Hierarchical hybrid simulation of biofilm growth dynamics in 3D porous media

Recently, we developed the first hierarchical, hybrid simulator for the prediction of the pattern of evolution and the rate of growth of heterogeneous biofilms within the pore space of porous media [Kapellos et al., Adv. Water Resour. (2007) 30:1648-1667]. A n improved version of our simulator is presented in this work. A continuum-based approach for fluid flow and solute transport is combined with individual-based approaches for biofilm growth, detachment, and migration in the pore space. The Navier-Stokes-Brinkman equations are solved numerically with a marker-and-cell finite difference scheme to determine the velocity and pressure fields in the pore space. Momentum transport in the biofilms is described in the context of biphasic poroelasticity and a Galerkin finite element method is used to determine the solid stress field. Shear-induced biofilm detachment is taken into account explicitly and a Lagrangian-type simulation is used to determine the trajectories of detached fragments. Nutrient transport in the pore space is described by the convectiondiffusion- reaction equation, which is solved numerically with an operator-splitting finite difference scheme. Further, a novel, physically-constrained cellular-automaton model is used for biofilm proliferation. As an example application, the simulator is used to investigate the impact of biofilm formation on the fate and transport of suspended particles in a network of three-dimensional pores

Computational study of the interaction between a newtonian fluid and a cellular biological medium in a straight vessel

In this work, we solve numerically the governing equations for quasi-steady Newtonian flow past and through a cellular biological medium, which is attached to the surface of a straight vessel. The flow past the cellular biological medium is described by the Navier-Stokes equations. For the modeling of momentum transfer within the cellular biological medium, we consider that the cellular biological medium constitutes a biphasic fluid-solid mixture with poroelastic behaviour. The system of governing equations is solved numerically with the mixed finite element method. The computational domain is discretized using an unstructured, variable density triangular element mesh. From the numerical solution we obtain the spatial distributions of: (i) the fluid velocity and pressure, and (ii) the displacement and stresses of the solid matrix within the cellular biological medium. Also, the components of the overall hydrodynamic force exerted by the flowing fluid on the cellular biological medium are calculated. A parametric analysis is performed with regard to the Reynolds and Darcy numbers that characterize the flow past and through the cellular biological medium