Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T19:42:45.263Z Has data issue: false hasContentIssue false
  • English
  • Français

Particle focusing in a suspension flow through a corrugated tube

Published online by Cambridge University Press:  21 July 2010

G. F. HEWITT  and
J. S. MARSHALL
G. F. HEWITT
Affiliation:
School of Engineering, University of Vermont, Burlington, VT 05405, USA
J. S. MARSHALL*
Affiliation:
School of Engineering, University of Vermont, Burlington, VT 05405, USA
*
†Email address for correspondence: jeffm@cems.uvm.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A computational study is performed of the transport of a particulate suspension through a corrugated tube using a discrete-element method (DEM). The tube is axisymmetric with a radius that varies sinusoidally along the tube length, which, in the presence of a mean suspension flow, leads to periodic inward and outward acceleration of the advected particles. The oscillations in radial acceleration and straining rate lead to a net radial drift, with mean acceleration measuring about an order of magnitude smaller than the instantaneous radial acceleration, which over time focuses small particles within the tube. The foundations of particle focusing in this flow are examined analytically using lubrication theory, together with a low-Stokes-number approximation for the particle drift. This lubrication-theory solution provides the basic scaling for how the particle drift will vary with wave amplitude and wavelength. Computations are then performed using a finite-volume method for a fluid flow in the tube at higher Reynolds numbers over a range of amplitudes, wavelengths and Reynolds numbers, examining the effect of each of these variables on the averaged radial fluid acceleration. A DEM is used to simulate particle behaviour at finite Stokes numbers, and the results are compared to an asymptotic approximation valid for low Stokes numbers. At low tube Reynolds number (e.g. Re = 10), the drift velocity induced by the tube corrugations focuses the particles onto the tube centreline, in accordance with the low-Stokes-number approximation based on the axial-averaged fluid radial acceleration. At higher tube Reynolds numbers (e.g. Re = 100), the correlation between the particle radial oscillation and the fluid acceleration field leads the outermost particles to drift into a ring at a finite radius from the tube centre, with little net motion of the particles in the innermost part of the tube. At larger Stokes numbers, particles can be dispersed to the outer regions of the tube due to particle outward dispersion from the large instantaneous radial acceleration. The effects of eddy formation within the corrugation crests on particle focusing are also examined.

JFM classification

Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 660 , 10 October 2010 , pp. 258 - 281
Copyright
Copyright © Cambridge University Press 2010

