شبیه‌سازی عددی جداسازی ذرات در جریان سیال در میکروکانال مرکب متشکل از ناحیه مارپیچ و آکوستیکی
نویسندگان
دانشکده مهندسی مکانیک، دانشگاه صنعتی اصفهان، اصفهان
چکیده
جداسازی ذرات، کاربردهای زیادی هم در پزشکی و بیولوژی و هم در صنعت دارد. در این پژوهش جداسازی ذرات پلی‌استایرن با قطر 10، 20 و 30 میکرومتر در جریان سیال در یک میکروکانال بررسی می‌شود. میکروکانال از یک ناحیه مارپیچ و یک ناحیه مستقیم ولی تحت اثر امواج آکوستیکی یا صوتی تشکیل شده است. در ناحیه مارپیچ، ذرات تحت اثرات هیدرودینامیکی جداسازی اولیه می‌شوند؛ سپس ذرات وارد ناحیه مستقیم میکروکانال می‌شوند و جداسازی نهایی ذرات تحت تأثیر نیروی ناشی از امواج صوتی صورت می‌گیرد. اثر فرکانس امواج صوتی و تعداد حلقه‌های ناحیه مارپیچ بر جداسازی بررسی می‌شود. نتایج نشان می‌دهد که برای ابعاد و پارامترهای جریان تعیین شده، در فرکانس 1 مگاهرتز موج صوتی و تعداد حلقه‌های 2 برای ناحیه مارپیچ میکروکانال، ذرات در انتهای مسیر، در موقعیت مناسبی برای جداسازی نسبت به یکدیگر قرار دارند. علاوه بر آن، نتایج به‌دست آمده نشان می‌دهد که جداسازی ذرات با این سیستم ترکیبی نسبت به روش‌های ساده عملکرد بهتری دارد و نرخ جداسازی می‌تواند 100 درصد نیز باشد.
کلیدواژه‌ها
عنوان مقاله [English]
Numerical Simulation of Particle Separation in the Fluid Flow in a Microchannel Including Spiral and Acoustic Regions
نویسندگان [English]
- F. Shabani
- M. Saghafian
- D. Saeidi
- F. F. Momennasab
Particulate separation has many applications in medicine, biology and industry. In this research, the separation of polystyrene particles with a diameter of 10, 20 and 30 μm in the fluid flow of a microchannel is investigated. The microchannel consists of a spiral region and a straight region under the influence of acoustic waves. In the spiral region, the particles under hydrodynamic effects undergo the initial separation; then the particles enter the straight region of the microchannel, and the final separation of the particles is done by the force generated and exerted through the acoustic waves. The effects of acoustic frequency and the number of spiral region loops on separation are investigated. The results show that for measured dimensions and parameters, at 1 MHz acoustic wave, when the number of loops is 2 for the spiral region, the particles at the end of the path are in a suitable position for separation. In addition, the results show that the separation of particles with this hybrid system is better than that done by the simple methods, and the separation rate can be as high as 100%
کلیدواژه‌ها [English]
- Acoustic wave
- Spiral microchannel
- Particle separation
- microfluidics
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2. Sajeesh, P., and Sen, A. K., “Particle Separation and Sorting in Microfluidic Devices: A Review”, Microfluidics and Nanofluidics, Vol. 17, No. 1, pp. 1-52, 2014.
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4. Jimenez, M., Miller, B., and Bridle, H. L., “Efficient Separation of Small Microparticles at High Flowrates Using Spiral Channels: Application to Waterborne Pathogens”, Chemical Engineering Science, Vol. 157, pp. 247-254, 2017.
5. Johansson, L., Singh, T., Leong, T., Mawson, R., McArthur, S., Manasseh, R., and Juliano, P., “Cavitation and Non-Cavitation Regime for Large-Scale Ultrasonic Standing Wave Particle Separation Systems–In Situ Gentle Cavitation Threshold Determination and Free Radical Related Oxidation”, Ultrasonics Sonochemistry, Vol. 28, pp. 346-356, 2016.
6. Yang, R.-J., Hou, H.-H., Wang, Y.-N., and Fu, L.-M., “Micro-Magnetofluidics in Microfluidic Systems: A Review”, Sensors and Actuators B: Chemical, Vol. 224, pp. 1-15, 2016.
