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Colloidal exchange flow in ducts

Published online by Cambridge University Press:  16 May 2022

K. Alba Open the ORCID record for K. Alba [Opens in a new window]
K. Alba*
Affiliation:
Mechanical Engineering Technology program, Department of Engineering Technology, University of Houston, Houston, TX 77204, USA
*
†Email address for correspondence: [email protected]
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Abstract

Buoyancy-driven exchange flow, i.e. drainage of a heavy colloidal suspension by an immiscible light pure fluid in a vertical duct, is studied analytically. A lubrication model is developed for two-dimensional channel and axisymmetric pipe geometries. The outcome transport equations are solved numerically to capture the effect of important governing dimensionless parameters: Péclet number, precursor film thickness, Reynolds number, mixtures’ viscosity ratio, initial volume fraction of hard-sphere particles, particles concentration within the precursor film, and capillary number. Recent study of colloidal film flow over a flat surface reveals interface thinning over time due to diffusion impact on suspension viscosity. However, the current model suggests that there is no such thinning phenomenon observed for colloidal flows within confined geometry unless in the absence of surface tension. The extent of the mixed particle zone along the duct grows as the Péclet number is decreased. Precursor film thickness is found to decrease the capillary ridge height forming at heavy suspension front. Either an increase in the Reynolds number or a decrease in light-to-heavy-fluid viscosity ratio extends the interpenetration rate of mixtures. As the bulk volume fraction of particles is increased close to 50 %, interesting secondary fronts emerge within the flow that coincide with the range where the diffusion coefficient is minimized. The heavy suspension layer drains slightly faster when the gradient in particle concentration between the bulk and precursor film regions is maximum. Finally, the non-monotonic impact of surface tension on the extent of mixtures’ exchange zone is uncovered via simulations conducted at various capillary numbers.

