The effects of magnetic field on paramagnetic species such as ions, biological molecules and solid particles have been investigated theoretically
1-4 and experimentally.
5,6 These paramagnetic species in the presence of an applied magnetic field experiences three kinds of body forces such as paramagnetic gradient force due to concentration gradient, field gradient force due to magnetic field gradient, and Lorentz force due to interaction of moving charged species with the magnetic field.
3,7 The flux of a population of paramagnetic species due to these magnetic body forces have been previously modeled using four different approaches- (A) the magnetic forces are included as the external body forces in the Navier-Stokes equation and the resulting velocity is added to the convective term of the flux expression,
2,3,8 (B) the velocity of paramagnetic particles is approximated as a product of mobility and a net magnetic force, which is then included in the convective term of the flux expression,
4,9,10 (C) the mobility in the migration term of the Nernst-Planck equation is modeled as a matrix containing Hall and Transversal mobilities, which are the functions of magnetic fields,
1 and (D) the diffusion coefficients are modified to include the effects from Lorentz force and the velocity in the convective term is modeled as a product of mobility and field gradient force.
11 The approaches A-D have a few common limitations that these models are not applicable to the concentrated solutions of paramagnetic particles, and they do not account for all magnetic forces including magnetic dipole interactions between particles. Here we propose a novel model for the flux of paramagnetic species that overcomes all the limitations of the preceding approaches. Moreover, the proposed model is based on the first principles that accounts for fluxes due all three magnetic forces with inter-particle interactions.
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