Effect Decomposition and Response Topology of Flow Behaviour in Natural–Synthetic Polymer Additives

Concentration, network interactions, and nonlinear response are key factors influencing the flow behaviour of multicomponent polymer additives. In this research, the rheological behaviour of aqueous blends of gum Arabic (GAR: 0.5–1.0 wt%), polyethene oxide (PEO: 0.25–0.70 wt%), and citric acid (CA: 0.05–0.10 wt%) was investigated. The formulation employs a fixed total solids content of 2 wt%. Water was adjusted to 98 wt% to reveal the influence of natural–synthetic polymer combinations on shear-dependent flow, which is relevant to irrigation flow enhancement. Hierarchical polynomial regression was used to relate component concentrations to the flow behaviour index (n) and resolve individual, interactive, and non-linear contributions through Power-law rheological data. Quadratic response surface models provided a consistent, local representation of flow behaviour. Variance decomposition showed PEO has the dominant monotonic influence on n, possibly due to entanglement-mediated resistance to shear-induced alignment. CA contributed mainly through nonlinear curvature, perhaps due to its role in network structure modification and sensitivity, rather than driving directional changes. GAR showed a relatively weak direct effect but participated in interaction terms that modulate the composite response. Response topology analysis highlighted anisotropic sensitivity in the formulation space, with steep gradients linked to PEO and smoother transitions governed by CA. Diagnostic evaluation supported a stable interpretation of the inferred effect hierarchy within the experimental domain. The results demonstrate that flow behaviour in hybrid polymer additives is controlled by dual mechanisms. Response magnitude is highly governed by synthetic polymer entanglement, while shape curvature and robustness are dominated by natural polymer and crosslinker.