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

REFERENCES

Amon, C. H., Guzmán, A. M. & Morel, M. B. 1996 Lagrangian chaos, Eulerian chaos, and mixing enhancement in converging–diverging channel flows. Phys. Fluids 8, 1192–1206.CrossRefGoogle Scholar
Asako, Y. & Faghri, M. 1987 Finite volume solutions for laminar flow and heat transfer in a corrugated duct. J. Heat Transfer 109, 627–634.CrossRefGoogle Scholar
Asai, M. & Floryan, J. M. 2006 Experiments on the linear instability of flow in a wavy channel. Eur. J. Mech. B/Fluids 25, 971–986.CrossRefGoogle Scholar
Cabal, A., Szumbarski, J. & Floryan, J. M. 2002 Stability of flow in a wavy channel. J. Fluid Mech. 457, 191–212.Google Scholar
Cho, K. J., Kim, M. & Shin, H. D. 1998 Linear stability of two-dimensional steady flow in wavy-walled channel. Fluid Dyn. Res. 23, 349–370.Google Scholar
Choi, S. & Park, J.-K. 2008 Sheathless hydrophoretic particle focusing in a microchannel with exponentially increasing obstacle arrays. Anal. Chem. 80, 3035–3039.CrossRefGoogle Scholar
Choi, S., Song, S., Choi, C. & Park, J.-K. 2008 Sheathless focusing of microbeads and blood cells based on hydrophoresis. Small 4 (5), 634–641.CrossRefGoogle ScholarPubMed
Christi, Y. 2007 Biodiesel from microalgae. Biotechnol. Adv. 25, 294–306.CrossRefGoogle Scholar
Crowe, C., Sommerfeld, M. & Tsuji, Y. 1998 Multiphase Flows with Droplets and Particles, pp. 24–32. CRC Press.Google Scholar
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assembles. Geotechnique 29 (1), 47–65.CrossRefGoogle Scholar
Davis, J. A., Inglis, D. W., Morton, K. J., Lawrence, D. A., Huang, L. R., Chou, S. Y., Sturm, J. C. & Austin, R. H. 2006 Deterministic hydrodynamics: taking blood apart. Proc. Natl. Acad. Sci. USA 103, 14779–14784.Google Scholar
Di Carlo, D., Irimia, D., Tompkins, R. G. & Toner, M. 2007 Continuous inertial focusing, ordering and separation of particles in microchannels. Proc. Natl. Acad. Sci. USA 104 (48), 18892–18897.Google Scholar
Di Felice, R. 1994 The voidage function for fluid–particle interaction systems. Intl J. Multiph. Flow 20, 153–159.Google Scholar
Ferry, J. & Balachandar, S. 2003 A locally implicit improvement of the equilibrium Eulerian method. Intl J. Multiph. Flow 29, 869–891.CrossRefGoogle Scholar
Gradeck, M., Hoareau, B. & Lebouché, M. 2005 Local analysis of heat transfer inside corrugated channel. Intl J. Heat Mass Transfer 48, 1909–1915.CrossRefGoogle Scholar
Gschwind, P., Regele, A. & Kottke, V. 1995 Sinusoidal wavy channels with Taylor–Goertler vortices. Exp. Thermal Fluid Sci. 11, 270–275.CrossRefGoogle Scholar
Guzmán, A. M. & Amon, C. H. 1994 Transition to chaos in converging–diverging channel flows: Ruelle–Takens–Newhouse scenario. Phys. Fluids 6 (6), 1994–2002.Google Scholar
Guzmán, A. M. & Amon, C. H. 1996 Dynamical flow characterization of transitional and chaotic regimes in converging diverging channels. J. Fluid Mech. 321, 25–57.Google Scholar
Hampton, R. E., Mammoli, A. A., Graham, A. L., Tetlow, N. & Altobelli, S. A. 1997 Migration of particles undergoing pressure-driven flow in a circular conduit. J. Rheol. 41, 621–640.CrossRefGoogle Scholar
Han, M., Kim, C., Kim, M. & Lee, S. 1999 Particle migration in tube flow of suspensions. J. Rheol. 43 (5), 1157–1174.CrossRefGoogle Scholar
Hertz, H. 1882 Über die Berührung fester elastische Körper. J. reine Angew. Math. 92, 156–171.CrossRefGoogle Scholar
Ho, B. P. & Leal, L. G. 1974 Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65, 365–400.Google Scholar
Huang, L. R., Cox, E. C., Austin, R. H. & Sturm, J. C. 2004 Continuous particle separation through deterministic lateral displacement. Science 304, 987–990.Google Scholar
Issa, R. 1985 Solution of the implicit discretized fluid flow equations by operator splitting. J. Comput. Phys. 62, 40–65.Google Scholar
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle–wall collisions in a viscous fluid. J. Fluid Mech. 433, 329–346.Google Scholar
Kim, S. K. 2001 An experimental study of developing and fully developed flows in a wavy channel by PIV. KSME Intl J. 15 (12), 1853–1859.CrossRefGoogle Scholar
Lai, Y. G. 2000 Unstructured grid arbitrarily shaped element method for fluid flow simulation. AIAA J. 38 (12), 2246–2252.CrossRefGoogle Scholar
