Immunomagnetic separation (IMS) is a method to isolate biomaterials from a host fluid in which specifically selected antibodies attached to magnetic particles bind with their corresponding antigens on the surface of the target biological entities. A magnet separates these entities from the fluid through magnetophoresis. The method has promising applications in microscale biosensors. We develop a comprehensive model to characterize the interaction between target species and magnetic particles in microfluidic channels. The mechanics of the separation of target nonmagnetic N particles by magnetic M particles are investigated using a particle dynamics simulation. We consider both interparticle magnetic interactions and the binding of the functionalizing strands of complementary particles. The temporal growth of a particle aggregate and the relative concentrations of M and N particles are investigated under different operating conditions. A particle aggregate first grows and then exhibits periodic washaway about a quasisteady mean size. The washaway frequency and amplitude depend on the initial fractional concentration of N particles while the aggregate size scales linearly with the dipole strength and inversely with the fluid flow rate.