Multiperiodic Dynamics of a Nanoparticle-Filled Hydrogel in Oscillating Magnetic Fields*

In our initial study, we examined the effect of superparamagnetic nanoparticles on a hydrogel exposed to an oscillating magnetic field directed tangent to the hydrogel surface. The nanoparticles were considered either in a freely oscillating state suspended in a solvent (water) or in a captured state within the hydrogel. The hydrogel was modeled as an Oldroyd-B viscoelastic fluid. An analytical solution was derived under the assumption of constant numbers of free and captured particles, revealing that the hydrogel’s inherent elastic properties introduced unique system dynamics not observed in Newtonian fluids.

Building on this foundational work, our current study extends the analysis to cases where the number of free and captured particles varies in time. This dynamic variation introduces a novel set of system behaviors, particularly multiperiodic oscillations driven by both the driving frequency of the oscillating magnetic field and the hydrogel’s natural elastic frequency. The primary dimensionless parameter governing this system is the ratio of the fluid retardation time to the relaxation time, with significant influences from the Deborah number and the interfacial resistance coefficient.

We observed that under certain conditions, the system exhibits bi-harmonic dynamics, oscillating at both the driving frequency and the natural frequency of the hydrogel. A bifurcation point was identified, demarcating a transition between elastic and viscous regimes. In the elastic regime, the system displays multiperiodic behavior, while in the viscous regime, it transitions to monoperiodic behavior dominated by the magnetic field’s driving frequency.

The comprehensive numerical simulations, validated by previous analytical solutions, underscore the complex interplay between the magnetic forces and the viscoelastic properties of the hydrogel. These findings have significant implications for biofilm characterization and disruption, suggesting new strategies for enhancing antimicrobial treatment efficacy through controlled magnetic field manipulation.