FIBER ORIENTATION DISTRIBUTION IN CONCENTRATED SUSPENSIONS: A PREDICTIVE MODEL

A model is developed for the orientation distribution of rigid rod-like particles in a concentrated suspension under deformation. A general equation for the orientation distribution function is derived from basic statistical mechanics consideration and simple assumptions. The most important of these is that interactions are irreversible and statistically equivalent, and produce angle changes which are independent, identically distributed and with a zero mean. A relationship for the unknown parameter in the general equation, i.e., the mean square angular change,(' )((DELTA)(alpha))('2), is derived. This is a function of suspension properties such as particle aspect ratio and volume fraction, as well as the interaction coefficient, C(,I). A relationship for the particle motion which accounts for hydrodynamic effects as well as interactions is also derived.;The results of the data during orientation transients indicate that the value of C(,I) changes during deformation, i.e., that it is a function of the state of the suspension. Flow reversal data demonstrate that particle interactions are irreversible. Applications of the theory to predict the orientation of fibers during processing of short fiber reinforced polymer composites have already taken place very successfully, as in the case of compression molding of sheet molding compound.;A model system of nylon or polyester fibers in silicone oil is deformed under simple shear flow conditions, using a concentric cylinder (Couette flow) apparatus. Pictures are taken at steady state from which the distribution of fiber angles is computed and compared to the theory using a non-linear least square scheme. This technique provides not only the means to characterize the suspensions with a single parameter, i.e., the interaction coefficient C(,I), but also to measure experimentally the remaining unknown in the theory.