolandKratz, Henrik, Uppsala University, SwedenKumar, Arun, University of South Florida, USAKumar, Subodh, National Physical Laboratory, IndiaKung, Chih-Hsien, Chang-Jung Christian University, TaiwanLacnjevac, Caslav, University of Belgrade, SerbiaLay-Ekuakille, Aime, University of Lecce, ItalyLee, Jang Myung, Pusan National University, Korea SouthLee, Jun Su, Amkor Technology, Inc. South KoreaLei, Hua, National Starch and Chemical Company, USALi, Genxi, Nanjing University, ChinaLi, Hui, Shanghai Jiaotong University, ChinaLi, Xian-Fang, Central South University, ChinaLiang, Yuanchang, University of Washington, USALiawruangrath, Saisunee, Chiang Mai University, ThailandLiew, Kim Meow, City University of Hong Kong, Hong KongLin, Hermann, National Kaohsiung University, TaiwanLin, Paul, Cleveland State University, USALinderholm, Pontus, EPFL - Microsystems Laboratory, SwitzerlandLiu, Aihua, University of Oklahoma, USALiu Changgeng, Louisiana State University, USALiu, Cheng-Hsien, National Tsing Hua University, TaiwanLiu, Songqin, Southeast University, ChinaLodeiro, Carlos, Universidade NOVA de Lisboa, PortugalLorenzo, Maria Encarnacio, Universidad Autonoma de Madrid, SpainLukaszewicz, Jerzy Pawel, Nicholas Copernicus University, PolandMa, Zhanfang, Northeast Normal University, ChinaMajstorovic, Vidosav, University of Belgrade, SerbiaMarquez, Alfredo, Centro de Investigacion en Materiales Avanzados,MexicoMatay, Ladislav, Slovak Academy of Sciences, SlovakiaMathur, Prafull, National Physical Laboratory, IndiaMaurya, D.K., Institute of Materials Research and Engineering, SingaporeMekid, Samir, University of Manchester, UKMelnyk, Ivan, Photon Control Inc., CanadaMendes, Paulo, University of Minho, PortugalMennell, Julie, Northumbria University, UKMi, Bin, Boston Scientific Corporation, USAMinas, Graca, University of Minho, PortugalMoghavvemi, Mahmoud, University of Malaya, MalaysiaMohammadi, Mohammad-Reza, University of Cambridge, UKMolina Flores, Esteban, Benemérita Universidad Autónoma de Puebla,MexicoMoradi, Majid, University of Kerman, IranMorello, Rosario, DIMET, University "Mediterranea" of Reggio Calabria,ItalyMounir, Ben Ali, University of Sousse, TunisiaMukhopadhyay, Subhas, Massey University, New ZealandNeelamegam, Periasamy, Sastra Deemed University, IndiaNeshkova, Milka, Bulgarian Academy of Sciences, BulgariaOberhammer, Joachim, Royal Institute of Technology, SwedenOuld Lahoucin, University of Guelma, AlgeriaPamidighanta, Sayanu, Bharat Electronics Limited (BEL), IndiaPan, Jisheng, Institute of Materials Research & Engineering, SingaporePark, Joon-Shik, Korea Electronics Technology Institute, Korea SouthPenza, Michele, ENEA C.R., ItalyPereira, Jose Miguel, Instituto Politecnico de Setebal, PortugalPetsev, Dimiter, University of New Mexico, USAPogacnik, Lea, University of Ljubljana, SloveniaPost, Michael, National Research Council, CanadaPrance, Robert, University of Sussex, UKPrasad, Ambika, Gulbarga University, IndiaPrateepasen, Asa, Kingmoungut's University of Technology, ThailandPullini, Daniele, Centro Ricerche FIAT, ItalyPumera, Martin, National Institute for Materials Science, JapanRadhakrishnan, S. National Chemical Laboratory, Pune, IndiaRajanna, K., Indian Institute of Science, IndiaRamadan, Qasem, Institute of Microelectronics, SingaporeRao, Basuthkar, Tata Inst. of Fundamental Research, IndiaRaoof, Kosai, Joseph Fourier University of Grenoble, FranceReig, Candid, University of Valencia, SpainRestivo, Maria Teresa, University of Porto, PortugalRobert, Michel, University Henri Poincare, FranceRezazadeh, Ghader, Urmia University, IranRoyo, Santiago, Universitat Politecnica de Catalunya, SpainRodriguez, Angel, Universidad Politecnica de Cataluna, SpainRothberg, Steve, Loughborough University, UKSadana, Ajit, University of Mississippi, USASadeghian Marnani, Hamed, TU Delft, The NetherlandsSapozhnikova, Ksenia, D.I.Mendeleyev Institute for Metrology, RussiaSaxena, Vibha, Bhbha Atomic Research Centre, Mumbai, IndiaSchneider, John K., Ultra-Scan Corporation, USASeif, Selemani, Alabama A & M