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Thermophoretic effects on instabilities of nanoflows in porous media

  • B. Dastvareh (a1) and J. Azaiez (a1)


Instabilities of nanoparticle-laden non-isothermal flows in homogeneous porous media are investigated. The study is conducted for two representative systems; a hot fluid displacing a cold one (HDC) and a cold fluid displacing a hot one (CDH). The effects of Brownian diffusion and of thermophoresis, representing the average motion of the nanoparticles as a result of temperature gradients, are analysed. In the HDC case, the synergetic Brownian and thermophoretic effects induce a migration of nanoparticles towards the cold fluid and tend systematically to enhance the instability. In particular, because of these combined effects, an initially stable displacement can actually be destabilized. In the CDH case however, Brownian diffusion still acts towards the transport of nanoparticles downstream into the hot fluid while thermophoresis tends to resist such migration. These counteracting effects lead to the generation of local accumulations of nanoparticles at the front and engender the development of local stable regions in the flow. These stable regions hinder the growth of the instabilities, especially those of backward-developing fingers. It is concluded that, in this case, thermophoresis acts against Brownian diffusion and results in less unstable displacements compared to flows where thermophoresis is absent. This effect, exclusively associated with thermophoresis, will not be observed in nanoparticle-free non-isothermal displacements. Finally, it is found that the main effects of Brownian diffusion and thermophoresis arise mainly from their contributions to nanoparticle transport while their effects on the energy balance are negligible and can be disregarded.


