A NONLOCAL THEORY FOR STRESS IN BOUND, BROWNIAN SUSPENSIONS OF SLENDER, RIGID FIBERS

A nonlocal theory for stress in bound suspensions of rigid, slender fi bres is developed and used to predict the theology of dilute, rigid po lymer suspensions when confined to capillaries or fine porous media. B ecause the theory is nonlocal, we describe transport in a fibre suspen sion where the velocity and concentration fields change rapidly on the fibre's characteristic length. Such rapid changes occur in a rigidly bound domain because suspended particles are sterically excluded from configurations near the boundaries. A rigorous no-flux condition resul ting from the presence of solid boundaries around the suspension is in cluded in our nonlocal stress theory and naturally gives rise to conce ntration gradients that scale on the length of the particle. Brownian motion of the rigid fibres is included within the nonlocal stress thro ugh a Fokker-Planck description of the fibres' probability density fun ction where gradients of this function are proportional to Brownian fo rces and torques exerted on the suspended fibres. This governing Fokke r-Planck probability density equation couples the fluid flow and the n onlocal stress resulting in a nonlinear set of integral-differential e quations for fluid stress, fluid velocity and fibre probability densit y. Using the method of averaged equations (Hinch 1977) and slender-bod y theory (Batchelor 1970), the system of equations is solved for a dil ute suspension of rigid fibres experiencing flow and strong Brownian m otion while confined to a gap of the same order in size as the fibre's intrinsic length. The full solution of this problem, as the fluid in the gap undergoes either simple shear or pressure-driven flow is solve d self-consistently yielding average fluid velocity, shear and normal stress profiles within the gap as well as the probability density func tion for the fibres' position and orientation. From these results we c alculate concentration profiles, effective viscosities and slip veloci ties and compare them to experimental data.