To elucidate the complex rheological behavior of non-Newtonian fluids in fluidic control components, this study systematically investigates the coupled control mechanism of rheological parameters—specifically, the flow behavior index n (representing shear-thinning capability) and the consistency index K (representing global viscous resistance) —along with the oscillation chamber expansion angle (\(\:\alpha\:\)) on the oscillation onset characteristics of a feedback fluidic oscillator. Based on unsteady numerical simulations, the topological bifurcation laws governing the evolution from “self-excited oscillation” to “steady straight jet” are revealed. The results indicate that: The strong coupling effect between the consistency index K and the flow behavior index n is the decisive factor for oscillation onset. The precise critical threshold is identified at \(\:n\approx\:0.61\)(K\(\:\approx\:\)0.163); exceeding this threshold causes the Coanda effect to fail due to excessive viscous barriers. Two distinct states of oscillation cessation are identified: “marginal locking” and “deep locking”. For the marginal condition (n = 0.61), increasing inlet velocity can break the viscous constraint to achieve dynamic unlocking, whereas the high-consistency condition (n = 0.71) exhibits an irreversible deadlock state. Furthermore, the expansion angle \(\:\alpha\:\) significantly suppresses oscillation stability. Even under strong shear-thinning conditions (n = 0.3) favorable for oscillation, an angle exceeding \(\:{20}^{\circ\:}\) accelerates flow degradation by weakening the wall-attachment pressure gradient. This study establishes a rheology-geometry-dynamics coupled criterion for oscillation onset, providing theoretical support for the optimization of fluidic components operating with complex working fluids.