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Ahmadi, M. H., Mirlohi, A., Alhuyi Nazari, M. & Ghasempour, R. 2018 A review of thermal conductivity of various nanofluids. J. Molecular Liquids 265, 181188.
Braibanti, M., Vigolo, D. & Piazza, R. 2008 Does thermophoretic mobility depend on particle size? Phys. Rev. Lett. 100 (10), 108303.
Buongiorno, J. 2006 Convective transport in nanofluids. Trans. ASME J. Heat Transfer 128 (3), 240250.
Chen, C.-Y., Chen, C.-H. & Miranda, J. A. 2005 Numerical study of miscible fingering in a time-dependent gap Hele-Shaw cell. Phys. Rev. E 71 (5), 056304.
Dastvareh, B. & Azaiez, J. 2017 Instabilities of nanofluid flow displacements in porous media. Phys. Fluids 29 (4), 044101.
De Wit, A., Bertho, Y. & Martin, M. 2005 Viscous fingering of miscible slices. Phys. Fluids 17 (5), 054114.
De Wit, A. & Homsy, G. M. 1999 Viscous fingering in reaction-diffusion systems. J. Chem. Phys. 110 (17), 86638675.
Deen, W. M. 1998 Analysis of Transport Phenomena. Oxford University Press.
Doorwar, Sh. & Mohanty, K. K. 2011 Viscous fingering during non-thermal heavy oil recovery. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.
Ensign, L. M., Cone, R. & Hanes, J. 2012 Oral drug delivery with polymeric nanoparticles: the gastrointestinal mucus barriers. Adv. Drug Deliv. Rev. 64 (6), 557570.
Gargiulo, J., Cerrota, S., Cortes, E., Violi, I. L. & Stefani, F. D. 2016 Connecting metallic nanoparticles by optical printing. Nano Lett. 16 (2), 12241229.
Ghesmat, K., Hassanzadeh, H., Abedi, J. & Chen, Zh. 2011 Influence of nanoparticles on the dynamics of miscible Hele-Shaw flows. J. Appl. Phys. 109 (10), 104907.
Giddings, J. C. 1993 Field-flow fractionation: analysis of macromolecular, colloidal, and particulate materials. Science 260 (5113), 14561465.
Golestanian, R., Liverpool, T. B. & Ajdari, A. 2007 Designing phoretic micro- and nano-swimmers. New J. Phys. 9 (5), 126.
Hashemi, R., Nassar, N. N. & Pereira Almao, P. 2014 Nanoparticle technology for heavy oil in-situ upgrading and recovery enhancement: opportunities and challenges. Applied Energy 133, 374387.
Islam, M. N. & Azaiez, J. 2005 Fully implicit finite difference pseudo-spectral method for simulating high mobility ratio miscible displacements. Intl J. Numer. Meth. Fluids 47 (2), 161183.
Jha, B., Cueto-Felgueroso, L. & Juanes, R. 2011 Fluid mixing from viscous fingering. Phys. Rev. Lett. 106 (19), 194502.
Malhotra, S., Sharma, M. M. & Lehman, E. R. 2015 Experimental study of the growth of mixing zone in miscible viscous fingering. Phys. Fluids 27 (1), 014105.
Manickam, O. & Homsy, G. M. 1994 Simulation of viscous fingering in miscible displacements with nonmonotonic viscosity profiles. Phys. Fluids 6 (1), 95107.
Martin, A. & Bou-Ali, M. M. 2011 Determination of thermal diffusion coefficient of nanofluid: fullerene–toluene. C. R. Méc 339 (5), 329334.
McNab, G. S. & Meisen, A. 1973 Thermophoresis in liquids. J. Colloid Interface Sci. 44 (2), 339346.
Michaelides, E. E. 2015 Brownian movement and thermophoresis of nanoparticles in liquids. Intl J. Heat Mass Transfer 81, 179187.
Mishra, M., Trevelyan, P. M., Almarcha, C. & De Wit, A. 2010 Influence of double diffusive effects on miscible viscous fingering. Phys. Rev. Lett. 105 (20), 204501.
Murshed, S. M. S. & Estelle, P. 2017 A state of the art review on viscosity of nanofluids. Renew. Sustainable Energy Rev. 76, 11341152.
Nield, D. A. & Kuznetsov, A. V. 2009 Thermal instability in a porous medium layer saturated by a nanofluid. Intl J. Heat Mass Transfer 52 (25), 57965801.
Nijjer, J. S., Hewitt, D. R. & Neufeld, J. A. 2018 The dynamics of miscible viscous fingering from onset to shutdown. J. Fluid Mech. 837, 520545.
Piazza, R. & Parola, A. 2008 Thermophoresis in colloidal suspensions. J. Phys.: Condens. Matter 20 (15), 153102.
Pritchard, D. 2009 The linear stability of double-diffusive miscible rectilinear displacements in a Hele-Shaw cell. Eur. J. Mech. (B/Fluids) 28 (4), 564577.
Rousseaux, G., Martin, M. & De Wit, A. 2011 Viscous fingering in packed chromatographic columns: non-linear dynamics. J. Chromatogr. A 1218 (46), 83538361.
Saffman, P. G. & Taylor, G. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245 (1242), 312329.
Sajjadi, M. & Azaiez, J. 2016 Hydrodynamic instabilities of flows involving melting in under-saturated porous media. Phys. Fluids 28 (3), 033104.
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech. 36 (1), 381411.
Tan, C. T. & Homsy, G. M. 1986 Stability of miscible displacements in porous media: rectilinear flow. Phys. Fluids 29 (11), 35493556.
Tan, C. T. & Homsy, G. M. 1992 Viscous fingering with permeability heterogeneity. Phys. Fluids A 4 (6), 10991101.
Tufenkji, N. & Elimelech, M. 2004 Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media. Environ. Sci. Technol. 38 (2), 529536.
Wen, J. & Wexler, A. S. 2007 Thermophoretic sampler and its application in ultrafine particle collection. Aerosol Sci. 41 (6), 624629.
Yao, K.-M., Habibian, M. T. & O’Melia, C. R. 1971 Water and waste water filtration: concepts and applications. Environ. Sci. Technol. 5 (11), 11051112.
Yu, W. & Xie, H. 2012 A review on nanofluids: preparation, stability mechanisms, and applications. J. Nanomaterials 2012, 435873.
Yuan, Q. & Azaiez, J. 2014 Miscible displacements in porous media with time-dependent injection velocities. Trans. Porous Med. 104 (1), 5776.
Zaraki, A., Ghalambaz, M., Chamkha, A. J., Ghalambaz, M. & De Rossi, D. 2015 Theoretical analysis of natural convection boundary layer heat and mass transfer of nanofluids: effects of size, shape and type of nanoparticles, type of base fluid and working temperature. Adv. Powder Technol. 26 (3), 935946.
Zargartalebi, M. & Azaiez, J. 2018 Mesoscopic study of miscible nanoflow instabilities. Phys. Fluids 30 (2), 024105.
Zhang, T.2012 Modeling of nanoparticle transport in porous media. PhD thesis, University of Texas at Austin.
Zhang, T., Murphy, M., Yu, H., Huh, C. & Bryant, S. L. 2016 Mechanistic model for nanoparticle retention in porous media. Trans. Porous Med. 115 (2), 387406.
Zimmerman, W. B. & Homsy, G. M. 1991 Nonlinear viscous fingering in miscible displacement with anisotropic dispersion. Phys. Fluids A 3 (8), 18591872.
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