Analytical modelling of bacterial migration and accumulation with rate-limited sorption in discrete fractures

An analytical model for bacterial accumulation in a discrete fractllre has been developed. The transport and accumlllation processes incorporate into the model include advection, dispersion, rate-limited adsorption, rate-limited desorption, irreversible adsorption, attachment, detachment, growth and first order decay botl1 in sorbed and aqueous phases. An analytical solution in Laplace space is derived and nlln1erically inverted. The model is implemented in the code BIOFRAC vvhich is written in Fortran 99. The model is derived for two phases, Phase I, where adsorption-desorption are dominant, and Phase II, where attachment-detachment are dominant. Phase I ends yvhen enollgh bacteria to fully cover the substratllm have accllillulated. The model for Phase I vvas verified by comparing to the Ogata-Banks solution and the model for Phase II was verified by comparing to a nonHomogenous version of the Ogata-Banks solution. After verification, a sensitiv"ity analysis on the inpllt parameters was performed. The sensitivity analysis was condllcted by varying one inpllt parameter vvhile all others were fixed and observing the impact on the shape of the clirve describing bacterial concentration verSllS time. Increasing fracture apertllre allovvs more transport and thus more accllffilliation, "Vvhich diminishes the dllration of Phase I. The larger the bacteria size, the faster the sllbstratum will be covered. Increasing adsorption rate, was observed to increase the dllration of Phase I. Contrary to the aSSllmption ofllniform biofilm thickness, the accllffilliation starts frOll1 the inlet, and the bacterial concentration in aqlleous phase moving towards the olitiet declines, sloyving the accumulation at the outlet. Increasing the desorption rate, redllces the dliration of Phase I, speeding IIp the accllmlilation. It was also observed that Phase II is of longer duration than Phase I. Increasing the attachment rate lengthens the accliffililation period. High rates of detachment speeds up the transport. The grovvth and decay rates have no significant effect on transport, althollgh increases the concentrations in both aqueous and sorbed phases are observed. Irreversible adsorption can stop accllillulation completely if the vallIes are high.

Cyclotetrasiloxane Frameworks for the Chemoenzymatic Synthesis of Oligoesters

Immobilized lipase B from Candida antarctica (Novozym® 435, N435) was utilized as part of a chemoenzymatic strategy for the synthesis of branched polyesters based on a cyclotetrasiloxane core in the absence of solvent. Nuclear magnetic resonance spectroscopy and matrix-assisted laser desorption ionization time-of-flight mass spectrometry were utilized to monitor the reactions between tetraester cyclotetrasiloxanes and aliphatic diols. The enzyme-mediated esterification reactions can achieve 65– 80% consumption of starting materials in 24–48 h. Longer reaction times, 72–96 h, resulted in the formation of cross-linked gel-like networks. Gel permeation chromatography of the polymers indicated that the masses were Mw ¼ 11 400, 13 100, and 19 400 g mol 1 for the substrate pairs of C7D4 ester/ octane-1,8-diol, C10D4 ester/pentane-1,5-diol and C10D4 ester/octane-1,8-diol respectively, after 48 h. Extending the polymerization for an additional 24 h with the C10D4 ester/octane-1,8-diol pair gave Mw ¼ 86 800 g mol 1. To the best of our knowledge this represents the first report using lipase catalysis to produce branched polymers that are built from a cyclotetrasiloxane core.