Research report: Nanoparticle diffusive transport in hydrogels

Hydrogels are everywhere in modern science: they carry drugs into wounds and tumors, cool solar panels, lubricate machines, and even form the slimy extracellular matrix that shields bacterial biofilms. Yet one of the most important questions about these water-soaked polymer networks is deceptively simple—how do nanoparticles actually move through them?

The review, published as an open-access article on 27 August 2026, begins with a taxonomy of the particles themselves. Inorganic nanoparticles—elemental metals, metal oxides and semiconductor nanocrystals—bring mechanical reinforcement, antimicrobial action and light-based sensing to hydrogel composites. Silver nanoparticles, for example, shed ions that disrupt bacterial cell membranes, deactivate respiratory enzymes and interfere with DNA replication. Gold nanoparticles kill bacteria photothermally, converting absorbed light into localized heat. Iron oxide nanoparticles, the most common superparamagnetic particles, can be steered by external magnetic fields to break apart biofilm matrices or to trigger local hyperthermia that weakens bacterial colonies. Lipid-based nanoparticles such as liposomes and solid lipid nanoparticles act as protective cargo vessels, while polymeric nanoparticles made from materials like PLGA and polycaprolactone offer tunable degradation rates and surface ligands for targeted cell adhesion.

But a particle’s chemistry is only half the story. The other half is the hydrogel itself. On the scale of a nanoparticle, a hydrogel is not a smooth fluid but a tangled forest of polymer chains surrounding water-filled pores. Those pores range from about one nanometer to more than 100 micrometers depending on the polymer chemistry and preparation method, spanning nanoporous, microporous, macroporous and superporous regimes. Biofilms typically fall in the macroporous range, though some contain larger channels. When a nanoparticle is much smaller than the pore space, it can diffuse almost freely; when it is comparable in size, it becomes trapped; and in the crucial intermediate regime—where most applications live—the particle repeatedly collides with, sticks to and detaches from the polymer mesh in a process the authors call hopping diffusion.

Hopping diffusion is the review’s central physical insight. A nanoparticle navigating a hydrogel alternates between a free state, drifting through water-filled pores under thermal motion, and a captured state, in which van der Waals forces, electrostatic interactions, hydrogen bonding or ligand-receptor binding anchor it to the polymer network. Sometimes capture is purely mechanical: the particle is simply too large for the local pore opening, and the chains wrap around it like a cage. Thermal fluctuations of the chains eventually release the particle, and it travels several pore lengths before the next capture event. The result is a stochastic stop-and-go journey that dramatically slows the effective spread of particles compared with free diffusion in water. Experimental data from Fatin-Rouge and colleagues in 1.5% agarose gels show that particles well below a critical trapping diameter behave nearly Fickian—their mean-square displacement grows linearly in time—but as particle size approaches that threshold, diffusion becomes anomalous, with uncertainty in the measurements growing sharply near the mobility limit.

To make sense of this zoo of behaviors, the review catalogs the major families of hindered-diffusion models. The classic Stokes–Einstein equation, which relates diffusion coefficient to temperature, solvent viscosity and particle diameter, works well only for particles far smaller than the polymer correlation length—the average distance between neighboring chain monomers, typically one to ten nanometers. Obstruction models treat the polymer network as a static maze, reducing accessible volume and forcing tortuous paths. Hydrodynamic models, such as Cukier’s exponential decay formula for Brownian spheres in semi-dilute polymer solutions, capture the extra drag a particle feels near polymer strands and pore walls. Free-volume models link diffusion to the space left unoccupied by polymer molecules, connecting swelling state and crosslink density to mobility. None of these alone explains adhesive sticking, mechanical caging or the intermittent capture-release dynamics that dominate in real gels, which is why the authors argue that model selection should follow the dominant physical bottleneck rather than a single fitted diffusion coefficient.

For elongated particles, the review highlights a third mechanism: reptation. Long polymer chains in an entangled network do not fluctuate randomly; they slither along a virtual tube formed by their neighbors, like a snake through a burrow. A nanoparticle captured by such a chain, with a diameter comparable to the tube, can be carried along for the ride. Cui and colleagues showed that hopping and reptation compete, with the dominant mode set by the ratio of particle diameter to tube diameter and a crossover diameter where the two time scales match. Below the crossover, hopping dominates and the diffusion coefficient decays exponentially with particle size; above it, reptation takes over and the Stokes–Einstein form reappears with an effective polymeric bulk viscosity replacing the solvent viscosity.