University, USASeifter, Achim, Los Alamos National Laboratory, USASengupta, Deepak, Advance Bio-Photonics, IndiaShankar, B. Baliga, General Monitors Transnational, USAShearwood, Christopher, Nanyang Technological University, SingaporeShin, Kyuho, Samsung Advanced Institute of Technology, KoreaShmaliy, Yuriy, Kharkiv National University of Radio Electronics,UkraineSilva Girao, Pedro, Technical University of Lisbon, PortugalSingh, V. R., National Physical Laboratory, IndiaSlomovitz, Daniel, UTE, UruguaySmith, Martin, Open University, UKSoleymanpour, Ahmad, Damghan Basic Science University, IranSomani, Prakash R., Centre for Materials for Electronics Technol., IndiaSrinivas, Talabattula, Indian Institute of Science, Bangalore, IndiaSrivastava, Arvind K., Northwestern University, USAStefan-van Staden, Raluca-Ioana, University of Pretoria, South AfricaSumriddetchka, Sarun, National Electronics and Computer TechnologyCenter, ThailandSun, Chengliang, Polytechnic University, Hong-KongSun, Dongming, Jilin University, ChinaSun, Junhua, Beijing University of Aeronautics and Astronautics, ChinaSun, Zhiqiang, Central South University, ChinaSuri, C. Raman, Institute of Microbial Technology, IndiaSysoev, Victor, Saratov State Technical University, RussiaSzewczyk, Roman, Industrial Research Institute for Automation andMeasurement, PolandTan, Ooi Kiang, Nanyang Technological University, Singapore,Tang, Dianping, Southwest University, ChinaTang, Jaw-Luen, National Chung Cheng University, TaiwanTeker, Kasif, Frostburg State University, USAThumbavanam Pad, Kartik, Carnegie Mellon University, USATian, Gui Yun, University of Newcastle, UKTsiantos, Vassilios, Technological Educational Institute of Kaval, GreeceTsigara, Anna, National Hellenic Research Foundation, GreeceTwomey, Karen, University College Cork, IrelandValente, Antonio, University, Vila Real, - U.T.A.D., PortugalVaseashta, Ashok, Marshall University, USAVazques, Carmen, Carlos III University in Madrid, SpainVieira, Manuela, Instituto Superior de Engenharia de Lisboa, PortugalVigna, Benedetto, STMicroelectronics, ItalyVrba, Radimir, Brno University of Technology, Czech RepublicWandelt, Barbara, Technical University of Lodz, PolandWang, Jiangping, Xi'an Shiyou University, ChinaWang, Kedong, Beihang University, ChinaWang, Liang, Advanced Micro Devices, USAWang, Mi, University of Leeds, UKWang, Shinn-Fwu, Ching Yun University, TaiwanWang, Wei-Chih, University of Washington, USAWang, Wensheng, University of Pennsylvania, USAWatson, Steven, Center for NanoSpace Technologies Inc., USAWeiping, Yan, Dalian University of Technology, ChinaWells, Stephen, Southern Company Services, USAWolkenberg, Andrzej, Institute of Electron Technology, PolandWoods, R. Clive, Louisiana State University, USAWu, DerHo, National Pingtung University of Science and Technology,TaiwanWu, Zhaoyang, Hunan University, ChinaXiu Tao, Ge, Chuzhou University, ChinaXu, Lisheng, The Chinese University of Hong Kong, Hong KongXu, Tao, University of California, Irvine, USAYang, Dongfang, National Research Council, CanadaYang, Wuqiang, The University of Manchester, UKYmeti, Aurel, University of Twente, NetherlandYong Zhao, Northeastern University, ChinaYu, Haihu, Wuhan University of Technology, ChinaYuan, Yong, Massey University, New ZealandYufera Garcia, Alberto, Seville University, SpainZagnoni, Michele, University of Southampton, UKZeni, Luigi, Second University of Naples, ItalyZhong, Haoxiang, Henan Normal University, ChinaZhang, Minglong, Shanghai University, ChinaZhang, Qintao, University of California at Berkeley, USAZhang, Weiping, Shanghai Jiao Tong University, ChinaZhang, Wenming, Shanghai Jiao Tong University, ChinaZhou, Zhi-Gang, Tsinghua University, ChinaZorzano, Luis, Universidad de La Rioja, SpainZourob, Mohammed, University of Cambridge, UKSensors & Transducers Journal (ISSN 1726-5479) is a peer review international journal published monthly online by International Frequency Sensor Association (IFSA).Available in electronic and CD-ROM. Copyright 2007 by International Frequency Sensor Association. All rights reserved.
