Modares Mechanical Engineering

Modares Mechanical Engineering

A 3D simulation of Thermal mixing on mesoscopic scale in an electromagnetic microchannel containing ionized gas

Authors
1 faculty of mechanical engineering, malekashtar university of technology, shahinshahr, isfahan
2 University of Kashan
3 Prof., Uni. of Kashan
Abstract
The purpose of this work is to provide a model in lattice Boltzmann method for D simulating thermal rarified gas flows. The study model is a microchannel with a square cross section. The magnetic field flux was created by the magnets on two facing walls. The electrodes are embedded on the walls adjacent to that of the magnets and DC voltage is applied at both ends. Compressible fluid behavior is compared in slip (Kn =0.15) and transient (Kn =0.1) regimes. There are assumptions of laminar and steady flow. Newtonian fluid is electrically and magnetically conductive. Slip and temperature jump on the microchannel walls are considered and the effects of electric double layer thickness and changes of Hartmann number are studied. Since the ionic process is non-isothermal, energy equation is coupled with that of the velocity and the magnetic field and the effects of interaction forces of Lorentz, electric and electrothermal have been entered into Boltzmann equations in separate terms. The outcomes show the interaction between an axial electric field and a transverse magnetic field results in three-dimensional nature of the flow. Navier-Maxwell second order slip boundary condition imposed on the electromagnetic channel walls plays an important role in the vortices formation and the temperature distribution across the channel goes out of the symmetric state. Mass flow rate loss along the channel, resulting from the fluid rarefaction, and pressure deviation from linearity, across and along the channel axis because of the compressibility, was observed
Keywords