JFM classification

Low-Reynolds-number flows: Lubrication theory Interfacial Flows (free surface): Thin films Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 942 , 10 July 2022 , A9
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Baird, M.H.I., Aravamudan, K., Rao, N.V.R., Chadam, J. & Peirce, A.P. 1992 Unsteady axial mixing by natural convection in vertical column. AIChE J. 38, 1825–1834.CrossRefGoogle Scholar
Bertozzi, A.L. & Brenner, M.P. 1997 Linear stability and transient growth in driven contact lines. Phys. Fluids 9 (3), 530–539.CrossRefGoogle Scholar
Birman, V.K., Battandier, B.A., Meiburg, E. & Linden, P.F. 2007 Lock-exchange flows in sloping channels. J. Fluid Mech. 577, 53–77.CrossRefGoogle Scholar
Birman, V.K., Martin, J.E., Meiburg, E. & Linden, P.F. 2005 The non-Boussinesq lock-exchange problem. Part 2. High-resolution simulations. J. Fluid Mech. 537, 125–144.CrossRefGoogle Scholar
Bonometti, T., Balachandar, S. & Magnaudet, J. 2008 Wall effects in non-Boussinesq density currents. J. Fluid Mech. 616, 445–475.CrossRefGoogle Scholar
Buchanan, M., Molenaar, D., de Villiers, S. & Evans, R.M.L. 2007 Pattern formation in draining thin film suspensions. Langmuir 23 (7), 3732–3736.CrossRefGoogle ScholarPubMed
Cook, B.P., Bertozzi, A.L. & Hosoi, A.E. 2008 Shock solutions for particle-laden thin films. SIAM J. Appl. Maths 68 (3), 760–783.CrossRefGoogle Scholar
Craster, R.V., Matar, O.K. & Sefiane, K. 2009 Pinning, retraction, and terracing of evaporating droplets containing nanoparticles. Langmuir 25 (6), 3601–3609.CrossRefGoogle ScholarPubMed
Espín, L. & Kumar, S. 2014 Forced spreading of films and droplets of colloidal suspensions. J. Fluid Mech. 742, 495–519.CrossRefGoogle Scholar
Ha, Y., Kim, Y.J. & Myers, T.G. 2008 On the numerical solution of a driven thin film equation. J. Comput. Phys. 227 (15), 7246–7263.CrossRefGoogle Scholar
Hasnain, A. & Alba, K. 2017 Buoyant displacement flow of immiscible fluids in inclined ducts: a theoretical approach. Phys. Fluids 29, 052102.CrossRefGoogle Scholar
Kurganov, A. & Tadmor, E. 2000 New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations. J. Comput. Phys. 160 (1), 241–282.CrossRefGoogle Scholar
Maki, K.L. & Kumar, S. 2011 Fast evaporation of spreading droplets of colloidal suspensions. Langmuir 27 (18), 11347–11363.CrossRefGoogle ScholarPubMed
Matar, O.K., Craster, R.V. & Sefiane, K. 2007 Dynamic spreading of droplets containing nanoparticles. Phys. Rev. E 76 (5), 056315.CrossRefGoogle ScholarPubMed
Matson, G.P. & Hogg, A.J. 2012 Viscous exchange flows. Phys. Fluids 24 (2), 023102.CrossRefGoogle Scholar
Merlin, A., Salmon, J.B. & Leng, J. 2012 Microfluidic-assisted growth of colloidal crystals. Soft Matt. 8 (13), 3526–3537.CrossRefGoogle Scholar
Mirzaeian, N. 2018 Buoyancy-driven particle-laden exchange flows in inclined conduits. Master's thesis, University of Houston, Houston, USA.CrossRefGoogle Scholar
Mirzaeian, N. & Alba, K. 2018 a Monodisperse particle-laden exchange flows in a vertical duct. J. Fluid Mech. 847, 134–160.CrossRefGoogle Scholar
Mirzaeian, N. & Alba, K. 2018 b Particle-laden exchange flows in inclined pipes. Phys. Rev. Fluids 3, 114301.CrossRefGoogle Scholar
Mirzaeian, N., Testik, F.Y. & Alba, K. 2020 Bidensity particle-laden exchange flows in a vertical duct. J. Fluid Mech. 891, A18.CrossRefGoogle Scholar
Murisic, N., Ho, J., Hu, V., Latterman, P., Koch, T., Lin, K., Mata, M. & Bertozzi, A.L. 2011 Particle-laden viscous thin-film flows on an incline: experiments compared with a theory based on shear-induced migration and particle settling. Physica D 240 (20), 1661–1673.CrossRefGoogle Scholar
Pham, T. & Kumar, S. 2017 Drying of droplets of colloidal suspensions on rough substrates. Langmuir 33 (38), 10061–10076.CrossRefGoogle ScholarPubMed
Pham, T. & Kumar, S. 2019 Imbibition and evaporation of droplets of colloidal suspensions on permeable substrates. Phys. Rev. Fluids 4 (3), 034004.CrossRefGoogle Scholar
Popescu, M.N., Oshanin, G., Dietrich, S. & Cazabat, A.M. 2012 Precursor films in wetting phenomena. J. Phys.: Condens. Matter 24 (24), 243102.Google ScholarPubMed
Russel, W.B., Saville, D.A. & Schowalter, W.R. 1989 Colloidal Dispersions. Cambridge University Press.CrossRefGoogle Scholar
Ruyer-Quil, C., Treveleyan, P., Giorgiutti-Dauphiné, F., Duprat, C. & Kalliadasis, S. 2008 Modelling film flows down a fibre. J. Fluid Mech. 603, 431–462.CrossRefGoogle Scholar
Seon, T., Hulin, J.-P., Salin, D., Perrin, B. & Hinch, E.J. 2005 Buoyancy driven miscible front dynamics in tilted tubes. Phys. Fluids 17, 031702.CrossRefGoogle Scholar
Spaid, M.A. & Homsy, G.M. 1996 Stability of Newtonian and viscoelastic dynamic contact lines. Phys. Fluids 8 (2), 460–478.CrossRefGoogle Scholar
Taghavi, S.M., Seon, T., Martinez, D.M. & Frigaard, I.A. 2009 Buoyancy-dominated displacement flows in near-horizontal channels: the viscous limit. J. Fluid Mech. 639, 1–35.CrossRefGoogle Scholar
Tsai, B., Carvalho, M.S. & Kumar, S. 2010 Leveling of thin films of colloidal suspensions. J. Colloid Interface Sci. 343 (1), 306–313.CrossRefGoogle ScholarPubMed
Warner, M.R.E., Craster, R.V. & Matar, O.K. 2003 Surface patterning via evaporation of ultrathin films containing nanoparticles. J. Colloid Interface Sci. 267 (1), 92–110.CrossRefGoogle ScholarPubMed
Yiantsios, S.G. & Higgins, B.G. 2006 Marangoni flows during drying of colloidal films. Phys. Fluids 18 (8), 082103.CrossRefGoogle Scholar
Zhou, J., Dupuy, B., Bertozzi, A.L. & Hosoi, A.E. 2005 Theory for shock dynamics in particle-laden thin films. Phys. Rev. Lett. 94 (11), 117803.CrossRefGoogle ScholarPubMed