Suspensions non-Brownian

From the 1970s, a large number of imaging studies of non-Brownian suspensions flowing in mm- to cm-sized channels have been performed via Laser Doppler Veiocimetry [120-123] and NMRI [124,125], but little information has been obtained at the single-particle level. Optical microscopy experiments on channel flows of colloids have only recently started to appear, often in relation to microfluidics applications [126]. To avoid image distortions, channels witli square or rectangular cross sections are preferred to cylindrical capillaries. 

Dbouk, T, Lobry, L., and Lemaire, E. 2013. Normal stresses in concentrated non-Brownian suspensions. /. Fluid Mech. 715, 239-272. 

Garland, S., Gauthier, G., Martin, J., and Morris, J. E. 2013. Normal stresses measurements in sheared non-Brownian suspensions. J. Rheol. 57, 71. 

Kromkamp, J., van den Ende, D. T. M., Kandhai, D., van der Sman, R. G. M., and Boom, R. M. 2005. Shear-induced self-diffusion and microstructure in non-Brownian suspensions at non-zero Reynolds numbers. /. Fluid Mech. 529, 253-278. 

The crossover from Brownian to non-Brownian behavior in a flowing suspension is controlled by a rotational Peclet number. 

Brownian rod-like objects of high aspect ratio are usually molecules, not colloidal particles. As exception is tobacco mosaic virus (TMV), which is a Brownian particle of length 300 nm and diameter 18 nm (Caspar 1963). For completeness, we shall discuss the theory of Brownian rod-like particles in this chapter, with the understanding that the theory for such particles is actually more relevant to long stiff molecules than to rod-like fibers. The behavior of non-Brownian fiber suspensions is covered in Section 6.3.2.2.------------------... 

As mentioned earlier, suspensions of particulate rods or fibers are almost always non-Brownian. Such fiber suspensions are important precursors to composite materials that use fiber inclusions as mechanical reinforcement agents or as modifiers of thermal, electrical, or dielectrical properties. A common example is that of glass-fiber-reinforced composites, in which the matrix is a thermoplastic or a thermosetting polymer (Darlington et al. 1977). Fiber suspensions are also important in the pulp and paper industry. These materials are often molded, cast, or coated in the liquid suspension state, and the flow properties of the suspension are therefore relevant to the final composite properties. Especially important is the distribution of fiber orientations, which controls transport properties in the composite. There have been many experimental and theoretical studies of the flow properties of fibrous suspensions, which have been reviewed by Ganani and Powell (1985) and by Zimsak et al. (1994). 

Figure 6.23 The relative viscosity at steady state of suspensions of non-Brownian rod-like particles versus dimensionless concentration vL. Simulations for p = L/d = 16.9 ( ), 31.9 (A) Bibbo s (1987) experimental results for L/d = 16.9 (O). and 31.9 (A). (Reprinted from J Non-Newt Fluid Mech 54 405, Yamane et al. (1994), with kind permission from Elsevier Science - NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

The viscous and elastic properties of orientable particles, especially of long, rod-like particles, are sensitive to particle orientation. Rods that are small enough to be Brownian are usually stiff molecules true particles or fibers are typically many microns long, and hence non-Brownian. The steady-state viscosity of a suspension of Brownian rods is very shear-rate- and concentration-dependent, much more so than non-Brownian fiber suspensions. The existence of significant normal stress differences in non-Brownian fiber suspensions is not yet well understood. 

This section reviews the application of (confocal) imaging to study the flow response of concentrated suspensions, with emphasis on quantitative analysis as described in the previous sections. We separately discuss disordered systems and systems in which order is present either before or as a result of flow. In each case, the focus is on Brownian systems, but we briefly review non-Brownian systems at the end of each subsection. 

A more fundamental approach is to consider the rheological properties with dynamical properties. For a given rate-of-strain tensor E and moments of the orientation vector p, Batchelor (110) derived an expression for the bulk average deviatoric stress a for a suspension of non-Brownian fibers of large aspect ratio given by... 

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