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8. Evander, M. and Nilsson, J., “Acoustofluidics 20: Applications in Acoustic Trapping”, Lab on a Chip, Vol. 12, No. 22, pp. 4667-4676, 2012.
9. Ebrahimi Warkiani, M., Guan, G., Luan, K., Lee, W., Bhagat, A., Chaudhuri, P., Tan, D., Lim, W., Lee, S., Chen, P., Lim, C. and Han, J., “Slanted Spiral Microfluidics for the Ultra-Fast, Label-Free Isolation of Circulating Tumor Cells”, Lab on a Chip, Vol. 14, No. 1, pp. 128-137, 2014.
10. Manneberg, O., Svennebring, J., Hertz, H. M., and Wiklund, M., “Wedge Transducer Design for Two-Dimensional Ultrasonic Manipulation in a Microfluidic Chip”, Journal of Micromechanics and Microengineering, Vol. 18, No. 9, p. 095025, 2008.
11. Antfolk, M., Muller, P. B., Augustsson, P., Bruus, H., and Laurell, T., “Focusing of Sub-Micrometer Particles and Bacteria Enabled by Two-Dimensional Acoustophoresis”, Lab on a Chip, Vol. 14, No. 15, pp. 2791-2799, 2014.
12. Siddique, A. H., Cho, S. H., Ahn, B., and Kim, C., “Ultrasonic Manipulation of Magnetic Particles in a Microfluidic Channel”, International Journal of Precision Engineering and Manufacturing, Vol. 15, No. 7, pp. 1411-1416, 2014.
13. Taha, T. E.-S., El-Dosoky, M. A., and El-Sayed, A. M., “On the Analysis of the Interaction Between Surface Acoustic Wave (SAW) and Adjacent Media”, Radio Science Conference, 2007. NRSC 2007. National, 2007, pp. 1-8: IEEE.
14. Yoon, Y., Kim, S., Lee, J., Choi, J., Kim, R., Lee, S., Sul, O. and Lee, S., “Clogging-Free Microfluidics for Continuous Size-Based Separation of Microparticles”, Scientific Reports, Vol. 6, p. 26531, 2016.
15. Lenshof, A., Evander, M., Laurell, T., and Nilsson, J., “Acoustofluidics 5: Building Microfluidic Acoustic Resonators”, Lab on a Chip, Vol. 12, No. 4, pp. 684-695, 2012.
16. Esmaeilsabzali, H., Beischlag. T. V., Cox, M. E., Parameswaran, A. M., and Park, E. J., “Detection and Isolation of Circulating Tumor Cells: Principles and Methods”, Biotechnology Advances, Vol. 31, No. 7, pp. 1063-1084, 2013.
17. Lin, Z., Chiang, N., Chai, N., Seshasayee, D., Lee, W., Balazs, M., Nakamura, G. and Swem, L., “In Vivo Antigen-Driven Plasmablast Enrichment in Combination with Antigen-Specific Cell Sorting to Facilitate the Isolation of Rare Monoclonal Antibodies from Human B Cells”, Nature Protocols, Vol. 9, No. 7, p. 1563, 2014.
18. Amini, H., Lee, W. and Di Carlo, D., “Inertial Microfluidic Physics”, Lab on a Chip, Vol. 14, No. 15, pp. 2739-2761, 2014.
19. Bhagat, A. A. S., Bow, H., Hou, H. W., Tan, S. J., Han, J., and Lim, C. T., “Microfluidics for Cell Separation”, Medical and Biological Engineering and Computing, Vol. 48, No. 10, pp. 999-1014, 2010.
20. Beebe, D. J., Mensing, G. A., and Walker, G. M., “Physics and Applications of Microfluidics in Biology”, Annual Review of Biomedical Engineering, Vol. 4, No. 1, pp. 261-286, 2002.
21. Zhang, J., Yan, S., Yuan, D., Alici, G., Nguyen, N., Ebrahimi Warkiani, M. and Li, W., “Fundamentals and Applications of Inertial Microfluidics: A Review”, Lab on a Chip, Vol. 16, No. 1, pp. 10-34, 2016.
22. Asmolov, E. S., “The Inertial Lift on a Spherical Particle in a Plane Poiseuille Flow at Large Channel Reynolds Number”, Journal of Fluid Mechanics, Vol. 381, pp. 63-87, 1999.
