Dynamics analysis of microparticles in inertial microfluidics for biomedical applications

Document Type: Research Paper

Authors

1 Faculty of Health and Medical Sciences, Adelaide Medical School, University of Adelaide

2 Borjavaran Center of Applied Science and Technology, University of Applied Science and Technology, Tehran, Iran

Abstract

Inertial microfluidics-based devices have recently attracted much interest and attention due to their simple structure, high throughput, fast processing and low cost. They have been utilised in a wide range of applications in microtechnology, especially for sorting and separating microparticles. This novel class of microfluidics-based devices works based on intrinsic forces, which cause microparticles to migrate laterally and locate at their equilibrium positions. In this article, a comprehensive theoretical formulation is presented for the dynamics of ultrasmall particles in microfluidics-based devices. Explicit expressions are presented for various important forces, which act on a microparticle, such as drag, Magnus, Saffman and wall-induced forces. In addition, the drag coefficient, diffusion phenomenon and Peclet number are formulated. Finally, the influences of particle size, as a crucial parameter, on various intrinsic forces including drag, Magnus and Saffman forces as well as the wall-induced force, are investigated. It is found that the drag, wall-induced and Saffman forces have an important role to play in the dynamics of microparticles in inertial microfluidics while the effects of Magnus force and diffusion can be ignored in most applications.

Keywords

Main Subjects


[1]           S. Asemi, A. Farajpour, M. Mohammadi, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory, Composite Structures, Vol. 116, pp. 703-712, 2014.

[2]           J. S. Bunch, A. M. Van Der Zande, S. S. Verbridge, I. W. Frank, D. M. Tanenbaum, J. M. Parpia, H. G. Craighead, P. L. McEuen, Electromechanical resonators from graphene sheets, Science, Vol. 315, No. 5811, pp. 490-493, 2007.

[3]           W. Guo, C. Cheng, Y. Wu, Y. Jiang, J. Gao, D. Li, L. Jiang, Bio‐inspired two‐dimensional nanofluidic generators based on a layered graphene hydrogel membrane, Advanced Materials, Vol. 25, No. 42, pp. 6064-6068, 2013.

[4]           M. R. Farajpour, A. Rastgoo, A. Farajpour, M. Mohammadi, Vibration of piezoelectric nanofilm-based electromechanical sensors via higher-order non-local strain gradient theory, IET Micro & Nano Letters, Vol. 11, No. 6, pp. 302-307, 2016.

[5]           Y. Shao, J. Wang, H. Wu, J. Liu, I. A. Aksay, Y. Lin, Graphene based electrochemical sensors and biosensors: a review, Electroanalysis: An International Journal Devoted to Fundamental and Practical Aspects of Electroanalysis, Vol. 22, No. 10, pp. 1027-1036, 2010.

[6]           M. R. Farajpour, A. R. Shahidi, A. Farajpour, Frequency behavior of ultrasmall sensors using vibrating SMA nanowire-reinforced sheets under a non-uniform biaxial preload, Materials Research Express, Vol. 6, pp. 065047, 2019.

[7]           M. M. Adeli, A. Hadi, M. Hosseini, H. H. Gorgani, Torsional vibration of nano-cone based on nonlocal strain gradient elasticity theory, The European Physical Journal Plus, Vol. 132, No. 9, pp. 393, 2017.

[8]           A. Daneshmehr, A. Rajabpoor, A. Hadi, Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories, International Journal of Engineering Science, Vol. 95, pp. 23-35, 2015.

[9]           A. Hadi, M. Z. Nejad, M. Hosseini, Vibrations of three-dimensionally graded nanobeams, International Journal of Engineering Science, Vol. 128, pp. 12-23, 2018.

[10]         M. Z. Nejad, A. Hadi, A. Rastgoo, Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory, International Journal of Engineering Science, Vol. 103, pp. 1-10, 2016.

[11]         S. S. Kuntaegowdanahalli, A. A. S. Bhagat, G. Kumar, I. Papautsky, Inertial microfluidics for continuous particle separation in spiral microchannels, Lab on a Chip, Vol. 9, No. 20, pp. 2973-2980, 2009.

[12]         H. Vahabi, E. R. Rad, T. Parpaite, V. Langlois, M. R. Saeb, Biodegradable polyester thin films and coatings in the line of fire: the time of polyhydroxyalkanoate (PHA)?, Progress in Organic Coatings, Vol. 133, pp. 85-89, 2019.

