Permeability and stress-jump effects on magnetic drug targeting in a permeable microvessel using Darcy model

In the present paper, we investigated the influence of permeability of the carrier particle and stress jump condition on the porous spherical surface in magnetic drug targeting through a permeable microvessel. The nature of blood is defined by non-Newtonian Casson fluid in the core region of the microvessel and Newtonian fluid in the peripheral region which is located near the surface of the wall of the microvessel. The magnetic particles are considered as spherical and in nanosize, embedded in the carrier particle along with drug particles. A magnet is placed near the tumor position to generate a magnetic field. The relative motion of the carrier particle is the resultant of the fluidic force, magnetic force and Saffman drag force which are calculated for the spherical carrier particle. Trajectories of the carrier particle along the radial and axial direction are calculated. Effect of different parameters such as stress-jump constant, permeability of the carrier particle, pressure gradient, yield stress, Saffman force, volume fraction of the embedded magnetic nanoparticles, permeability of the microvessel wall, and the radius of the carrier particle on the trajectory of the carrier particle are discussed and displayed graphically.