23. Di Carlo, D., “Inertial Microfluidics”, Lab on a Chip, Vol. 9, No. 21, pp. 3038-3046, 2009.
24. Gossett, D. R., and Carlo, D. D., “Particle Focusing Mechanisms in Curving Confined Flows”, Analytical Chemistry, Vol. 81, No. 20, pp. 8459-8465, 2009.
25. Guan, G., Wu, L., Bhagat, A., Li, Z., Chen, P., Chao, S., Ong, C. and Han, J., “Spiral Microchannel with Rectangular and Trapezoidal Cross-Sections for Size Based Particle Separation”, Scientific Reports, Vol. 3, p. 1475, 2013.
26. Kuntaegowdanahalli, S. S., Bhagat, A. A. S., Kumar, G., and Papautsky, I., “Inertial Microfluidics for Continuous Particle Separation in Spiral Microchannels”, Lab on a Chip, Vol. 9, No. 20, pp. 2973-2980, 2009.
27. Nivedita, N., Giridhar, P., Kasper, S., and Papautsky, I., “Sorting Human Prostate Epithelial (HPET) Cells in an Inertial Microfluidic Device”, in Proceedings of MicroTAS, pp. 1230-1232, 2011.
28. Nivedita, N., and Papautsky, I., “Continuous Separation of Blood Cells in Spiral Microfluidic Devices”, Biomicrofluidics, Vol. 7, No. 5, p. 054101, 2013.
29. Bhagat, A. A. S., Kuntaegowdanahalli, S. S., and Papautsky, I., “Continuous Particle Separation in Spiral Microchannels Using Dean Flows and Differential Migration”, Lab on a Chip, Vol. 8, No. 11, pp. 1906-1914, 2008.
30. Nivedita, N., Ligrani, P., and Papautsky, I., “Dean Flow Dynamics in Low-Aspect Ratio Spiral Microchannels”, Scientific Reports, Vol. 7, 2017.
31. Skotis, G., Cumming, D., Roberts, J., Riehle, M., and Bernassau, A., “Dynamic Acoustic Field Activated Cell Separation (DAFACS)”, Lab on a Chip, Vol. 15, No. 3, pp. 802-810, 2015.
32. Kim, T. H., Yoon, H. J., Stella, P., and Nagrath, S., “Cascaded Spiral Microfluidic Device for Deterministic and High Purity Continuous Separation of Circulating Tumor Cells”, Biomicrofluidics, Vol. 8, No. 6, p. 064117, 2014.
33. Karniadakis, G., Beskok, A. and Aluru, N., “Microflows and Nanoflows: Fundamentals and Simulation”, Springer Science & Business Media, 2006.
34. Cherukat, P., and Mclaughlin, J. B., “The Inertial Lift on a Rigid Sphere in a Linear Shear Flow Field Near a Flat Wall”, Journal of Fluid Mechanics, Vol. 263, pp. 1-18, 1994.
35. Saffman, P., “The Lift on a Small Sphere in a Slow Shear Flow”, Journal of Fluid Mechanics, Vol. 22, No. 2, pp. 385-400, 1965.
36. Rubinow, S., and Keller, J. B., “The Transverse Force on a Spinning Sphere Moving in a Viscous Fluid”, Journal of Fluid Mechanics, Vol. 11, No. 3, pp. 447-459, 1961.
37. Soliman, A. M., Eldosoky, M. A., and Taha, T. E., “Modelling and Simulation of Microparticles Separation Using Standing Surface Acoustic Waves (SSAWs) Microfluidic Devices for Biomedical Applications”, International Journal of Computer Applications, Vol. 129, pp. 30-38, 2015.
38. Dean, W., “LXXII. The Stream-Line Motion of Fluid in a Curved Pipe (Second paper)”, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 5, No. 30, pp. 673-695, 1928.
39. Mishra, P., Hill, M., and Glynne-Jones, P., “Deformation of Red Blood Cells Using Acoustic Radiation Forces”, Biomicrofluidics, Vol. 8, No. 3, p. 034109, 2014.
40. Gor'Kov, L., “On the Forces Acting on a Small Particle in an Acoustical Field in an Ideal Fluid”, in Soviet Physics, Doklady, 1962, Vol. 6, pp. 773-775.
