(148b) A Lagrangian Particle Method as An Alternative to Solute Lattice Boltzmann: Investigation of Mass Transfer in Biological Porous Media

Voronov, R. S., University of Oklahoma
VanGordon, S., University of Oklahoma
Landy, B., University of Oklahoma
Sikavitsas, V. I., University of Oklahoma

An effective and inherently parallelizable numerical method for the simulation of microfluidic flows in complicated geometries is the Lattice Boltzmann Method (LBM). Although several methods exist for modeling solute transport with LBM (for example in multi-component LBM the second component can mimic a solute, when its non-local interaction with the bulk fluid is grossly reduced), these methods are set in the Eulerian framework. Useful statistical quantities, such as the solute survival distance, survival time, effective diffusion coefficient, collision frequency, etc. cannot be extracted directly from such simulations. Moreover, just as in the case of classical LBM, the range of solute diffusivity that can be modeled is limited by the numerical solute's relaxation time. As an alternative to these methods, our work presents a Lagrangian approach to simulating convective scalar transfer in conjunction with LBM.

A house hybrid MPI/Open MP parallelized scheme is employed in order to take advantage of the inherent LBM parallelizability. Macroscopic mass transfer is modeled using the Lagrangian scalar tracking (LST) method (Papavassiliou, Int. J. Heat Mass Transfer, 45(17), 3571-3583, 2002) in conjunction with the LBM algorithm. In LST, the motion of scalar markers is used to synthesize the scalar profile. The trajectories of these markers are composed by a convection part (obtained using the velocity field from the LBM simulations) and a diffusion part (i.e., Brownian motion obtained from a mesoscopic Monte-Carlo approach). This method is resourceful in terms of computational efficiency, in that it can be used to simulate various Schmidt number fluids with a single flow field resulting from an LBM simulation. In addition, modifications of the LST algorithm allow the simulation of a whole spectrum of solute reaction rates, also using just a single flow field obtained from LBM.

The presentation will include the description of the numerical methodology and the validation of the method for known cases of flow in porous media. The usefulness of LST will be demonstrated for the particular case of flow through biodegradable synthetic porous polymer scaffolds, which are used in flow perfusion bioreactors for the growth of bone tissue as potential replacement therapies for damaged or lost bone tissue. Knowledge of the mechanism of mass transfer of nutrients to osteoblast cells growing within the porous scaffold can be obtained from LST simulations, allowing the optimization of the 3D scaffold structure for enhanced tissue growth. Micro-Computed Tomography scans of the bone tissue growth along with computer simulation results are used to obtain insights into the tissue growth process with the ultimate goal of being able to predict where the tissue will grow a priori ? based only on the plain scaffold geometry and the flow rates.