OSCILLATORY SHEAR OF A CONFINED FIBER SUSPENSION

Starting from a nonlocal description of the stress in a slender, rigid fiber:suspension [Schiek and Shaqfeh (1995)], we calculate the dynami c properties of a free-fiber suspension under oscillatory shear ina ve ry narrow gap. For a fiber suspension, three held quantities including the fluid velocity, the fiber concentration, and the fiber configurat ion strongly affect the suspension's behavior. When the width of the g ap confining the suspension is of the same scale as a suspended fiber' s length, then all three of the important field quantities change rapi dly on that scale. The nonlocal stress equation is coupled to the mome ntum conservation equation for the fluid velocity and a Fokker-Plank e quation for the fiber's probability density function resulting in a cl osed set of nonlinear, integrodifferential equations. These equations were solved in the limit of a small Peclet number, where Brownian moti on dominates, for arbitrary gap widths and oscillation frequencies. Fr om the calculated stress fields, we: obtained the real and imaginary v iscosities that one would measure in flow experiments. The dependence of all four dynamic properties on gap width was investigated and we fi nd that below a critical gap width (equivalent to one full fiber lengt h) all dynamic properties undergo dramatic changes. Additionally, as t he gap width shrinks, the relaxation time of the suspension was found to decrease, approaching the relaxation time of the pure Newtonian sol vent in the limit of zero gap width. Scalings for the relaxation time as a function of small gap width are also presented. (C) 1997 The Soci ety of Rheology.