[13]         M. R. Farajpour, A. R. Shahidi, A. Farajpour, Elastic waves in fluid-conveying carbon nanotubes under magneto-hygro-mechanical loads via a two-phase local/nonlocal mixture model, Materials Research Express, Vol. 6, pp. 0850a8, 2019.

[14]         M. Farajpour, A. Shahidi, A. Farajpour, Influences of non-uniform initial stresses on vibration of small-scale sheets reinforced by shape memory alloy nanofibers, The European Physical Journal Plus, Vol. 134, No. 5, pp. 218, 2019.

[15]         A. Farajpour, A. Rastgoo, M. Farajpour, Nonlinear buckling analysis of magneto-electro-elastic CNT-MT hybrid nanoshells based on the nonlocal continuum mechanics, Composite Structures, Vol. 180, pp. 179-191, 2017.

[16]         M. Farajpour, A. Shahidi, A. Farajpour, A nonlocal continuum model for the biaxial buckling analysis of composite nanoplates with shape memory alloy nanowires, Materials Research Express, Vol. 5, No. 3, pp. 035026, 2018.

[17]         M. Farajpour, A. Shahidi, A. Hadi, A. Farajpour, Influence of initial edge displacement on the nonlinear vibration, electrical and magnetic instabilities of magneto-electro-elastic nanofilms, Mechanics of Advanced Materials and Structures, Vol. DOI: 10.1080/15376494.2018.1432820, 2018.

[18]         M. Farajpour, A. Shahidi, F. Tabataba’i-Nasab, A. Farajpour, Vibration of initially stressed carbon nanotubes under magneto-thermal environment for nanoparticle delivery via higher-order nonlocal strain gradient theory, The European Physical Journal Plus, Vol. 133, No. 6, pp. 219, 2018.

[19]         M. R. Farajpour, A. Shahidi, A. Farajpour, Resonant frequency tuning of nanobeams by piezoelectric nanowires under thermo-electro-magnetic field: a theoretical study, Micro & Nano Letters, Vol. 13, No. 11, pp. 1627-1632, 2018.

[20]         M. Hosseini, M. Shishesaz, K. N. Tahan, A. Hadi, Stress analysis of rotating nano-disks of variable thickness made of functionally graded materials, International Journal of Engineering Science, Vol. 109, pp. 29-53, 2016.

[21]         M. Z. Nejad, A. Hadi, A. Farajpour, Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials, Structural Engineering and Mechanics, Vol. 63, No. 2, pp. 161-169, 2017.

[22]         M. Hosseini, A. Hadi, A. Malekshahi, M. Shishesaz, A review of size-dependent elasticity for nanostructures, Journal of Computational Applied Mechanics, Vol. 49, No. 1, pp. 197-211, 2018.

[23]         N. Kordani, A. Fereidoon, M. Divsalar, A. Farajpour, Forced vibration of piezoelectric nanowires based on nonlocal elasticity theory, Journal of Computational Applied Mechanics, Vol. 47, No. 2, pp. 137-150, 2016.

[24]         E. Rohani Rad, M. R. Farajpour, Influence of taxol and CNTs on the stability analysis of protein microtubules, Journal of Computational Applied Mechanics, Vol. DOI: 10.22059/JCAMECH.2019.277874.369, 2019.

[25]         M. Abdelgawad, A. R. Wheeler, Low-cost, rapid-prototyping of digital microfluidics devices, Microfluidics and nanofluidics, Vol. 4, No. 4, pp. 349, 2008.

[26]         J. Zhang, S. Yan, D. Yuan, G. Alici, N.-T. Nguyen, M. E. Warkiani, W. Li, Fundamentals and applications of inertial microfluidics: A review, Lab on a Chip, Vol. 16, No. 1, pp. 10-34, 2016.

[27]         M. E. Warkiani, B. L. Khoo, L. Wu, A. K. P. Tay, A. A. S. Bhagat, J. Han, C. T. Lim, Ultra-fast, label-free isolation of circulating tumor cells from blood using spiral microfluidics, Nature protocols, Vol. 11, No. 1, pp. 134, 2016.