41. Momennnasab, F., “2D simulation of isolation of circulating tumor cells by acoustic waves”, MSc thesis, Department of Mechanical Engineering, Isfahan University of Technology, 2017 (In Persian).
42. Maxey, M. R., and Riley, J. J., “Equation of Motion for a Small Rigid Sphere in a Nonuniform Flow”, The Physics of Fluids, Vol. 26, No. 4, pp. 883-889, 1983.
43. Soliman, A. M., Eldosoky, M. A. and Taha, T. E., “Analysis Improvement of Standing Surface Acoustic Wave Microfluidic Devices for Bio-Particles Separation”, International Journal of Computer Applications in Technology, Vol. 55, No. 3, pp. 244-256, 2017.
44. Nivedita, N., Ligrani, P. and Papautsky, I., “Spiral Inertial Microfluidic Devices for Continuous Blood Cell Separation”, Microfluidics, BioMEMS, and Medical Microsystems X, 2012, Vol. 8251, p. 82510R: International Society for Optics and Photonics.
45. Bruus, H., “Acoustofluidics 2: Perturbation Theory and Ultrasound Resonance Modes”, Lab on a Chip, Vol. 12, No. 1, pp. 20-28, 2012.
2. Sajeesh, P., and Sen, A. K., “Particle Separation and Sorting in Microfluidic Devices: A Review”, Microfluidics and Nanofluidics, Vol. 17, No. 1, pp. 1-52, 2014.
3. Petersson, F., Nilsson, A., Holm, C., Jönsson, H., and Laurell, T., “Continuous Separation of Lipid Particles from Erythrocytes by Means of Laminar Flow and Acoustic Standing Wave Forces”, Lab on a Chip, Vol. 5, No. 1, pp. 20-22, 2005.
4. Jimenez, M., Miller, B., and Bridle, H. L., “Efficient Separation of Small Microparticles at High Flowrates Using Spiral Channels: Application to Waterborne Pathogens”, Chemical Engineering Science, Vol. 157, pp. 247-254, 2017.
5. Johansson, L., Singh, T., Leong, T., Mawson, R., McArthur, S., Manasseh, R., and Juliano, P., “Cavitation and Non-Cavitation Regime for Large-Scale Ultrasonic Standing Wave Particle Separation Systems–In Situ Gentle Cavitation Threshold Determination and Free Radical Related Oxidation”, Ultrasonics Sonochemistry, Vol. 28, pp. 346-356, 2016.
6. Yang, R.-J., Hou, H.-H., Wang, Y.-N., and Fu, L.-M., “Micro-Magnetofluidics in Microfluidic Systems: A Review”, Sensors and Actuators B: Chemical, Vol. 224, pp. 1-15, 2016.
7. Song, Y., Sonnenberg, A., Heaney, Y., and Heller, M. J., “Device for Dielectrophoretic Separation and Collection of Nanoparticles and DNA under High Conductance Conditions”, Electrophoresis, Vol. 36, No. 9-10, pp. 1107-1114, 2015.
8. Evander, M. and Nilsson, J., “Acoustofluidics 20: Applications in Acoustic Trapping”, Lab on a Chip, Vol. 12, No. 22, pp. 4667-4676, 2012.
9. Ebrahimi Warkiani, M., Guan, G., Luan, K., Lee, W., Bhagat, A., Chaudhuri, P., Tan, D., Lim, W., Lee, S., Chen, P., Lim, C. and Han, J., “Slanted Spiral Microfluidics for the Ultra-Fast, Label-Free Isolation of Circulating Tumor Cells”, Lab on a Chip, Vol. 14, No. 1, pp. 128-137, 2014.
10. Manneberg, O., Svennebring, J., Hertz, H. M., and Wiklund, M., “Wedge Transducer Design for Two-Dimensional Ultrasonic Manipulation in a Microfluidic Chip”, Journal of Micromechanics and Microengineering, Vol. 18, No. 9, p. 095025, 2008.
11. Antfolk, M., Muller, P. B., Augustsson, P., Bruus, H., and Laurell, T., “Focusing of Sub-Micrometer Particles and Bacteria Enabled by Two-Dimensional Acoustophoresis”, Lab on a Chip, Vol. 14, No. 15, pp. 2791-2799, 2014.
