A numerical study of heat and mass transport in fibre suspensions
Abstract
Using slender body theory, periodic boxes, and the periodic solution to Laplace's equation, we develop a set of integral equations that are numerically solved to determine the effective conductivity of suspensions of highly conducting fibers and the effective reaction rate coefficient for the classical diffusioncontrolled reaction problem. Our problem formulation explicitly considers all fiberfiber interactions. It is valid for suspension concentrations up through the semidilute regime and for a wide variety of fiber shapes, including bluntended bodies. For the effective conductivity problem, fiberfiber interactions act to substantially enhance the effective conductivity beyond dilute theory predictions at suspension concentrations of nl(exp) equal to or greater than O(1), where n is the number density of fibers and l is the characteristic fiber halflength. The corresponding condition for the diffusioncontrolled reaction problem is nl(exp 3) equal to or greater than O(10(exp 3)). It is shown that for nl(exp 3) greater than O(1), the nondimensionalized screening length in the suspension depends only on the volume fraction of the inclusions both for aligned and isotropic suspensions. We believe this is the first computational verification of this prediction made originally by E. S. G. Shaqfeh and G. H. Fredrickson. The conductivity and reaction rate coefficients of the suspensions both through the dilute/semidilute transition and well into the semidilute regime are well predicted by dilute theories that consider some fiberfiber interactions. The same scaling behaviour for the transport coefficients and screening lengths is observed for both suspensions of spheroidal and cylindrical inclusions.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 October 1994
 DOI:
 10.1098/rspa.1994.0130
 Bibcode:
 1994RSPSA.447...77M
 Keywords:

 Conductors;
 Fibers;
 Heat Transfer;
 Mass Transfer;
 Slender Bodies;
 Suspending (Mixing);
 Concentration (Composition);
 Mathematical Models;
 Predictions;
 Proving;
 Fluid Mechanics and Heat Transfer