Non-Brownian Fiber Suspensions

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). 

Since Brownian motion can be neglected, the stress tensor for a suspension of rigid fibers can be obtained from Eq. (6-36) simply by dropping the Brownian term  

In a dilute suspension of cylindrical fibers, the coefficient is given by Eqs. (6-37) and (6-38). As discussed in Section 6.3.2.1, suspensions of high-aspect-ratio rods are not dilute 

For semidilute suspensions of long rods, Batchelor (1971) developed a theory of hydrodynamic screening, from which he estimated 

A semirigorous multiple-scattering theory of Shaqfeh and Fredrickson (1990) that accounts for multiparticle hydrodynamic interactions for slender bodies has verified Batchelor s theory and has given a slightly improved formula for str  

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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.------------------... 

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. 

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... 

Ottinger (1996) combined the Brownian dynamics simulation technique with finite elements to solve polymer flow problems. The approach has been introduced as the CONNFFESSIT (Calculation of Non-Newtonian Flow Finite Element and Stochastic Simulation Techniques) approach. Hulsen et al. (1997) extended the approach to the so-called Brownian configuration field (BCF) method, which treats the stochastic equation as the stochastic field equation, and hence avoids the difficulties associated with individual molecule tracking. If the BCF is applied to fiber suspension flows, the vectors p and q will be functions of space and time. The discrete equation for the time evolution is... 

Chaouche, M. Koch, D.L. 2001. Rheology of non-Brownian Rigid Fiber Suspensions with Adhesive Contacts. J. Rheol. 45 (2) 369-382... 

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