12. Siddique, A. H., Cho, S. H., Ahn, B., and Kim, C., “Ultrasonic Manipulation of Magnetic Particles in a Microfluidic Channel”, International Journal of Precision Engineering and Manufacturing, Vol. 15, No. 7, pp. 1411-1416, 2014.
13. Taha, T. E.-S., El-Dosoky, M. A., and El-Sayed, A. M., “On the Analysis of the Interaction Between Surface Acoustic Wave (SAW) and Adjacent Media”, Radio Science Conference, 2007. NRSC 2007. National, 2007, pp. 1-8: IEEE.
14. Yoon, Y., Kim, S., Lee, J., Choi, J., Kim, R., Lee, S., Sul, O. and Lee, S., “Clogging-Free Microfluidics for Continuous Size-Based Separation of Microparticles”, Scientific Reports, Vol. 6, p. 26531, 2016.
15. Lenshof, A., Evander, M., Laurell, T., and Nilsson, J., “Acoustofluidics 5: Building Microfluidic Acoustic Resonators”, Lab on a Chip, Vol. 12, No. 4, pp. 684-695, 2012.
16. Esmaeilsabzali, H., Beischlag. T. V., Cox, M. E., Parameswaran, A. M., and Park, E. J., “Detection and Isolation of Circulating Tumor Cells: Principles and Methods”, Biotechnology Advances, Vol. 31, No. 7, pp. 1063-1084, 2013.
17. Lin, Z., Chiang, N., Chai, N., Seshasayee, D., Lee, W., Balazs, M., Nakamura, G. and Swem, L., “In Vivo Antigen-Driven Plasmablast Enrichment in Combination with Antigen-Specific Cell Sorting to Facilitate the Isolation of Rare Monoclonal Antibodies from Human B Cells”, Nature Protocols, Vol. 9, No. 7, p. 1563, 2014.
18. Amini, H., Lee, W. and Di Carlo, D., “Inertial Microfluidic Physics”, Lab on a Chip, Vol. 14, No. 15, pp. 2739-2761, 2014.
19. Bhagat, A. A. S., Bow, H., Hou, H. W., Tan, S. J., Han, J., and Lim, C. T., “Microfluidics for Cell Separation”, Medical and Biological Engineering and Computing, Vol. 48, No. 10, pp. 999-1014, 2010.
20. Beebe, D. J., Mensing, G. A., and Walker, G. M., “Physics and Applications of Microfluidics in Biology”, Annual Review of Biomedical Engineering, Vol. 4, No. 1, pp. 261-286, 2002.
21. Zhang, J., Yan, S., Yuan, D., Alici, G., Nguyen, N., Ebrahimi Warkiani, M. and Li, W., “Fundamentals and Applications of Inertial Microfluidics: A Review”, Lab on a Chip, Vol. 16, No. 1, pp. 10-34, 2016.
22. Asmolov, E. S., “The Inertial Lift on a Spherical Particle in a Plane Poiseuille Flow at Large Channel Reynolds Number”, Journal of Fluid Mechanics, Vol. 381, pp. 63-87, 1999.
23. Di Carlo, D., “Inertial Microfluidics”, Lab on a Chip, Vol. 9, No. 21, pp. 3038-3046, 2009.
24. Gossett, D. R., and Carlo, D. D., “Particle Focusing Mechanisms in Curving Confined Flows”, Analytical Chemistry, Vol. 81, No. 20, pp. 8459-8465, 2009.
25. Guan, G., Wu, L., Bhagat, A., Li, Z., Chen, P., Chao, S., Ong, C. and Han, J., “Spiral Microchannel with Rectangular and Trapezoidal Cross-Sections for Size Based Particle Separation”, Scientific Reports, Vol. 3, p. 1475, 2013.
26. Kuntaegowdanahalli, S. S., Bhagat, A. A. S., Kumar, G., and Papautsky, I., “Inertial Microfluidics for Continuous Particle Separation in Spiral Microchannels”, Lab on a Chip, Vol. 9, No. 20, pp. 2973-2980, 2009.
27. Nivedita, N., Giridhar, P., Kasper, S., and Papautsky, I., “Sorting Human Prostate Epithelial (HPET) Cells in an Inertial Microfluidic Device”, in Proceedings of MicroTAS, pp. 1230-1232, 2011.
