Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-27T01:20:51.389Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermophoretic effects on instabilities of nanoflows in porous media

Published online by Cambridge University Press:  22 October 2018

B. Dastvareh  and
J. Azaiez Open the ORCID record for J. Azaiez [Opens in a new window]
B. Dastvareh
Affiliation:
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB T2N 4V8, Canada
J. Azaiez*
Affiliation:
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB T2N 4V8, Canada
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Interfacial Flows (free surface): Fingering instability Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Low-Reynolds-number flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 857 , 25 December 2018 , pp. 173 - 199
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahmadi, M. H., Mirlohi, A., Alhuyi Nazari, M. & Ghasempour, R. 2018 A review of thermal conductivity of various nanofluids. J. Molecular Liquids 265, 181–188.Google Scholar
Braibanti, M., Vigolo, D. & Piazza, R. 2008 Does thermophoretic mobility depend on particle size? Phys. Rev. Lett. 100 (10), 108303.Google Scholar
Buongiorno, J. 2006 Convective transport in nanofluids. Trans. ASME J. Heat Transfer 128 (3), 240–250.Google Scholar
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.Google Scholar
Dastvareh, B. & Azaiez, J. 2017 Instabilities of nanofluid flow displacements in porous media. Phys. Fluids 29 (4), 044101.Google Scholar
De Wit, A., Bertho, Y. & Martin, M. 2005 Viscous fingering of miscible slices. Phys. Fluids 17 (5), 054114.Google Scholar
De Wit, A. & Homsy, G. M. 1999 Viscous fingering in reaction-diffusion systems. J. Chem. Phys. 110 (17), 8663–8675.Google Scholar
Deen, W. M. 1998 Analysis of Transport Phenomena. Oxford University Press.Google Scholar
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.Google Scholar
Ensign, L. M., Cone, R. & Hanes, J. 2012 Oral drug delivery with polymeric nanoparticles: the gastrointestinal mucus barriers. Adv. Drug Deliv. Rev. 64 (6), 557–570.Google Scholar
Gargiulo, J., Cerrota, S., Cortes, E., Violi, I. L. & Stefani, F. D. 2016 Connecting metallic nanoparticles by optical printing. Nano Lett. 16 (2), 1224–1229.Google Scholar
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.Google Scholar
Giddings, J. C. 1993 Field-flow fractionation: analysis of macromolecular, colloidal, and particulate materials. Science 260 (5113), 1456–1465.Google Scholar
Golestanian, R., Liverpool, T. B. & Ajdari, A. 2007 Designing phoretic micro- and nano-swimmers. New J. Phys. 9 (5), 126.Google Scholar
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, 374–387.Google Scholar
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), 161–183.Google Scholar
Jha, B., Cueto-Felgueroso, L. & Juanes, R. 2011 Fluid mixing from viscous fingering. Phys. Rev. Lett. 106 (19), 194502.Google Scholar
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.Google Scholar
Manickam, O. & Homsy, G. M. 1994 Simulation of viscous fingering in miscible displacements with nonmonotonic viscosity profiles. Phys. Fluids 6 (1), 95–107.Google Scholar
Martin, A. & Bou-Ali, M. M. 2011 Determination of thermal diffusion coefficient of nanofluid: fullerene–toluene. C. R. Méc 339 (5), 329–334.Google Scholar
McNab, G. S. & Meisen, A. 1973 Thermophoresis in liquids. J. Colloid Interface Sci. 44 (2), 339–346.Google Scholar
Michaelides, E. E. 2015 Brownian movement and thermophoresis of nanoparticles in liquids. Intl J. Heat Mass Transfer 81, 179–187.Google Scholar
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.Google Scholar
Murshed, S. M. S. & Estelle, P. 2017 A state of the art review on viscosity of nanofluids. Renew. Sustainable Energy Rev. 76, 1134–1152.Google Scholar
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), 5796–5801.Google Scholar
Nijjer, J. S., Hewitt, D. R. & Neufeld, J. A. 2018 The dynamics of miscible viscous fingering from onset to shutdown. J. Fluid Mech. 837, 520–545.Google Scholar
Piazza, R. & Parola, A. 2008 Thermophoresis in colloidal suspensions. J. Phys.: Condens. Matter 20 (15), 153102.Google Scholar
Pritchard, D. 2009 The linear stability of double-diffusive miscible rectilinear displacements in a Hele-Shaw cell. Eur. J. Mech. (B/Fluids) 28 (4), 564–577.Google Scholar
Rousseaux, G., Martin, M. & De Wit, A. 2011 Viscous fingering in packed chromatographic columns: non-linear dynamics. J. Chromatogr. A 1218 (46), 8353–8361.Google Scholar
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), 312–329.Google Scholar
Sajjadi, M. & Azaiez, J. 2016 Hydrodynamic instabilities of flows involving melting in under-saturated porous media. Phys. Fluids 28 (3), 033104.Google Scholar
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), 381–411.Google Scholar
Tan, C. T. & Homsy, G. M. 1986 Stability of miscible displacements in porous media: rectilinear flow. Phys. Fluids 29 (11), 3549–3556.Google Scholar
Tan, C. T. & Homsy, G. M. 1992 Viscous fingering with permeability heterogeneity. Phys. Fluids A 4 (6), 1099–1101.Google Scholar
Tufenkji, N. & Elimelech, M. 2004 Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media. Environ. Sci. Technol. 38 (2), 529–536.Google Scholar
Wen, J. & Wexler, A. S. 2007 Thermophoretic sampler and its application in ultrafine particle collection. Aerosol Sci. 41 (6), 624–629.Google Scholar
Yao, K.-M., Habibian, M. T. & O’Melia, C. R. 1971 Water and waste water filtration: concepts and applications. Environ. Sci. Technol. 5 (11), 1105–1112.Google Scholar
Yu, W. & Xie, H. 2012 A review on nanofluids: preparation, stability mechanisms, and applications. J. Nanomaterials 2012, 435873.Google Scholar
Yuan, Q. & Azaiez, J. 2014 Miscible displacements in porous media with time-dependent injection velocities. Trans. Porous Med. 104 (1), 57–76.Google Scholar
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), 935–946.Google Scholar
Zargartalebi, M. & Azaiez, J. 2018 Mesoscopic study of miscible nanoflow instabilities. Phys. Fluids 30 (2), 024105.Google Scholar
Zhang, T.2012 Modeling of nanoparticle transport in porous media. PhD thesis, University of Texas at Austin.Google Scholar
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), 387–406.Google Scholar
Zimmerman, W. B. & Homsy, G. M. 1991 Nonlinear viscous fingering in miscible displacement with anisotropic dispersion. Phys. Fluids A 3 (8), 1859–1872.Google Scholar