Prediction Models of Inertial Particle Transport Using a Combined Lattice Boltzmann - Immersed Boundary Method

Low Reynolds number flows involve different fields of technical interest, such as flows confined to very small section ducts, or generally flows involving small geometries, such as those of interest in the biomedical field; or flows for which viscous forces have a dominant role as in the case of lubrication problems. At very small scales the distance between the molecules constituting the fluid becomes comparable to the cha-racteristic size of the problem, so that their mutual behavior, in terms of collisions, has to be modelled. At this scales and low Reynolds flows, the continuos model described by Navier-Stokes equation can become inadequate, where instead the so called mesoscopic approach is justified. It is placed in an intermediate position between the molecular dynamics, and the description based on the continuous fluid of the Navier-Stokes equations. The model based on the Boltzmann equation provides a mesoscopic approach based on a probability density function, commonly called distribution function.The model can describe non-stationary flows at scales of interest in the biological field. The numerical method used to solve the boltzmann equation for the problems on which the work is focused is the Lattice-Boltzmann Method (LBM), and a parallel three-dimensional code for the simulation of low Reynolds number flows was developed and tested. The unsteady problem of technological interest is the transport of nanoparticles and microparticles, it involves the study of the fluid structure interaction over time. An Immersed Boundary (IB) method was implemented into the code to simulate the presence of bodies surrounded by the flow. and is used to compute the hydrodynamic stresses acting on an immersed rigid or deformable particle. The combined Lattice Boltzmann-Immersed Boundary method represents a good compromise between accuracy and computational burden into the simulation of rigid and deformable moving particles. The fluid–structure interaction has often been investigated through kinetic models, in which the immersed particles motion depends only on the velocity field surrounding them, the peculiar novelty and improvement of this work is to consider a dynamic fluid–structure interaction method, for which the motion is solved considering the hydrodynamics forces exchanged through the body boundaries. A set of other models are selected to simulate the deformation of the particles and the adhesion phenomena and behaviour in walls proximity. This allows the study of several biomedical cases with the accuracy that some physical phenomena require.