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 fibres and the effective reaction rate coefficient for the classical diffusion-controlled reaction problem. Our problem formulation explicitly considers all fibre–fibre interactions. It is valid for suspension concentrations up through the semi-dilute régime and for a wide variety of fibre shapes, including blunt-ended bodies. For the effective conductivity problem, fibre–fibre interactions act to substantially enhance the effective conductivity beyond dilute theory predictions at suspension concentrations of
nl
3
≽
O
(1), where
n
is the number density of fibres and
l
is the characteristic fibre half-length. The corresponding condition for the diffusion-controlled reaction problem is
nl
3
≽
O
(10
-5
). It is shown that for
nl
3
>
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 régime are well predicted by dilute theories that consider some fibre–fibre interactions. The same scaling behaviour for the transport coefficients and screening lengths is observed for both suspensions of spheroidal and cylindrical inclusions.
1P281 Diffusion-controlled reaction rate-laws in intracellular environment with molecular crowding: A single-particle-level simulation study(24. Mathematical biology,Poster)
