Problem Formulation and Initial Integral Equations; Averaging Method

2008 ◽  
pp. 1-14
Author(s):  
Mikhail V. Nesterenko ◽  
Victor A. Katrich ◽  
Yuriy M. Penkin ◽  
Sergey L. Berdnik
Keyword(s):  
Integral Equations ◽  
Averaging Method ◽  
Problem Formulation

A numerical study of the rheological properties of suspensions of rigid, non-Brownian fibres

1996 ◽  
Vol 329 ◽  
pp. 155-186 ◽  
Author(s):  
Michael B. Mackaplow ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Integral Equations ◽  
Numerical Study ◽  
Problem Formulation ◽  
Viscosity Data ◽  
Slender Body Theory ◽  
Aspect Ratios ◽  
Wide Range ◽  
Orientation Distributions ◽  
Theological Properties ◽  
Body Theory

Using techniques developed in our previous publication (Mackaplow et al. 1994), we complete a comprehensive set of numerical simulations of the volume-averaged stress tensor in a suspension of rigid, non-Brownian slender fibres at zero Reynolds number. In our problem formulation, we use slender-body theory to develop a set of integral equations to describe the interfibre hydrodynamic interactions at all orders. These integral equations are solved for a large number of interacting fibres in a periodically extended box. The simulations thus developed are an accurate representation of the suspensions at concentrations up to and including the semidilute regime. Thus, large changes in the suspensions properties can be obtained. The Theological properties of suspensions with concentrations ranging from the dilute regime, through the dilute/semi-dilute transition, and into the semi-dilute regime, are surprisingly well predicted by a dilute theory that takes into account two-body interactions. The accuracy of our simulations is verified by their ability to reproduce published suspension extensional and shear viscosity data for a variety of fibre aspect ratios and orientation distributions, as well as a wide range of suspension concentrations.

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