Application of Method-of-Lines Numerical Solutions to Nernst-Plank-Diffusion-Binding Mass Transport Equations to Quantum Dot Accumulation in Bacillus Subtilis Biofilms

Interactions between biofilms and nanoparticles (NPs) have gotten increasing interest amongst scientists for applications in medicine, ecotoxicity and biogeochemical cycling. Comprehensive health and safety assessments in these areas require models which quantify nanoparticle uptake into biofilms and consequent toxic effects, or nanoparticle-biofilm interaction models. To develop the nanoparticle-biofilm interaction models necessary for these applications, a mass-transport model for nanoparticle transport in biofilms was developed which accounts for nanoparticle diffusion and macro/microscale electrostatic interactions within biofilms. Nanoparticle diffusion and macroscale electrostatic interactions were captured using a modified Nernst-Plank equation. Microscale electrostatic interactions were accounted for using protein-type binding kinetics.  Dimensionless mass-transfer relations were developed from this model for different rate-limiting assumptions by solving the general component balance using both analytical and numerical techniques.  These relations were then applied to charged quantum dots diffusing in B. subtilis biofilms to predict qualitative behaviors of this system.