Anisotropic rotary diffusion model

There is no compelling reason to assume isotropy in the rotary diffusivity, and in the general case, one may expect an anisotropic interaction coefficient and write it in a tensor form (see. Fan et al. 1998 Phan-Thien et al. 2002). The scale value of Cl shown in Fig. 5.3 can be defined as one-third of the trace of the interaction coefficient tensor. The anisotropic rotary diffusion model will be described in the next Section. 

5 Modifications to Folgar-Tucker Model 5.5.1 Anisotropic Rotary Diffusion Model 

Fan et al. (1998) considered that the diffusion constant could be anisotropic, and they still assumed it proportional to the generalized shear rate, with the constant of proportionality given by a second-order symmetric tensor C. 

5 Flow-Induced Alignment in Short-Fiber Reinforced Polymers 

Phelps and Tucker (2009) further assumed that C could also be a function of the orientation tensor, and they proposed the following expression  

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J. H. Phelps and C. L. Tucker m. An anisotropic rotary diffusion model for fiber orientation in short-and long-fiber thermoplastics. Journal of Non-Newtonian Fluid Mechanics, 156,165-176 (2009). 

Before discussing theoretical models for the rheology of fiber suspensions and its connection to fiber orientation, there are three topics that must be discussed Brownian motion, concentration regimes, and fiber flexibility. Brownian motion refers to the random movement of any sufficiently small particle as a result of the momentum transfer from suspending medium molecules. The relative effect that Brownian motion may have on orientation of anisotropic particles in a dynamic system can be estimated using the rotary Peclet number, Pe s y Dm, where y is the shear rate and Ao is the rotary diffusivity, which defines the ratio of the thermal energy in the system to the resistance to rotation. Doi and Edwards (1988) estimated the rotary diffusivity, Ao, to be... 

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