Diffusion Reaction Interaction for a Pair of Spheres - ETD ...

Marshall, 1990; Converti et al., 1997), production of foods such as tea, coffee,
and fruit juices (Geankoplis, 1993), mold fermentations (Shuler and Kargi, 1992)
and cellular communication (Lauffenberger and Linderman, 1993). The
Smoluchowski (1916) solution only covers the infinitely dilute system where each
particle acts as an independent entity and there is no interaction between
neighboring spheres (Mattern and Felderhof, 1987). Truly, in most natural and
industrial applications this solution is inadequate because neighboring particles
are close enough to influence each other.
In the natural, chemical and biological systems mentioned above there is a
significant amount of diversity. In biological systems diffusion controls the
kinetic rates of many processes from protein-protein encounters (Zhou, 1997 and
Northrup and Erickson, 1992), to ligand binding (Lesyng and McCammon, 1993
and Northrup et al., 1984) to signal transmission across synaptic interfaces (Frank
et al., 2002 and Zoli and Agnati, 1996). In particular, the biotechnology industry
mammalian cells and microorganisms are used to biologically synthesize a wide
range of products from polymers to antibiotics to insulin (Converti et al., 1994).
This industry has grown to exceed $17 billion (Amundson, 1988). Biosynthesis
usually involves many types of microorganisms and each organism may be
capable of more than 1,000 different reactions (Bailey and Ollis, 1986) therefore
there is significant variation in microorganism type, shape, size, kinetic type and
strength of the cells (Wang et al., 1979). One positive implication of diversity is
bioremediation where co-metabolism by a consortia, or multiple species working
together, allows otherwise persistent pollutants to be degraded to benign
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