[28]         M. E. Warkiani, A. K. P. Tay, B. L. Khoo, X. Xiaofeng, J. Han, C. T. Lim, Malaria detection using inertial microfluidics, Lab on a Chip, Vol. 15, No. 4, pp. 1101-1109, 2015.

[29]         V. Potluri, P. S. Kathiresan, H. Kandula, P. Thirumalaraju, M. K. Kanakasabapathy, S. K. S. Pavan, D. Yarravarapu, A. Soundararajan, K. Baskar, R. Gupta, An inexpensive smartphone-based device for point-of-care ovulation testing, Lab on a Chip, Vol. 19, No. 1, pp. 59-67, 2019.

[30]         A. J. Chung, A Minireview on Inertial Microfluidics Fundamentals: Inertial Particle Focusing and Secondary Flow, BioChip Journal, Vol. 13, No. 1, pp. 53-63, 2019.

[31]         D. Di Carlo, Inertial microfluidics, Lab on a Chip, Vol. 9, No. 21, pp. 3038-3046, 2009.

[32]         A. Kommajosula, D. Stoecklein, D. Di Carlo, B. Ganapathysubramanian, Shape-design for stabilizing micro-particles in inertial microfluidic flows, arXiv preprint arXiv:1902.05935, 2019.

[33]         N. Liu, C. Petchakup, H. M. Tay, K. H. H. Li, H. W. Hou, Spiral Inertial Microfluidics for Cell Separation and Biomedical Applications,  in: Applications of Microfluidic Systems in Biology and Medicine, Eds., pp. 99-150: Springer, 2019.

[34]         J. M. Coulson, J. F. Richardson, J. R. Backhurst, J. H. Harker, 1991, Particle technology and separation processes, Pergamon Press,

[35]         S. R. Asemi, A. Farajpour, Vibration characteristics of double-piezoelectric-nanoplate-systems, Micro & Nano Letters, Vol. 9, No. 4, pp. 280-285, 2014.

[36]         S. R. Asemi, A. Farajpour, M. Borghei, A. H. Hassani, Thermal effects on the stability of circular graphene sheets via nonlocal continuum mechanics, Latin American Journal of Solids and Structures, Vol. 11, No. 4, pp. 704-724, 2014.

[37]         A. Farajpour, A. Rastgoo, Influence of carbon nanotubes on the buckling of microtubule bundles in viscoelastic cytoplasm using nonlocal strain gradient theory, Results in physics, Vol. 7, pp. 1367-1375, 2017.

[38]         A. Farajpour, A. Rastgoo, M. Mohammadi, Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment, Physica B: Condensed Matter, Vol. 509, pp. 100-114, 2017.

[39]         M. Farajpour, A. Shahidi, A. Farajpour, Influence of shear preload on wave propagation in small-scale plates with nanofibers, Structural Engineering and Mechanics Vol. 70, No. 4, pp. 407-420 2019.

[40]         M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco-Pasternak foundation, Journal of Solid Mechanics, Vol. 6, pp. 98-121, 2014.

[41]         S. R. Asemi, M. Mohammadi, A. Farajpour, A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, Vol. 11, No. 9, pp. 1515-1540, 2014.

[42]         M. Safarabadi, M. Mohammadi, A. Farajpour, M. Goodarzi, Effect of surface energy on the vibration analysis of rotating nanobeam, Journal of Solid Mechanics, Vol. 7, No. 3, pp. 299-311, 2015.

[43]         R. M. Mazo, 2002, Brownian motion: fluctuations, dynamics, and applications, Oxford University Press on Demand,

[44]         R. Clift, J. R. Grace, M. E. Weber, 2005, Bubbles, drops, and particles, Courier Corporation,

[45]         E. Michaelides, 2006, Particles, bubbles & drops: their motion, heat and mass transfer, World Scientific,

[46]         P. Saffman, The lift on a small sphere in a slow shear flow, Journal of fluid mechanics, Vol. 22, No. 2, pp. 385-400, 1965.

[47]         H. Brenner, The slow motion of a sphere through a viscous fluid towards a plane surface, Chemical engineering science, Vol. 16, No. 3-4, pp. 242-251, 1961.

[48]         R. Cox, S. Hsu, The lateral migration of solid particles in a laminar flow near a plane, International Journal of Multiphase Flow, Vol. 3, No. 3, pp. 201-222, 1977.