A Swirl-Driven Grouting Control Method for Non-Newtonian Fluids: 2.5D Seepage Model and Stability Analysis of Fractal-like Viscous Fingering

In porous media grouting, highly viscous non-Newtonian fluids often trigger viscous fingering (Saffman–Taylor instability) due to adverse mobility ratios, creating fractal-like preferential channels that severely weaken the reinforcement volume. To overcome this, a novel swirl-driven grouting method is proposed. A 2.5D swirl seepage model is established to derive the analytical solution for tangential velocity spatial decay. Integrating the Capillary Bundle and Herschel–Bulkley models elucidates the nonlinear coupling mechanism of centrifugal force and shear-thinning. The swirl flow creates an in situ centrifugal pump, reshaping pressure gradients and triggering a sudden viscosity plunge via extremely high comprehensive shear rates. Furthermore, a modified Saffman–Taylor dispersion relation is constructed and validated via indoor sandbox experiments. Theoretical analysis yields a conditional critical Swirl Number threshold of approximately 0.6 under the tested parameters to suppress the fractal-like evolution of fingering. Experiments demonstrate that exceeding this threshold transitions the grout from preferential seepage to uniform isotropic diffusion. The measured isotropic index is closely enveloped within the 10% theoretical error band. Consequently, the effective projected area experiences a substantial leap of 83.3% due to synergistically enhanced driving forces and reduced medium resistance. This mechanism fundamentally overcomes viscous fingering and suppresses the fractal-like growth tendency of the displacement front, providing a solid theoretical basis for controlling grout diffusion morphology in underground engineering.