Lee, B. S., Kang, I. S. & Lim, H. C. 1999 Chaotic mixing and mass transfer enhancement by pulsatile laminar flow in an axisymmetric wavy channel. Intl J. Heat Mass Transfer 42, 2571–2581.Google Scholar
Leighton, D. & Acrivos, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.Google Scholar
Mahmud, S., Islam, A. K. M. S. & Mamun, M. A. H. 2002 Separation characteristics of fluid flow inside two parallel plates with wavy surface. Intl J. Engng Sci. 40, 1495–1509.Google Scholar
Marshall, J. S. 2006 Effect of shear-induced migration on the expulsion of heavy particles from a vortex core. Phys. Fluids 18 (11), 113301-1–113301-12.CrossRefGoogle Scholar
Marshall, J. S. 2007 Particle aggregation and capture by walls in a particulate aerosol channel flow. J. Aerosol Sci. 38, 333–351.CrossRefGoogle Scholar
Marshall, J. S. 2009 a Particle clustering in periodically-forced straining flows. J. Fluid Mech. 624, 69–100.CrossRefGoogle Scholar
Marshall, J. S. 2009 b Discrete-element modeling of particulate aerosol flows. J. Comput. Phys. 228, 1541–1561.CrossRefGoogle Scholar
Nieno, B. & Nobile, E. 2001 Numerical analysis of fluid flow and heat transfer in periodic wavy channels. Intl J. Heat Fluid Flow 22, 156–167.Google Scholar
Nishimura, T., Arakawa, S., Murakami, S. & Kawamura, Y. 1989 Oscillatory viscous flow in symmetric wavy-walled channels. Chem. Eng. Sci. 44 (10), 2137–2148.Google Scholar
Nishimura, T. & Kawamura, Y. 1995 Three-dimensionality of oscillatory flow in a two-dimensional symmetric sinusoidal wavy-walled channel. Exp. Thermal Fluid Sci. 10, 62–73.CrossRefGoogle Scholar
Nishimura, T., Murakami, S., Arakawa, S. & Kawamura, Y. 1990 Flow observations and mass transfer characteristics in symmetrical wavy-walled channels at moderate Reynolds numbers for steady flow. Intl J. Heat Mass Transfer 33 (5), 835–845.Google Scholar
Ormerod, M. G. 1999 Flow Cytometry. Springer-Verlag.Google Scholar
Oviedo-Tolentino, F., Romero-Méndez, R., Hernántez-Guerrero, A. & Girón-Palomares, B. 2008 Experimental study of fluid flow in the entrance of a sinusoidal channel. Intl J. Heat Fluid Flow 29, 1233–1239.Google Scholar
Putz, R. & Pabst, R. 2000 Sobotta Atlas of Human Anatomy, 13th edn., vol. 2. Lippincott, Williams and Wilkins.Google Scholar
Ralph, M. E. 1986 Oscillatory flows in wavy-walled tubes. J. Fluid Mech. 168, 515–540.Google Scholar
Rubinow, S. I. & Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447–459.Google Scholar
Rush, T. A., Newell, T. A. & Jacobi, A. M. 1999 An experimental study of flow and heat transfer in sinusoidal wavy passages. Intl J. Heat Mass Transfer 42, 1541–1553.Google Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400.Google Scholar
Saffman, P. G. 1968 Corrigendum to ‘The lift force on a small sphere in a slow shear flow’. J. Fluid Mech. 31, 624.Google Scholar
Sastre, R. R., Csögör, Z., Perner-Nochta, I., Fleck-Schneider, P. & Posten, C. 2007 Scale-down of microalgae cultivations in tubular photo-bioreactors – a conceptual approach. J. Biotechnol. 132, 127–133.Google Scholar
Savvides, G. N. & Gerrard, J. H. 1984 Numerical analysis of the flow through a corrugated tube with the application to arterial prosthesis. J. Fluid Mech. 138, 129–160.Google Scholar
Segre, G. & Silberberg, A. 1962 Behavior of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation. J. Fluid Mech. 14, 136–157.Google Scholar
Selvarajan, S., Tulapurkara, E. G. & Ram, V. V. 1999 Stability characteristics of wavy walled channel flows. Phys. Fluids 11 (3), 579–589.Google Scholar
Sobey, I. J. 1980 On flow through furrowed channels. Part 1. Calculated flow patterns. J. Fluid Mech. 96 (1), 1–26.Google Scholar
Stephanoff, K. D., Sobey, I. J. & Bellhouse, B. J. 1980 On flow through furrowed channels. Part 2. Observed flow patterns. J. Fluid Mech. 96 (1), 27–32.Google Scholar
Tsuji, Y., Tanaka, T. & Ishida, T. 1992 Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol. 71, 239–250.Google Scholar
Usha, R., Senthilkumar, S. & Tulapurkara, E. G. 2005 Stability characteristics of suspension flow through wavy-walled channels. Acta Mech. 176, 1–26.Google Scholar
Vasudeviah, M. & Balamurugan, K. 2001 On forced convective heat transfer for a Stokes flow in a wavy channel. Intl Commun. Heat Mass Transfer 28 (2), 289–297.Google Scholar