In this paper, an efficient ghost-cell
based immersed boundary
method is applied to perform direct numerical simulation (DNS) of
mass transfer problems in particle clusters. To be specific, a nine-sphere
cuboid cluster and a random-generated spherical cluster consisting
of 100 spheres are studied. In both cases, the cluster is composed
of active catalysts and inert particles, and the mutual influence
of particles on their mass transfer performance is studied. To simulate
active catalysts the Dirichlet boundary condition is imposed at the
external surface of spheres, while the zero-flux Neumann boundary
condition is applied for inert particles. Through our studies, clustering
is found to have negative influence on the mass transfer performance,
which can be then improved by dilution with inert particles and higher
Reynolds numbers. The distribution of active/inert particles may lead
to large variations of the cluster mass transfer performance, and
individual particle deep inside the cluster may possess a high Sherwood
number.