Paper number 339


Charles A. Petty, Steven M. Parks, Shiwei, M. Shao

Department of Chemical Engineering
Michigan State University
East Lansing, MI 48824, USA

Summary 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.
Keywords 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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