Analytical model for the magnetic field and force in a magnetophoretic microsystem

A model is presented for predicting the magnetic field, and the magnetic and fluidic forces on micro/nano-particles in a magnetophoretic microsystem. The microsystem consists of a linear array of soft-magnetic elements embedded beneath a microfluidic channel. The magnetic elements are magnetized using an external bias field, and produce a nonuniform field distribution that permeates the microchannel. This gives rise to a magnetic force on particles as they flow through the microsystem. Analytical expressions are derived for the field distribution within the microchannel, and the magnetic force on the particles. A linear magnetization model is used to predict the magnetic response of the particles, and the magnetic field and force expressions are verified using finite element analysis. The particles also experience a fluidic force, which is predicted using Stokes' law for the drag on a sphere in laminar flow. The model presented here includes magnetic and fluidic analysis, and enables rapid predictions of the field and force throughout the microsystem as a function of key variables including the particle size and properties, the properties and spacing of the magnetic elements, the bias field source, the dimensions of the microchannel, the fluid properties, and the flow rate. The model is well-suited for parametric analysis, and is demonstrated via practical calculations.