Paper number 339
Charles A. Petty, Steven M. Parks, Shiwei, M. Shao
Department of Chemical Engineering
Michigan State University
East Lansing, MI 48824, USA
||The temporal response of a fiber suspension subjected to a homogeneous shear field is examined by solving a closed evolution equation for the second-order moment of the orientation distribution function. The dyadic-valued moment equation is integrated from three different initial states: isotropic, planar isotropic, and uniaxially aligned. For all cases, the suspension relaxes to a unique orientation state parameterized by a fiber/fiber interaction coefficient. All the instantaneous states predicted by the theory are physically realizable inasmuch as the eigenvalues of the orientation dyadic are non-negative. Closure of the moment equation is achieved by using an approximate model for the orientation tetradic that preserves the six-fold symmetry and contraction properties of the exact tetradic operator. The calculations compare favorably with the temporal response of the orientation dyadic calculated directly from the fiber orientation distribution function.
|| fiber alignment, orientation distribution function, orientation dyadic, orientation tetradic, realizability, fiber/fluid interactions, fiber/fiber interactions, closure approximation, homogeneous shear.
Theme : Processing, Integrated Design and Manufacturing ; Machining and Tooling
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