Subjects


[1] D. Kandhai, D. Vidal, A. Hoekstra, H. Hoefsloot, P. Iedema, P. Sloot, Lattice‐Boltzmann and finite element simulations of fluid flow in a SMRX Static Mixer Reactor, International Journal for Numerical Methods in Fluids, vol. 31, no. 6, pp. 1019-1033, 1999.
[2] T. S. Mautner, Application of synthetic jets to low Reynolds number biosensor microfluidic flows for enhanced mixing: a numerical study using the lattice Boltzmann method, Biosensors and Bioelectronics, vol. 19, no. 11, pp. 1409-1419, 2004.
[3] M. Chitsaz, M. Fathali, The effect of external magnetic field on mixing characteristics of two-dimensional isotropic MHD, Modares Mechanical Engineering, Vol. 17, No. 12, pp. 319-327, 2018 (in Persianفارسی )
[4] F. Tian, B. Li, D. Y. Kwok, Tradeoff between Mixing and Transport for Electroosmotic Flow in Heterogeneous Microchannels with Nonuniform Surface Potentials, Langmuir, vol. 21, no. 3, pp. 1126-1131, 2005.
[5] J. Wang, M. Wang, Z. Li, Lattice Boltzmann simulations of mixing enhancement by the electro-osmotic flow in microchannels, Modern Physics Letters B, vol. 19, no. 28n29, pp. 1515-1518, 2005.
[6] J. Wang, M. Wang, Z. Li, Lattice Poisson–Boltzmann simulations of electro-osmotic flows in microchannels, Journal of Colloid and Interface Science, vol. 296, no. 2, pp. 729-736, 2006.
[7] J. Kang, Y. K. Suh, H. S. Heo, Z. Li, Numerical Simulation of Fluids Mixing Enhancement by Effect of Heterogeneous Distributed Zeta-potential in Microchannel, Proceedings of the Fourth national congress on Fluids Engineering, Kyungju, Korea, August 23–25, 2006.
[8] S.-J. An, Y.-D. Kim, J.-S. Maeng, A Study on Mixing Enhancement by Rotating and Oscillating Stirrers in the Micro Channel, Transactions of the Korean Society of Mechanical Engineers B, vol. 30, no. 5, pp. 430-437, 2006.
[9] E. Monaco, K. Luo, R. Qin, Lattice Boltzmann simulations for microfluidics and mesoscale phenomena, New Trends in Fluid Mechanics Research, pp. 654-657: Springer, 2007.
[10] F. Varnik, D. Raabe, Chaotic flows in microchannels: A lattice Boltzmann study, Molecular Simulation, vol. 33, no. 7, pp. 583-587, 2007.
[11] D. Wang, J. Summers, P. Gaskell, Modeling of electrokinetically driven flow mixing enhancement in microchannels with patterned heterogeneous surface and blocks, Nanoscale and microscale thermophysical engineering, vol. 11, no. 1-2, pp. 1-13, 2007.
[12] A. M. Guzmán, L. E. Sanhueza, A. J. Díaz, R. A. Escobar, Stretching Fields and Flow Mixing Enhancement of Rarefied Gases in Micro-Grooved Channels by the Lattice-Boltzmann Method, Proceedings of FEDSM2008, 2008 ASME Fluids Engineering Conference, Jacksonville, Florida, USA, August 10–14, 2008.
[13] L. E. Sanhueza, A. M. Guzman, Future and Past Stretching and Flow Mixing Enhancement in Wavy Channels by the Lattice-Boltzmann Method, Proceedings of IMECE2008, 2008 ASME International Mechanical Engineering Congress and Exposition, Boston, Massachusetts, USA, October 31–November 6, 2008.
[14] J. Derksen, Mixing by solid particles, Chemical Engineering Research and Design, vol. 86, no. 12, pp. 1363-1368, 2008.
[15] J. Kang, H. S. Heo, Y. K. Suh, LBM simulation on mixing enhancement by the effect of heterogeneous zeta-potential in a microchannel, Journal of Mechanical Science and Technology, vol. 22, no. 6, pp. 1181-1191, 2008.
[16] A. K. De, Numerical modeling of microscale mixing using lattice Boltzmann method, PhD Thesis, Virginia Polytechnic Institute and State University, 2008.
[17] C.-C. Chang, Y.-T. Yang, T.-H. Yen, C. o.-K. Chen, Numerical investigation into thermal mixing efficiency in Y-shaped channel using Lattice Boltzmann method and field synergy principle, International Journal of Thermal Sciences, vol. 48, no. 11, pp. 2092-2099, 2009.
[18] A. Osorio Nesme, High Performance Computations of Transient Transport in Microchannels using Lattice Boltzmann Methods, PhD Thesis, Technischen Fakult¨at der Universit¨at Erlangen-N¨urnberg, 2010.
[19] J. Đ. Marković, N. L. Lukić, D. Z. Jovičević, Application of Lattice-Boltzmann method and analysis of fluid flow between two sinusoidal plates, Acta Periodica Technologica, vol. 41, pp. 121-129, 2010.