The most striking part of the review, and the one most likely to inspire new experiments, is its treatment of transport enhancement. If a hydrogel passively hinders nanoparticles, can external fields actively un-hinder them? The answer, according to Marshall and Ahmadinejad, is a resounding yes, through a phenomenon called oscillatory diffusion. When particles are driven back and forth by an oscillating force—acoustic pressure from ultrasound, or magnetic force from an alternating field—and simultaneously experience random capture and release by the porous matrix, the combination produces a stochastic random walk superimposed on the periodic motion. The particle oscillates, gets trapped at a random phase, is released when the driving force reverses, and wanders to a new position. Over many cycles, this yields a net diffusive spread in the direction of the oscillation, on top of ordinary molecular diffusion in all three directions.

The theoretical foundation comes from Balakrishnan and Venkataraman, who modeled the process as a two-state continuous-time random walk in which particles flip between freely oscillating and captured states with Poisson-distributed holding times. Their theory yields an explicit expression for the acoustic diffusion coefficient, predicting that it scales with the square of the oscillation amplitude and follows a specific saturating function of frequency. Stochastic simulations by Marshall and colleagues, in which particles occupy randomly sized pores in a model bead bed and are released with a probabilistic threshold when the fluid velocity changes sign, reproduce the statistical fingerprints of a random walk: linearly growing variance, kurtosis-to-variance-squared ratio near three, and a power spectrum close to the characteristic inverse-square law. Crucially, the theory survived experimental testing. Ma, Karki and colleagues seeded fluorescent nanoparticles in two-layer agarose hydrogels, applied low-intensity ultrasound from above, and measured the resulting diffusion enhancement. The measured acoustic diffusion coefficients fit the predicted quadratic dependence on ultrasound amplitude and the predicted frequency dependence with what the review describes as excellent agreement, for both 20-nanometer and 40-nanometer particles.

Magnetic fields offer a complementary route, one that works without pressure-driven flow and can be applied from outside the system. A steady, spatially varying magnetic field exerts a translational force on superparamagnetic particles proportional to their volume, susceptibility and the field gradient, producing directed drift through the gel. Li and colleagues showed that magnetically driven iron oxide nanoparticles can disrupt biofilm matrices, and Quan and colleagues demonstrated that forcing such particles through a Staphylococcus aureus biofilm creates artificial channels that boost antibiotic penetration and bacterial killing. But steady fields have drawbacks: the gradient decays rapidly with distance, only strongly magnetizable particles respond, and the forcing can promote aggregation or chain formation that enlarges the effective particle size and undermines transport. Oscillating magnetic fields sidestep some of these limits. Recent work by Zhang and colleagues quantified enhanced nanoparticle diffusion in biological tissues and tumors under a low-frequency oscillating field of 30 millitesla at 15 hertz, reporting a larger diffusivity increase than magnetothermal heating alone—evidence that purely mechanical oscillations, not just heat, can drive transport in soft porous materials.

The review closes with a candid assessment of what remains unknown. Modeling nanoparticle capture and release remains difficult because multiple adhesive forces and entanglement effects overlap, and few standardized benchmarks exist for validating models across different hydrogel types. Secondary consequences of oscillatory forcing—viscous heating, bursting of soft liposomes under intense ultrasound, tunnel formation by large magnetic particles—have not been thoroughly quantified. Most models assume dilute, single-particle suspensions, yet acoustic and magnetic fields are known to promote agglomeration, and little is known about how particle clusters remodel during hopping diffusion. The authors also identify a structural gap: experiments typically report only an effective diffusion coefficient, while models need pore geometry, polymer dynamics, particle shape, deformability and binding strength. Closing that gap, they argue, will require simultaneous measurement of particle trajectories, pore-size distributions, hydrogel rheology and particle-matrix interaction strength in the same system.

Subject of Research: Diffusive transport of nanoparticles in hydrogels and its enhancement by acoustic and magnetic fields

Article Title: Nanoparticle diffusive transport in hydrogels

Article References: Marshall, J. S., & Ahmadinejad, M. (2026). Nanoparticle diffusive transport in hydrogels. Discover Fluid Mechanics, 2(1), Article 10. https://doi.org/10.1007/s44369-026-00015-5

Image Credits: AI Generated

DOI: 10.1007/s44369-026-00015-5

Keywords: hydrogels, nanoparticles, diffusion, hopping diffusion, oscillatory diffusion, ultrasound, magnetic fields, biofilms, drug delivery, reptation, Stokes-Einstein, porous media