PRESSURE-DROP SCALING LAWS AND STRUCTURAL STRESS CONTRIBUTIONS FOR COMPLEX FLOWS OF FLEXIBLE POLYMER-SOLUTIONS IN THICK SOLVENTS

Previous experiments showed that the flow through an orifice die of dilute solutions of flexible coils in thick solvents is characterised by three flow regimes. In each regime, pressure drop P(g) scales with flow rate q(v) according to a specific law. The objective of this work is to show how these scaling laws can be related to molecular stress-producing mechanisms, via a similarity analysis based on pertinent structural models. The essence of chain conformation is described by a vector and a simple constitutive equation is developed by using assumptions typical of dumbbell models. However, further constitutive elements are incorporated in order to represent molecular distortion and resulting stress at conditions far away from equilibrium. Besides the usual elastic term accounting for chain resistance to stretching, the stress tensor contains an additional dissipative term arising from important hydrodynamic interactions among chains when chains are highly distorted. The analysis shows how each regime is related to a distinct molecular behaviour and associated tensile stress growth. In the initial linear viscous Newtonian regime, where P(g) is linear in q(v), molecules are slightly deformed and the solvent Newtonian stresses govern the flow. In the intermediate quadratic regime, where P(g) varies as q(v)2, molecules unravel considerably and elastic stresses dominate. In the ultimate linear viscous regime, where P(g) is again linear in q(v), molecules are fully stretched and viscous stresses due to hydrodynamic interaction prevail. The model indicates that transient effects should be taken into account when experimental results in shear-free spatially varying flows are interpreted in terms of the fluid's elongational properties. Its predictions also suggest that an additional scaling of P(g) as q(v)4 should be observed in the orifice flow of more concentrated polymer solutions.