[20] Y. Wang, J. G. Brasseur, G. G. Banco, A. G. Webb, A. C. Ailiani, T. Neuberger, A multiscale lattice Boltzmann model of macro- to micro-scale transport, with applications to gut function, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 368, no. 1921, pp. 2863-2880, 2010.
[21] G. Tang, Y. He, W. Tao, Numerical analysis of mixing enhancement for micro-electroosmotic flow, Journal of Applied Physics, vol. 107, no. 10, pp. 104906, 2010.
[22] G. Tang, F. Wang, W. Tao, Lattice Boltzmann Simulation of Electroosmotic Micromixing by Heterogeneous Surface Charge, International Journal of Modern Physics C, vol. 21, no. 02, pp. 261-274, 2010.
[23] M. Wang, Q. Kang, Modeling electrokinetic flows in microchannels using coupled lattice Boltzmann methods, Journal of Computational Physics, vol. 229, no. 3, pp. 728-744, 2010.
[24] S. Gokaltun, D. McDaniel, D. Roelant, Three Dimensional Simulations of Multiphase Flows Using a Lattice Boltzmann Method Suitable for High Density Ratios, Waste Management 2012 conference on improving the future in waste management, Phoenix, AZ (United States), 26 Feb - 1 Mar, 2012.
[25] F. Muggli, L. Chatagny, J. Latt, Lattice boltzmann method for the simulation of laminar mixers, 14th European Conference on Mixing, Warszawa, 10-13 September, 2012.
[26] A. Alizadeh, J. Wang, S. Pooyan, S. Mirbozorgi, M. Wang, Numerical study of active control of mixing in electro-osmotic flows by temperature difference using lattice Boltzmann methods, Journal of colloid and interface science, vol. 407, pp. 546-555, 2013.
[27] A. Alizadeh, L. Zhang, M. Wang, Mixing enhancement of low-Reynolds electro-osmotic flows in microchannels with temperature-patterned walls, Journal of colloid and interface science, vol. 431, pp. 50-63, 2014.
[28] C. Flint, G. Vahala, Lattice Boltzmann large eddy simulation model of MHD, Radiation Effects and Defects in Solids, vol 172, no 2, pp.12-22, 2017.
[29] N. Xie, C.W. Jiang, Y.H. He M. Yao, Lattice Boltzmann method for thermomagnetic convection of paramagnetic fluid in square cavity under a magnetic quadrupole field, Journal of Central South University, vol 24, no 5, pp.1174-1182, 2017.
[30] A. R. Rahmati, H. Khorasanizadeh, M. R. Arabyarmohammadi, Application of Lattice Boltzmann Method for Simulating MGD in a Microchannel under Magnetic Field Effects, Modares Mechanical Engineering, Vol. 16, no 7, pp 229-240, 2016. (in Persianفارسی )
[31] Y. Shi, T. Zhao, Z. Guo, Simplified model and lattice Boltzmann algorithm for microscale electro-osmotic flows and heat transfer, International journal of heat and mass transfer, vol. 51, no. 3, pp. 586-596, 2008.
[32] Y. Shi, T. Zhao, Z. Guo, Lattice Boltzmann simulation of thermal electro-osmotic flows in micro/nanochannels, Journal of Computational and Theoretical Nanoscience, vol. 5, no. 2, pp. 236-246, 2008.
[33] P. J. Dellar, Moment-based boundary conditions for lattice Boltzmann magnetohydrodynamics, Proceedings of the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011.
[34] A.A. Mohamad A. Kuzmin, A critical evaluation of force term in lattice Boltzmann method, natural convection problem, International Journal of Heat and Mass Transfer, vol. 53, no. 5, pp. 990-996, 2010.
[35] K. Mattila, Implementation techniques for the lattice Boltzmann method, PhD Thesis, University of Jyväskylä, 2010.
[36] A. Agrawal, A comprehensive review on gas flow in microchannels, International Journal of MicroNano Scale Transport, Vol. 2, No. 1, pp. 1–40, 2011.
[37] R. Agarwal, Lattice Boltzmann simulation of magnetohydrodynamic slip flow in microchannels, Bulletin of the American Physical Society, vol. 48, no. 10, pp. 93-98, 2003.
[38] L. Ribetto, Microfabricated All-Around-Electrode AC Electro-osmotic Micropump, PhD Thesis, École Polytechnique Fédérale De Lausanne, 2012.
[39] P. J. Dellar, Lattice kinetic schemes for magnetohydrodynamics, Journal of Computational Physics, vol. 179, no. 1, pp. 95-126, 2002.
[40] R.K. Agarwal, L. Chusak, Oscillatory magnetogasdynamic slip flow in a microchannel, Journal of Engineering Mathematics, vol. 84, no. 1, pp. 135-146, 2014.
[41] L. D. Landau, E. M. Lifshitz, Course of Theoretical Physics. T. 8: Electrodynamics of continuous media, Second Impression, pp. 224-238, New York: Pergamon Press Ltd, 1963.