Sensors & Transducers JournalContentsVolume 3Special IssueDecember 2008www.sensorsportal.comISSN 1726-5479Research ArticlesForewordElena Gaura and James Brusey .1Novel Synchronous Linear and Rotatory Micro Motors Based on Polymer Magnets withOrganic and Inorganic Insulation LayersAndreas Waldschik, Marco Feldmann and Stephanus Büttgenbach .3Adaptive Subband Filtering Method for MEMS Accelerometer Noise ReductionPiotr Pietrzak, Barosz Pekoslawski, Maciej Makowski, Andrzej Napieralski .14Fluido-Dynamic and Electromagnetic Characterization of 3D Carbon Dielectrophoresis withFinite Element AnalysisRodrigo Martinez-Duarte, Salvatore Cito, Esther Collado-Arredondo, Sergio O. Martinez andMarc J. Madou .25Membranous Bypass Valves for Discrete Drop Mixing and Routing in MicrochannelsMinsoung Rhee and Mark A. Burns .37Ultrasound-driven Viscous Streaming, Modelled via Momentum InjectionJames Packer, Daniel Attinger and Yiannis Ventikos .47Multi-Functional Sensor System for Heart Rate, Body Position and Movement IntensityAnalysisMichael Mao, Bozena Kaminska, Yindar Chuo .59NIR FRET Fluorophores for Use as an Implantable Glucose BiosensorMajed Dweik and Sheila A. Grant.71Electrostatic Voltage Sensors Based on Micro Machined Rotational Actuators: Modelingand DesignJan Dittmer, Rolf Judaschke and Stephanus Büttgenbach.80Optimization of Phage-Based Magnetoelastic Biosensor PerformanceS. Huang, S.-Q. Li, H. Yang, M. Johnson, J. Wan, I. Chen, V. A. Petrenko, J. M. Barbaree, andB. A. Chin.87Contribution of NIEL for Gain Degradation (β) in Si8 Ion Irradiated Silicon Power TransistorC. M. Dinesh, Ramani, M. C. Radhakrishna, S. A. Khan, D. Kanjilal.97Authors are encouraged to submit article in MS Word (doc) and Acrobat (pdf) formats by e-mail: [email protected] visit journal’s webpage with preparation instructions: .htmInternational Frequency Sensor Association (IFSA).
Sensors & Transducers Journal, Vol. 3, Special Issue, December 2008, pp. 47-58Sensors & TransducersISSN 1726-5479 2008 by IFSAhttp://www.sensorsportal.comUltrasound-driven Viscous Streaming, Modelledvia Momentum Injection1James PACKER, 2 Daniel ATTINGER and 1Yiannis VENTIKOS1Fluidics and Biocomplexity Group, Department for Engineering Science,University of Oxford, Oxford, OX1 3PJ, UKTel.: 44(0)1865-2834522Laboratory for Microscale Transport Phenomena,Department of Mechanical Engineering, Columbia University, tel.: 1 212 854 28 41E-mail: [email protected], [email protected]: 31 October 2008 /Accepted: 7 November 2008 /Published: 8 December 2008Abstract: Microfluidic devices can use steady streaming caused by the ultrasonic oscillation of one ormany gas bubbles in a liquid to drive small scale flow. Such streaming flows are difficult to evaluate,as analytic solutions are not available for any but the simplest cases, and direct computational fluiddynamics models are unsatisfactory due to the large difference in flow velocity between the steadystreaming and the leading order oscillatory motion. We develop a numerical technique which uses atwo-stage multiscale computational fluid dynamics approach to find the streaming flow as a steadyproblem, and validate this model against experimental results. Copyright 2008 IFSA.Keywords: Acoustic streaming, CFD, Lab-on-a-chip, Microfluidic devices, Multiscale1. IntroductionIn addition to the first order oscillating flow generated by a gas bubble in a fluid excited by ultrasoundpressure waves, a steady second order flow is generated, , . This is difficult to model withstandard computational fluid dynamics (CFD) techniques, due to the difference in time scalesexhibited by the first order oscillating flow (O(kHz) or higher) and the steady second order flow(O(10Hz)) in the configurations considered. Were the second order flow to be determined by standardtransient CFD modelling, many thousands of cycles would need to be calculated to determine thenature of the steady flow with reasonable accuracy, as the magnitude of the steady flow is many orderslower than that of the first order oscillating flow.47
Sensors & Transducers Journal, Vol. 3, Special Issue, December 2008, pp. 47-58In this paper, a novel technique for modelling this steady flow is proposed, where the flow isconsidered to have two parts, the steady second order flow and the time-varying first order flow. Inthis technique the first order flow is found directly with a CFD modelling technique, and the flowproperties are used to calculate the forcing which drives the second order flow. This second order flowis then modelled as a steady state CFD problem, using the calculated forcing to drive the model.2. Computational Fluid Dynamics Modelling2.1. First OrderThe first order model involves a standard CFD approach, where the flow is excited by a movingboundary. In this paper the case of a hemispherical