Homotopy-based solution of Navier-Stokes equations for two-phase flow during magnetic drug targeting

As one of the promising innovative methods of drug delivery, magnetic drug targeting (MDT) ideally contains three main steps to treat localized diseases; chemically attaching drugs to magnetic nanoparticles and their injection to a proper local blood stream, control and steering the cluster of particles in the arterial network with a proper external magnetic field and finally, trapping them and releasing the drugs at the diseased part of body. Focusing on the third step, some mathematical models, followed by uncountable numerical simulations, have been developed; keeping in mind this fact that by having answers which are functions of temporal, spatial and other related variables which make it possible to consider this kind of two-phase flows much easier, homotopy analysis method (HAM) was used to solve one of the most comprehensive models developed for such system. An artery-inspired geometry was a straight tube through which the supposed mixture is passing. Due to demanding results, only four steps of Maclaurin series were able to be computed; with this insufficient number of steps, acceptable accordance with numerical results was achieved.