Magnetic nanoparticle interaction with a hydrogel in an oscillating magnetic field

A study was conducted of the effect of superparamagnetic nanoparticles on a hydrogel in the presence of an oscillating magnetic field directed tangent to the hydrogel surface. The oscillating magnetic field causes the particles to oscillate laterally in the hydrogel, with some of the particles adhering to the hydrogel matrix and other particles moving freely through the hydrogel pore spaces. The analysis was performed for a three-phase matrix-water-particles model, in which the solvent (water) and hydrogel matrix are interacting continua and the particles are a discrete phase. The study examined the effect of fluid elasticity on wave propagation due to the no-slip boundary condition acting under the transversely oscillating magnetic field. A memory effect within the fluid results in a deviation of the minimum and maximum shear rates observed in one half of the oscillation period from those observed in the other half of the oscillation period. The behavior of the hydrogel with different values of the governing dimensionless parameters was assessed. The matrix Reynolds number, the Deborah number, and the ratio of matrix relaxation to retardation times were all observed to have significant influence on the hydrogel viscoelastic response and on the wave propagation within the hydrogel. The phase difference between the water and matrix oscillations is strongly influenced by the phase interaction force coefficient, the Deborah number, and the ratio of free to captured particles. The system is found to approach an asymptotic state at a high Deborah number, which is independent of the value of the Deborah number.