Erratum to “Parallel simulation of concentration dynamics of nano-particles in High Gradient Magnetic Separation [Simul. Modell. Pract. Theory 19 (2011) 847–871]”

Magnetic microreactors for efficient and reliable magnetic nanoparticle surface functionalization

“…Simulation of magnetic separation units has a long history 20,33,[35][36][37][38][39][40] . A great deal of modeling work has been carried out in the eighties and in the nineties, with the objective to quantify the performances of high gradient magnetic separation (HGMS) units, as they are commonly referred to.…”

“…The equilibrium is more complex in the presence of convection. A comprehensive description of the accumulation kinetics of NPs around an isolated wire requires the solution of a two-dimensional convection-diffusion equation including all the above mentioned mechanisms 39,40 . The detailed equation is reported in the Supplementary Information.…”

“…The detailed equation is reported in the Supplementary Information. Such a solution has been carried out only for a few conditions using a finite difference method 39 . The objective of solving such equation was to find an angular average expression for both the velocity profile and the magnetic interaction potential.…”

“…Simulation of magnetic separation units has a long history. 20,33,[35][36][37][38][39][40] A great deal of modeling work has been carried out in the eighties and in the nineties, with the objective of quantifying the performance of high gradient magnetic separation (HGMS) units, as they are commonly referred to. Most of the work has focused on predicting the amount of NPs that can be trapped in a HGMS unit at steady states under the given conditions.…”

“…In order to solve eqn (1)-( 3), the rate of NP trapping by the wires (K) is required, as well as its dependence on the operating conditions, such as the magnetic field strength used, flow rate and particle concentration; the retention of NPs by a magnetic wire results from the competition of three mechanisms: magnetic interactions, diffusion and convection. 20,33,39,40 Magnetic interactions are responsible for the accumulation of NPs around a wire, creating strong concentration gradients of NPs, thus leading to high diffusion fluxes that tend to counterbalance magnetic interactions. In the absence of convection, at steady state, diffusion and magnetic interaction counterbalance each other.…”