Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T03:09:47.858Z Has data issue: false hasContentIssue false
  • English
  • Français

Cross-streamline migration of slender Brownian fibres in plane Poiseuille flow

Published online by Cambridge University Press:  10 February 1997

Richard L. Schiek  and
Eric S. G. Shaqfeh
Richard L. Schiek
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305-5025, USA
Eric S. G. Shaqfeh
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305-5025, USA
Get access Rights & Permissions [Opens in a new window]

Extract

We consider fibre migration across streamlines in a suspension under plane Poiseuille flow. The flow investigated lies between two infinite, parallel plates separated by a distance comparable to the length of a suspended fibre. We consider the weak flow limit such that Brownian motion strongly affects the fibre position and orientation. Under these conditions, the fibre distribution, fibre mobility and fluid velocity field all vary on scales comparable to the fibre's length thus complicating a traditional volumeaveraging approach to solving this problem. Therefore, we use a non-local derivation of the stress. The resulting fully coupled problem for the fluid velocity, fibre stress contribution and fibre distribution function is solved self-consistently in the limit of strong Brownian motion. When calculated in this manner, we show that at steady state the fibres’ centre-of-mass distribution function shows a net migration of fibres away from the centre of the channel and towards the channel walls. The fibre migration occurs for all gap widths (0 ≤ λ ≤ 35) and fibre concentrations (0 ≤ c ≤ 1.0) investigated. Additionally, the fibre concentration reaches a maximum value around one fibre half-length from the channel walls. However, we find that the net fibre migration is a relatively small change over the fibre's uniform bulk distribution, and typically the centre-of-mass migration changes the uniform concentration profile by only a few percent.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 332 , February 1997 , pp. 23 - 39
Copyright
Copyright © Cambridge University Press 1997

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

Aubert, J. H. & Tirrell, M. 1982 Effective viscosity of dilute polymer solutions near confining boundaries. J. Chem. Phys. 77, 553–561.CrossRefGoogle Scholar
Agarwal, U. S., Dutta, A. & Mashelkar, R. A. 1994 Migration of macromolecules under flow: the physical origin and engineering implications. Chem. Engng Sci. 49, 1693–1717.CrossRefGoogle Scholar
Ausserre, D., Edwards, J., Lecourtier, J., Hervet, H. & Rondelex, F. 1991 Hydro-dynamic thickening of depletion layers in colloidal solutions. Europhys. Lett, 14, 33–38.Google Scholar
Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419–140.CrossRefGoogle Scholar
Brenner, H. 1973 Rheology of a dilute suspension of axisymmetric Brownian particles. Intl J. Multiphase Flow 1, 195–341.CrossRefGoogle Scholar
Brunn, P. O. & Kaloni, P. N. 1985 Concentrated polymer solutions: nonuniform concentration profiles in tube flow. J. Chem. Phys. 83, 2497–2503.Google Scholar
Chandrasekhar, S. 1943 Stochastic problms in physics and astronomy. Rev. Mod. Phys. 15, 1–89.CrossRefGoogle Scholar
Chauveteau, G. 1982 Rodlike polymer solution flow through fine pores: influence of por size on rheological behavior. J. Rheol. 26, 111–142.CrossRefGoogle Scholar
Doi, M. & Edwards, S. F. 1989 The Theory of Polymer Dynamics. Oxford Science Publications.Google Scholar
Erdélyi, A. 1956 Asymptotic Expansions. Dover.Google Scholar
Hinch, E. J. & Leal, L. G. 1992 The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J. Fluid Mech. 52, 683–712.CrossRefGoogle Scholar
Hinch, E. J. & Leal, L. G. 1975 Constitutive equations in suspension mechanics. Part 1. General formulation. J. Fluid Mech. 71, 418–495.CrossRefGoogle Scholar
Hinch, E. J. & Leal, L. G. 1976 Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations. J. Fluid Mech. 76, 187–208.Google Scholar
Magda, J. J., Tirrell, M. & Davis, H. 1988 The transport properties of rod-like particles. II. Narrow slit pores. J. Chem. Phys. 88, 1207–1213.Google Scholar
McQuarrie, D. A. 1976 Statistical Mechanics. Harper Collins.Google Scholar
Metzner, A. B., Cohen, Y. & Rangel-Nafaile, C. 1979 Inhomogeneous flows of non-Newtonian fluids: generation of spatial concentrations gradients. J. Non-Newtonian Fluid Mech. 5, 449–462.Google Scholar
Nitsche, J. M. 1991 Hydrodynamic coupling and non-equilibrium distribution in pore diffusion of nonspherical fine particles. Particulate Sci. Tech. 9, 135–148.Google Scholar
Nitsche, J. M. & Brenner, H. 1990 On the formulation of boundary conditions for rigid nonspherical Brownian particles near solid walls: applications to orientation-specific reactions with immobilized enzymes. J. Colloid Interface Sci. 138, 21–41.Google Scholar
Nitsche, L. C. & Hinch, E. J. 1997 Shear-induced lateral migration of Brownian rigid rods in parabolic channel flow. J. Fluid Mech. 332, 1–21.CrossRefGoogle Scholar
Schiek, R. L. & Shaqfeh, E. S. G. 1995 A nonlocal theory for stress in bound, Brownian suspensions of slender, rigid fibers. J. Fluid Mech. 296, 271–324.Google Scholar
Sorbie, K. S. & Huang, Y. 1991 Rheological and transport effects in the flow of low-concentration Xanthan solution through porous media. J. Colloidal Interface Sci. 145, no. 1, 74–89.CrossRefGoogle Scholar
Stryer, L. 1988 Biochemistry. W. H. Freeman.Google Scholar
Weisel, J. W., Phillips, G. N. Jr & Cohen, C. 1981 A model from electron microscopy for the molecular structure of fibrinogen and fibrin. Nature 289, 263–267.CrossRefGoogle Scholar