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 diffusion-controlled reaction problem. Our problem formulation explicitly considers all fiber-fiber interactions. It is valid for suspension concentrations up through the semi-dilute regime and for a wide variety of fiber shapes, including blunt-ended bodies. For the effective conductivity problem, fiber-fiber 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 half-length. The corresponding condition for the diffusion-controlled 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 non-dimensionalized 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/semi-dilute transition and well into the semi-dilute regime are well predicted by dilute theories that consider some fiber-fiber 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