Computational simulations of magnetic particle capture in arterial flows.

The aim of Magnetic Drug Targeting (MDT) is to concentrate drugs, attached to magnetic particles, in a specific part of the human body by applying a magnetic field. Computational simulations are performed of blood flow and magnetic particle motion in a left coronary artery and a carotid artery, using the properties of presently available magnetic carriers and strong superconducting magnets (up to B approximately 2 T). For simple tube geometries it is deduced theoretically that the particle capture efficiency scales as [see text], with Mn (p) the characteristic ratio of the particle magnetization force and the drag force. This relation is found to hold quite well for the carotid artery. For the coronary artery, the presence of side branches and domain curvature causes deviations from this scaling rule, viz. eta approximately Mn (p) (beta) , with beta > 1/2. The simulations demonstrate that approximately a quarter of the inserted 4 microm particles can be captured from the bloodstream of the left coronary artery, when the magnet is placed at a distance of 4.25 cm. When the same magnet is placed at a distance of 1 cm from a carotid artery, almost all of the inserted 4 microm particles are captured. The performed simulations, therefore, reveal significant potential for the application of MDT to the treatment of atherosclerosis.

Magnetic particle motion in a Poiseuille flow.

The manipulation of magnetic particles in a continuous flow with magnetic fields is central to several biomedical applications, including magnetic cell separation and magnetic drug targeting. A simplified two-dimensional (2D) equation describing the motion of particles in a planar Poiseuille flow is considered for various magnetic field configurations. Exact analytical solutions are derived for the particle motion under the influence of a constant magnetization force and a force decaying as a power of the source distance, e.g., due to a current carrying wire or a magnetized cylinder. For a source distance much larger than the transversal size of the flow, a general solution is derived and applied to the important case of a magnetic dipole. This solution is used to investigate the dependence of the particle capture efficiency on the dipole orientation. A correction factor to convert the obtained 2D results to a three-dimensional cylindrical geometry is derived and validated against computational simulations. Simulations are also used to investigate parameter ranges beyond the region of applicability of the analytical results and to investigate more complex magnetic field configurations.

Influence of rarefaction on the flow dynamics of a stationary supersonic hot-gas expansion.

The gas dynamics of a stationary hot-gas jet supersonically expanding into a low pressure environment is studied through numerical simulations. A hybrid coupled continuum-molecular approach is used to model the flow field. Due to the low pressure and high thermodynamic gradients, continuum mechanics results are doubtful, while, because of its excessive time expenses, a full molecular method is not feasible. The results of the hybrid coupled continuum-molecular approach proposed have been successfully validated against experimental data by R. Engeln [Plasma Sources Sci. Technol. 10, 595 (2001)] obtained by means of laser induced fluorescence. Two main questions are addressed: the necessity of applying a molecular approach where rarefaction effects are present in order to correctly model the flow and the demonstration of an invasion of the supersonic part of the flow by background particles. A comparison between the hybrid method and full continuum simulations demonstrates the inadequacy of the latter, due to the influence of rarefaction effects on both velocity and temperature fields. An analysis of the particle velocity distribution in the expansion-shock region shows clear departure from thermodynamic equilibrium and confirms the invasion of the supersonic part of the flow by background particles. A study made through particles and collisions tracking in the supersonic region further proves the presence of background particles in this region and explains how they cause thermodynamic nonequilibrium by colliding and interacting with the local particles.

Hydraulic permeability of ordered and disordered single-layer arrays of cylinders.

The hydraulic permeability of single-layer fibrous media is studied through two-dimensional (2D) and three-dimensional Navier-Stokes based flow simulations. As simple representations of such materials, one-dimensional arrays of parallel cylinders as well as two-dimensional arrays of perpendicularly crossing cylinders were used. The distance between the cylinders was either constant (ordered layers) or variable (disordered layers). For both 1D and 2D ordered layers, we propose a geometrical scaling rule for the hydraulic permeability as a function of cylinder radius and solid volume fraction (porosity), which is a modification of a scaling rule previously reported by Clague and co-workers. The proposed modification is based on theoretical considerations and leads to significantly improved correspondence with simulation results. The hydraulic permeability of unstructured layers is found to be higher than that of structured layers of equal porosity for both 1D and 2D arrays. We propose a single parameter that can be easily determined experimentally to characterize the degree of disorder, as well as a generally valid correction factor in the proposed geometrical scaling rule to account for the influence of disorder on the hydraulic permeability.