Modeling transport of hydrogel particles through porous media: An energy method and experimental guide

The transport of soft particles through porous media is critical in natural and industrial processes, yet quantifying the relationship between pressure drop and key parameters such as particle size, concentration, and flow rate remains challenging. Using an energy-based method, we derive a governing equation for pressure by balancing energy dissipation from frictional and viscous losses with energy input. The model reveals exponential dependences of pressure drop on particle concentration and porous medium length, and a double exponential dependence on the ratio of particle size to pore throat size. A characteristic length emerges, beyond which the pressure increases sharply, indicating a plugging effect. Incorporating a velocity-dependent friction coefficient further uncovers a nonlinear pressure–flow rate relationship, deviating from Darcy’s law. Validated against experimental data, the model provides a comprehensive framework for understanding particle transport in porous media, with applications to filtration, drug delivery, and enhanced oil recovery.