A nonlocal theory for stress in bound suspensions of rigid, slender fibres is developed and used to predict the rheology of dilute, rigid polymer suspensions when confined to capillaries or fine porous media. Because the theory is nonlocal, we describe transport in a fibre suspension 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 resulting from the presence of solid boundaries around the suspension is included in our nonlocal stress theory and naturally gives rise to concentration gradients that scale on the length of the particle. Brownian motion of the rigid fibres is included within the nonlocal stress through a Fokker–Planck description of the fibres’ probability density function where gradients of this function are proportional to Brownian forces and torques exerted on the suspended fibres. This governing Fokker–Planck probability density equation couples the fluid flow and the nonlocal stress resulting in a nonlinear set of integral-differential equations for fluid stress, fluid velocity and fibre probability density. Using the method of averaged equations (Hinch 1977) and slender-body theory (Batchelor 1970), the system of equations is solved for a dilute suspension of rigid fibres experiencing flow and strong Brownian motion 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 solved self-consistently yielding average fluid velocity, shear and normal stress profiles within the gap as well as the probability density function for the fibres’ position and orientation. From these results we calculate concentration profiles, effective viscosities and slip velocities and compare them to experimental data.

This document is a reference guide to the Xyce Parallel Electronic Simulator, and is a companion document to the Xyce Users' Guide. The focus of this document is (to the extent possible) exhaustively list device parameters, solver options, parser options, and other usage details of Xyce. This document is not intended to be a tutorial. Users who are new to circuit simulation are better served by the Xyce Users' Guide. Trademarks The information herein is subject to change without notice.

We consider fibre migration across streamlines in a suspension under plane Poiseuille flow. The flow investigated lies between two infinite, parallel plates separated by a distance comparable to the length of a suspended fibre. We consider the weak flow limit such that Brownian motion strongly affects the fibre position and orientation. Under these conditions, the fibre distribution, fibre mobility and fluid velocity field all vary on scales comparable to the fibre's length thus complicating a traditional volumeaveraging approach to solving this problem. Therefore, we use a non-local derivation of the stress. The resulting fully coupled problem for the fluid velocity, fibre stress contribution and fibre distribution function is solved self-consistently in the limit of strong Brownian motion. When calculated in this manner, we show that at steady state the fibres’ centre-of-mass distribution function shows a net migration of fibres away from the centre of the channel and towards the channel walls. The fibre migration occurs for all gap widths (0 ≤ λ ≤ 35) and fibre concentrations (0 ≤ c ≤ 1.0) investigated. Additionally, the fibre concentration reaches a maximum value around one fibre half-length from the channel walls. However, we find that the net fibre migration is a relatively small change over the fibre's uniform bulk distribution, and typically the centre-of-mass migration changes the uniform concentration profile by only a few percent.

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This document is a reference guide to the Xyce Parallel Electronic Simulator, and is a companion document to the Xyce Users' Guide [1] . The focus of this document is (to the extent possible) exhaustively list device parameters, solver options, parser options, and other usage details of Xyce. This document is not intended to be a tutorial. Users who are new to circuit simulation are better served by the Xyce Users' Guide [1] . TrademarksThe information herein is subject to change without notice.