bubble in water is considered, where the bubblewall is displaced sinusoidally, modelling periodic volumetric oscillation. The first order simulation istransient, with three full periods of oscillation modelled. This allows post-transient conditions to bereached, confirmed by comparing the results of the second and third period.2.2. Second OrderThe second order CFD model predicts the steady streaming expected for the configuration chosen. Thegeometric model used is the same as that for the first order, but is established within a steady flowmodel: The moving bubble wall is not modelled, and replaced in the simulation with a static boundaryat the mean position. To excite the steady streaming flow, forcing terms are calculated from the firstorder flow, and added to the fluid volume, as momentum sources, in the region where a viscous sublayer would exist. The method of calculation of the forcing and the layer thickness is outlined below.3. Calculation of Forcing3.1. TheoryThe momentum injection is calculated following the analysis of Lighthill, , finding the forcing fromthe gradients of the Reynolds stresses. The techniques used have been developed to describe turbulentflow, but are equally applicable to the flow considered, as both flow types have constant and timevarying flow components interacting. The Reynolds decomposition allows the constant and timevarying flow parts to be considered separately, with the time varying first order flow driven by theoscillating boundary conditions, and the steady second order flow driven by the Reynolds stresses,which are calculated using the first order flow velocities. If u, v and w are the first order flow velocitiesin the three Cartesian directions, ρ the fluid density, Fu,v,w is the force per unit volume caused by theReynolds stresses and driving the steady second order flow in the three Cartesian directions, and isgiven by:(1)(2)(3)48
Sensors & Transducers Journal, Vol. 3, Special Issue, December 2008, pp. 47-58Therefore, the mean values over one complete cycle of u.u, u.v, u.w, v.v, v.w and w.w are found foreach cell. The differentials of these mean values must then be found in order to find the forcing. Oncethe differentials are known, as covered in section 3.2.2, the forcing can be calculated for each cell byadding the three appropriate partial differentials.This forcing only affects the viscous sub-layer adjacent to the boundary , , as outside this layerthe forcing is absorbed into a hydrostatic pressure field . Different authors give slightly differentapproximations to the thickness of this viscous layer, with Marmottant et. al.  giving the thicknessas:(4)and Lee & Wang  as:(5)Here δ is the thickness, µ the absolute viscosity, ω the excitation frequency and ρ the fluid density.Recalling that both expressions are approximations, the difference is not considered significant. In thispaper, Marmottant et. al.'s  approximation is used. In section 4.3 of this publication, the accuracy ofthis approximation is analyzed further.3.2. Numerical Techniques3.2.1. Mean ValuesFrom the first order model, the flow velocities u, v and w of each cell in the volume around the bubblewall are found at each time-step for one complete period of oscillation, once post-transient conditionshave been reached. For each cell, the values of u.u, u.v, u.w, v.v, v.w and w.w are computed and theirmean value is estimated for the complete period., are known at the centre of each cell. TheseTherefore values of each mean multiplecan be treated as scattered data points, for which the differentials in the x, y and z directions areneeded.3.2.2. Numerical DifferentiationIn order to find the differentials of the mean values at each location, the approach taken is to find thedifference in value and difference in position for three surrounding points, and to find the Cartesianpartial derivatives from this by solving the set of three equations of the form:,where V is the relevant value to be differentiated(6). As we know three sets of49
Sensors & Transducers Journal, Vol. 3, Special Issue, December 2008, pp. 47-58we can solve at each point for.We achieve this by solving the equation:(7),where the subscripts 1,2 and 3 refer to the values for the three surrounding points chosen. If the threepoints chosen are nearly collinear or coplanar, this will lead to an ill-conditioned solution.Consequently the solution is found by selecting the three points in close proximity which give a wellconditioned behaviour. The closest 15 points are found and the best combination of three selected.This is found by considering all possible combinations, and finding a parameter which describes thequality of the solution. First the condition number of the matrix(8),is found for all possible combinations of three of the close points, here referred to by the