The Magnetophoretic Force causes motion of permeable particles toward regions where the magnetic field is stronger. The magnetophoretic force is applicable for particles which are charge neutral and have a different relative permeability than the background fluid. The magnetophoretic force is defined as:

where H is the magnetic field, μr is the fluid relative permeability, μr,p is the particle relative permeability, and K is defined as:

As shown in Equation 5-15, the magnetophoretic force is a function of derivatives of the components of the magnetic field H. Depending on the physics interface used to compute the magnetic field, its derivatives may not be available.

For example, in instances of the Magnetic Fields interface, the degrees of freedom correspond to components of the magnetic vector potential A (SI unit: Wb/m). The magnetic field can be derived from the magnetic vector potential using the relations

where B (SI unit: T) is the magnetic flux density and M (SI unit: A/m) is the magnetization vector. Thus, derivatives of the magnetic field components correspond to second derivatives of the degrees of freedom, the components of A. However, the second derivative is not defined for the vector (curl) elements that are used to discretize the components of A in 3D or the in-plane components of A in 2D. In these situations, the derivatives of the magnetic field components will be evaluated as zero everywhere, resulting in zero magnetophoretic force.

Therefore, depending on the formulation used to compute the magnetic potential, it may be necessary to select the User defined option from the Magnetic field list and use the second order laginterp operator to evaluate the derivatives of the magnetic field components. For example, in instances of the Magnetic Fields interface, type laginterp(2,mf.Hx), laginterp(2,mf.Hy), and laginterp(2,mf.Hz) in the x, y, and z (SI unit: A/m) text fields respectively.