28. Nivedita, N., and Papautsky, I., “Continuous Separation of Blood Cells in Spiral Microfluidic Devices”, Biomicrofluidics, Vol. 7, No. 5, p. 054101, 2013.
29. Bhagat, A. A. S., Kuntaegowdanahalli, S. S., and Papautsky, I., “Continuous Particle Separation in Spiral Microchannels Using Dean Flows and Differential Migration”, Lab on a Chip, Vol. 8, No. 11, pp. 1906-1914, 2008.
30. Nivedita, N., Ligrani, P., and Papautsky, I., “Dean Flow Dynamics in Low-Aspect Ratio Spiral Microchannels”, Scientific Reports, Vol. 7, 2017.
31. Skotis, G., Cumming, D., Roberts, J., Riehle, M., and Bernassau, A., “Dynamic Acoustic Field Activated Cell Separation (DAFACS)”, Lab on a Chip, Vol. 15, No. 3, pp. 802-810, 2015.
32. Kim, T. H., Yoon, H. J., Stella, P., and Nagrath, S., “Cascaded Spiral Microfluidic Device for Deterministic and High Purity Continuous Separation of Circulating Tumor Cells”, Biomicrofluidics, Vol. 8, No. 6, p. 064117, 2014.
33. Karniadakis, G., Beskok, A. and Aluru, N., “Microflows and Nanoflows: Fundamentals and Simulation”, Springer Science & Business Media, 2006.
34. Cherukat, P., and Mclaughlin, J. B., “The Inertial Lift on a Rigid Sphere in a Linear Shear Flow Field Near a Flat Wall”, Journal of Fluid Mechanics, Vol. 263, pp. 1-18, 1994.
35. Saffman, P., “The Lift on a Small Sphere in a Slow Shear Flow”, Journal of Fluid Mechanics, Vol. 22, No. 2, pp. 385-400, 1965.
36. Rubinow, S., and Keller, J. B., “The Transverse Force on a Spinning Sphere Moving in a Viscous Fluid”, Journal of Fluid Mechanics, Vol. 11, No. 3, pp. 447-459, 1961.
37. Soliman, A. M., Eldosoky, M. A., and Taha, T. E., “Modelling and Simulation of Microparticles Separation Using Standing Surface Acoustic Waves (SSAWs) Microfluidic Devices for Biomedical Applications”, International Journal of Computer Applications, Vol. 129, pp. 30-38, 2015.
38. Dean, W., “LXXII. The Stream-Line Motion of Fluid in a Curved Pipe (Second paper)”, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 5, No. 30, pp. 673-695, 1928.
39. Mishra, P., Hill, M., and Glynne-Jones, P., “Deformation of Red Blood Cells Using Acoustic Radiation Forces”, Biomicrofluidics, Vol. 8, No. 3, p. 034109, 2014.
40. Gor'Kov, L., “On the Forces Acting on a Small Particle in an Acoustical Field in an Ideal Fluid”, in Soviet Physics, Doklady, 1962, Vol. 6, pp. 773-775.
41. Momennnasab, F., “2D simulation of isolation of circulating tumor cells by acoustic waves”, MSc thesis, Department of Mechanical Engineering, Isfahan University of Technology, 2017 (In Persian).
42. Maxey, M. R., and Riley, J. J., “Equation of Motion for a Small Rigid Sphere in a Nonuniform Flow”, The Physics of Fluids, Vol. 26, No. 4, pp. 883-889, 1983.
43. Soliman, A. M., Eldosoky, M. A. and Taha, T. E., “Analysis Improvement of Standing Surface Acoustic Wave Microfluidic Devices for Bio-Particles Separation”, International Journal of Computer Applications in Technology, Vol. 55, No. 3, pp. 244-256, 2017.
44. Nivedita, N., Ligrani, P. and Papautsky, I., “Spiral Inertial Microfluidic Devices for Continuous Blood Cell Separation”, Microfluidics, BioMEMS, and Medical Microsystems X, 2012, Vol. 8251, p. 82510R: International Society for Optics and Photonics.
45. Bruus, H., “Acoustofluidics 2: Perturbation Theory and Ultrasound Resonance Modes”, Lab on a Chip, Vol. 12, No. 1, pp. 20-28, 2012.
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