subscripts 1,2, 3. The higher this condition number, the more poorly conditioned the set of equations is. This is thenmultiplied by the product of the distances to the three points under consideration. The combinationwith the lowest value of this parameter is chosen, as it is the best-conditioned set of points closest tothe point at which the differential is required. This technique is an approximate method ofdifferentiation, which can be applied to any arbitrary three dimensional data set.The differentiation method is essentially a forwards difference method, extended to three dimensionsand applied to a scattered data field.3.2.3. Forcingare known for each cell in the viscous subOnce the differentials of the mean valueslayer region, the forcing can be found from equations 1, 2 and 3. The forcing is then used in the secondorder steady-state CDF model as a momentum injection to force the steady streaming. The forcing foreach cell is used within the CFD-ACE2007 solver (ESI Group, Paris, France) package, in which theforcing per unit volume for each forced cell is multiplied by the cell volume to find the absolute force,and this force used in the equilibrium equations used by the solver, allowing the streaming flow to becomputed.4. ValidationThe numerical modelling technique proposed is tested against the experimental results of Tho et. al., as their results give both the streaming generated and the bubble motion for different modes of50
Sensors & Transducers Journal, Vol. 3, Special Issue, December 2008, pp. 47-58bubble oscillation. Tho et. al.'s experimental conditions correspond to a bubble of mean radius varyingbetween 202 and 274 µm. Several modes of bubble vibration are examined, with case 4 being purevolume oscillation of the bubble. This is the case we chose to present in this paper.4.1. Tho et. al.'s Case4.1.1. GridTho et. al.'s experimental volume is a thin chamber, of height 0.66 mm, as described in Fig. 1, Tho et.al., . The hemispherical bubble is on the top wall. Only the region near the bubble is used for ourCFD modelling to make the problem more tractable. The grid used is shown in Fig. 1. The grid isdivided into different volumes so that the required velocities can be output from the first order model,and the forcing applied only to the viscous sub-layer adjacent to the bubble wall in the second ordermodel. These zones are shown in Fig. 2.Fig. 1. CFD grid.Fig. 2. Grid detail.51
Sensors & Transducers Journal, Vol. 3, Special Issue, December 2008, pp. 47-584.1.2. Boundary ConditionsIn the first order model, the hemispherical bubble is of radius 270 µm, and the bubble wall is oscillatedat 8.658 kHz, with a magnitude of 1.41% of the bubble radius, corresponding to case 4 in Tho et. al.'sexperiments . The boundary condition at the bubble wall is taken as zero slip, since the particlesused in the flow visualization congregate at the interface and allow little slip flow . For comparisona model is also computed for zero shear at the bubble wall, which would be expected for perfectly purefluid, neglecting the viscosity of the bubble gas. The other boundary conditions are the same for thetwo cases. If the bubble is on the top surface, the top and bottom surfaces have wall boundaryconditions (zero tangential and normal flow velocity) and the four edges have fixed pressure boundaryconditions, allowing flow between the volume modelled and the large microchamber usedexperimentally.4.1.3. Convergence to Post-transient ConditionsFor the first order model, 90 time steps are used per period, and three complete periods modelled. Toensure that the model has reached post-transient conditions, the results of period 2 and 3 are comparedand found to be essentially similar, with an average difference of 0.11 % between velocities atequivalent time steps within the period.4.1.4. Data ProcessingThe flow velocities u, v, w are found for the volume adjacent to the bubble (the viscous sub-layervolume) and the cells immediately adjacent to this. From the velocity values for the final period(timesteps 181-270), the forcing in the viscous sub-layer is calculated numerically, following theanalysis described above. All calculations were undertaken with Octave 2.9 & 3.0 (The GNU Project,Boston, USA). Due to the grid deformation in the first order model, the position of the cell centres inthe layer vary through the period, so their mean positions are used.4.1.5. Second Order ModelThe same grid and boundary conditions are used for the second order simulation as for the firs
Sensors & Transducers Volume 3 Special Issue December 2008 www.sensorsportal.com ISSN 1726-5479 Editor-in-Chief: professor Sergey Y. Yurish, phone: 34 696067716, fax: 34 93 4011989, e-mail: [email protected] Guest Editors: Dr. Elena Gaura and Dr. James P. Brusey Editors for Western Europe