Abstract
In this chapterSuspension, we consider the simplest possible situation, namely, (rigid) solid particles that are much larger than the constituent elements (atoms or molecules) of the liquid in which they are immersed. A mixture of such particles and liquid is able to flow by virtue of the flow of interstitial liquid and the relative motions of the particles. As long as the particles are not in direct contact with one another, viscous energy dissipation is of hydrodynamic origin, which is to say, related to the flow of interstitial liquid. We begin by discussing the mechanical characteristics of a homogeneous and stable suspension of particles in a Newtonian liquid. We then review the specific effects of particle concentration, the orientation of anisotropic particles, a non-uniform spatial distribution of particles, and indeed the structure of this distribution. Finally, we discuss the case of particle suspensions in yield stress fluids.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A more direct mathematical demonstration is obtained by noting that the velocity can be expressed in the form \(\mathbf {u} = V\mathbf {u}^+\) and the length terms in the form \(\mathbf {x} = d\mathbf {x}^+\). The area terms can thus be written \(s=d^2s^+\) and the shear rates (components of \(\mathbf {D}\)) \(\dot{\gamma }_{ij}=(V/d)\dot{\gamma }_{ij}^+\). The drag force is then \(\mathbf {F}=2\mu Vd\int _{\mathrm{A}^+} \mathbf {D}^+\,\mathbf {\cdot \,n}\,\text {d}s^+\). In this expression, the integral is computed in terms of dimensionless variables \(\mathbf {x}^+,\mathbf {u}^+\), etc., and so depends only on the shape of the object. When one of the system parameters is modified, e.g., the speed or size of the object, we obtain a solution to the problem which is the unique solution by using the solution in terms of dimensionless variables and multiplying the lengths or velocities by the appropriate factor.
- 2.
See Ref. [10].
References
Richardson, J.F., Zaki, W.N.: Sedimentation and fluidisation, Part 1. Trans. Inst. Chem. Eng. 32, 35–53 (1954)
Batchelor, G.K.: The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570 (1970)
Einstein, A.: Eine neue bestimmung der moleküldimensionen. Ann. Physik 19, 289–306 (1906)
Krieger, I.M., Dougherty, T.J.: A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3, 137–152 (1959)
Jeffery, G.B.: The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179 (1922)
Shaqfeh, E.S.G., Fredrickson, G.H.: The hydrodynamic stress in a suspension of rods. Phys. Fluids A 2, 7–24 (1990)
Wagner, N.J., Brady, J.F.: Shear thickening in colloidal dispersions. Phys. Today 62, 27–32 (2009)
Beris, A.N., Tsamopoulos, J.A., Armstrong, R.C., Brown, R.A.: Creeping motion of a sphere through a Bingham plastic. J. Fluid Mech. 158, 219–244 (1985)
Ovarlez, G., Barral, Q., Coussot, P.: 3D jamming and flows of glassy materials. Nat. Mater. 9, 115–119 (2010)
Chateau, X., Ovarlez, G., Luu, T.K.: Homogenization approach to the behavior of suspensions of noncolloidal particles in yield stress fluids. J. Rheol. 52, 489–506 (2008)
Further Readings
Barthès-Biesel, D.: Microhydrodynamics and Complex Fluids. CRC Press, New York (2012)
Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (1967)
Guazzelli, E., Morris, J.F.: A Physical Introduction to Suspension Dynamics. Cambridge University Press, Cambridge (2011)
Guyon, E., Hulin, J.P., Petit, L.: Physical Hydrodynamics. Oxford University Press, Oxford (2001)
Munson, B.R., Young, D.F., Okiishi, T.H.: Fundamentals of Fluid Mechanics, 2nd edn. Wiley, New York (1994)
Ottino, J.M.: The Kinematics of Mixing: Stretching. Cambridge University Press, Cambridge, Chaos and Transport (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Coussot, P. (2014). Suspensions. In: Rheophysics. Soft and Biological Matter. Springer, Cham. https://doi.org/10.1007/978-3-319-06148-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-06148-1_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06147-4
Online ISBN: 978-3-319-06148-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)