Non-Newtonian matrix suspensions

Most suspension theories assume that the suspending medium is a Newtonian fluid. However, in the injection molding process, fibers are dispersed in polymeric liquids, which in most cases are non-Newtonian. Joseph and Liu (1993) have 

5 Flow-Induced Alignment in Short-Fiber Reinforced Polymers 

Housiadas and Tanner (2009), following the approach of Greco et al. (2005), have used a perturbation analysis to obtain the analytical solution for the pressure and the velocity field up to 0 (pDe) of a dilute suspension of rigid spheres in a weakly viscoelastic fluid, where p is the volume fraction of the spheres and De is the Deborah number of the viscoelastic fluid. The analytical solution was used to calculate the bulk first and second normal stress in simple shear flows and the elongational viscosity. The main results are 

Tanner et al. (2010a) have extended the above results to concentrated regimes by using the Roscoe procedure (Roscoe 1952, also see Phan-Thien and Pham 2000). In concentrated suspensions, some of the fluid is trapped between particles, and hence Roscoe (1952) suggested that the increment of small amount of volume fraction d(p results in an effective increase of concentration of d(p/ — (p/(p ), which is called the crowding function, where (j is the maximum volume fraction. We use N ) as an example to describe the procedure. From Eq. 5.61, one has 

From what was described above, the Roscoe approach can be briefly summarized as follows  

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