Abstract.
The results of a theoretical study are presented dealing with convective heat and mass transfer in a colloidal suspension through a Hele-Shaw cell heated from below. The numerical analysis, based on a multi-component model, reveals that for a certain range of parameter values the dynamical regimes of travelling waves as well as oscillatory fingering formation are stable. The bifurcation phenomena and nonlinear evolution of spatiotemporal patterns that develop in the colloid suspension are modeled and discussed, paying special attention to the combined effects of gravity sedimentation, thermal diffusion with positive separation ratio and convection.
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References
T.M. Squires, S.R. Quake, Rev. Mod. Phys. 77, 977 (2005)
J.K.G. Dhont, An Introduction to Dynamics of Colloids (Elsevier, Amsterdam, 1996)
J. Buongiorno, Trans. ASME, J. Heat Transf. 128, 240 (2006)
G. Ciccotti, M. Ferrario, Ch. Schütte (Editors), Molecular Dynamics Simulation (MDPI, Basel, Beijing, 2014)
H. Tanaka, T. Araki, Phys. Rev. Lett. 85, 1338 (2000)
H. Löwen, Soft Matter 6, 3133 (2010)
A. Podolny, A. Nepomnyashchy, A. Oron, in Thermal Nonequilibrium, Lecture Notes of the 8th International Meeting on Thermodiffusion, edited by S. Wiegand, W. Köhler, J.K.G. Dhont, Vol. 3 (Key Technologies, Jülich, 2008) p. 235
W. Köhler, K. Morozov, J. Non-Equilib. Thermodyn. 41, 151 (2016)
M.I. Shliomis, M. Souhar, Europhys. Lett. 49, 55 (2000)
M.I. Shliomis, B.L. Smorodin, S. Kamiyama, Philos. Mag. 83, 2139 (2003)
M.I. Shliomis, B.L. Smorodin, Phys. Rev. E 71, 036312 (2005)
B.L. Smorodin, I.N. Cherepanov, B.I. Myznikova, M.I. Shliomis, Phys. Rev. E 84, 026305 (2011)
B.L. Smorodin, I.N. Cherepanov, Eur. Phys. J. E 37, 118 (2014)
B. Huke, H. Pleiner, M. Lücke, Phys. Rev. E 75, 036203 (2007)
R. Cerbino, A. Vailati, M. Giglio, Phys. Rev. E 66, 055301 (2002)
R. Cerbino, A. Vailati, M. Giglio, Philos. Mag. 83, 2023 (2003)
S. Mazzoni, R. Cerbino, D. Brogioli, A. Vailati, M. Giglio, Eur. Phys. J. E 15, 305 (2004)
R. Cerbino, S. Mazzoni, A. Vailati, M. Giglio, Phys. Rev. Lett. 94, 064501 (2005)
G. Donzelli, R. Cerbino, A. Vailati, Phys. Rev. Lett. 102, 104503 (2009)
M. Bernardin, F. Comitani, A. Vailati, Phys. Rev. E 85, 066321 (2012)
B.H. Chang, A.F. Mills, E. Hernandez, Int. J. Heat Mass Transf. 51, 1332 (2008)
H.S. Hele-Shaw, Nature 58, 34 (1898)
H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1993)
B.I. Myznikova, in Studies on natural convection and conductive heat transfer (Ural Branch Acad. Sci. USSR, Sverdlovsk, 1981) p. 23 (in Russian)
K.A. Gavrilov, V.A. Demin, G.F. Putin, Tech. Phys. Lett. 36, 181 (2010)
D. Yadav, M.C. Kim, Comput. Fluids 117, 139 (2015)
M.C. Kim, Korean J. Chem. Eng. 34, 189 (2017)
F. Winkel, S. Messlinger, W. Schöpf, I. Rehberg, M. Siebenbürger, M. Ballauff, New J. Phys. 12, 053003 (2010)
S. Messlinger, C. Kramer, J.J. Schmied, F. Winkel, W. Schöpf, I. Rehberg, Phys. Rev. E 88, 053019 (2013)
J.K. Platten, J.C. Legros, Convection in Liquids (Springer-Verlag, Berlin, Heidelberg, 1984)
L.D. Landau, E.M. Lifschits, Course of Theoretical Physics, Vol. 6 (Pergamon Press, Oxford, 1993)
I.I. Ryzhkov, I.V. Stepanova, Int. J. Heat Mass Transf. 86, 268 (2015)
L.V. Kantorovich, V.I. Krylov, Approximate Methods of Higher Analysis (Groningen, Noordhoff, 1958)
P.J. Roache, Computational Fluid Dynamics (Hermosa, Albuquerque, New Mexico, 1976)
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Smorodin, B.L., Cherepanov, I.N., Ishutov, S.N. et al. Convection of a colloidal suspension in a Hele-Shaw cell. Eur. Phys. J. E 40, 18 (2017). https://doi.org/10.1140/epje/i2017-11502-0
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DOI: https://doi.org/10.1140/epje/i2017-11502-0