In this work, the most recent Bautista-Manero-Puig (BMP) constitutive model-variant, i.e., the BMP+ \(\_\tau _p\) rheological equation-of-state, is used as a theoretical approach to describe the thixo-viscoelastoplastic characteristics of human mucus-sputum in rheometric flows, focused on healthy, Cystic Fibrosis (CF) and Chronic Obstructive Pulmonary Disease (COPD) affected samples, to determine its mechanical-to-biological response interplay. The BMP+ \(\_\tau _p\) model reproduces quantitatively the mucus-sputum rheological behaviour in steady and unsteady shearing flows under conventional protocols. From such theoretical characterisation, predictions are presented for LAOS and uniaxial extension, evidencing that thixotropy impacts strongly on sputum rheological behaviour. On plasticity and thixotropy, an explicit inverse relationship between a fluidisation stress and the BMP+ \(\_\tau _p\) thixotropic parameters is found and tested against independent measurements, giving: (i) quantitative agreement with medical reports; and (ii) evidence of a highly non-linear internal-structure rearrangement under LAOS. In the scarcely-treated mucus-sputum extensional deformations, BMP+ \(\_\tau _p\) predictions provide a rheological signature as augmented strain-hardening extensional-viscosity peaks: an additional source of flow-resistance in expectoration processes, with mixed shear-to-extensional flows. This may serve as: (i) an advanced rheological basis for biomarker development to determine the patient state, (ii) a tool for the efficacy-of-treatment evaluation with potential application for newly-emerging illnesses, e.g., COVID-19, closely-related with CF in sputum consistency and symptoms.
