Predictive Modeling and Experimental Validation of Magnetophoretic Delivery of Magnetic Nanocultures

Abstract

Magnetophoresis offers a powerful strategy for the targeted delivery of functional microcapsules. Here, we present a combined theoretical and experimental framework to predict the magnetophoretic transport of magnetic nanocultures-microcapsules embedded with magnetic nanoparticles and living cells. We derive a novel analytical expression for the terminal velocity of microcapsules under a spatially decaying magnetic field. The model incorporates magnetic and hydrodynamic forces in low Reynolds number regimes and predicts microcapsule velocity variations with nanoparticle size and field strength. Experimental validation using nanocultures containing nanoparticles 5, 10, and 20 nm in size confirms the model's accuracy, with 10-nm particles showing optimal magnetophoretic response. The model also accounts for hindered motion at high microcapsule densities. This work provides a predictive tool for designing magnetically guided systems for microbial delivery, localization, and patterning, with applications in bioreactors, therapy, and engineered living materials.

1

Development of magnetic microcapsules and nanocultures. (A) Schematic of the polymer cross-linking chemistry and the incorporation of magnetic nanoparticles into the PDMS matrix. (B) The three liquid phases (water for microcapsules and aqueous culture medium for nanocultures), actuated PDMS mixtures, and PVA solution) were introduced into the microfluidic device and directed into a three-phase interface for high-throughput generation of W/O/W emulsions. (C) Representative scanning electron microscopy image of magnetic microcapsules. Scale bar = 50 μm, (D) Confocal image of green fluorescent protein-tagged P. aeruginosa encapsulated in the magnetic nanocultures (MNCs). The polymeric shell of the MNCs was stained with lipophilic stain (Nile Red) to enhance image contrast. Scale bar = 50 μm.

2

Magnetic actuation of microcapsules under a nonuniform magnetic. Panels (A–C) show microcapsules loaded with 500 ppm of 5-, 10-, or 20-nm iron oxide nanoparticles that were exposed to a nonuniform magnetic field. The first column shows raw ImageJ-processed images capturing the directional migration of microcapsules toward the magnet over time. Panels (D–F) display MATLAB-rendered trajectories colored by time, demonstrating microcapsule displacement as a function of distance from the magnet. Panels (G–I) present the corresponding velocity profiles extracted from tracked microcapsules, illustrating increasing velocity as the microcapsules approach the magnet. Panels (J–L) show curve-fitted average velocity versus distance data, revealing a nonlinear increase in magnetophoretic velocity consistent with the expected gradient-driven behavior. These results highlight the influence of nanoparticle size on microcapsule motion and were used to inform simulation parameters in subsequent modeling efforts. The number of individual MNCs tracked (n) was 12 for 5 nm, 15 for 10 nm, and 14 for 20 nm. [Figure reproduced from ref under CC-BY 4.0 license. Copyright 2025.]

3

Influence of a static magnetic field. (A) The distribution of magnetic flux density around a magnet. The suspension of magnetic particles is placed on a narrow plate between two white horizontal lines on top of the magnet. (B) Magnetic flux density along the narrow plate and its fitting by an exponential decay function.

4

Effect of microcapsule/nanocultures’ physical properties on magnetophoretic velocity. Velocity distribution for (A) increasing applied magnetic field strength, and (B) increasing effective susceptibility.

5

Validation of the theoretical model developed for velocity predictions. Experimental (dotted lines) and predicted (solid lines) velocity of the microcapsules with MNP of sizes 5-, 10-, and 20-nm nanoparticles, and 5-nm nanocultures with bacteria.