Viscoelastic computations for reverse roll coating with dynamic wetting lines and the Phan-Thien-Tanner models

The computational modelling of reverse roll coating with dynamic wetting line has been analysed for various non-Newtonian viscoelastic materials appealing to the Phan-Thien-Tanner (PTT) network class of models suitable for typical polymer solutions, with properties of shear thinning and strain hardening/softening. The numerical technique utilizes a hybrid finite element-sub-cell finite volume algorithm with a dynamic free-surface location, drawing upon a fractional-staged predictor-corrector semi-implicit time-stepping procedure of an incremental pressure-correction form. The numerical solution is investigated following a systematic study which allows for parametric variation in elasticity (We-variation), extensional hardening-softening (e), and solvent fraction (β). Under incompressible flow conditions, linear PTT (LPTT) and exponential PTT (EPTT) models were used to solve the paint strip coatings, under reverse roll-coating configuration. This involves two-dimensional planar reverse roll-coating domains, considering a range of Weissenberg numbers (We) up to critical levels, addressing velocity fields and vortex development, pressure and lift profiles, shear rate, and stress fields. Various differences are observed when comparing solutions for these constitutive models. Concerning the effects of elasticity, increase in We stimulates vortex structures, which are visible at both the downstream meniscus and upstream narrowest nip region, whilst decreasing the peak pressure and lift values at the nip constriction. At low values (e > 0.5, β = 0.1) of extensional viscosity, the LPTT flow fields were much easier to extract, attaining critical We levels up to unity, in contrast to critical We levels of 0.4 for EPTT solutions. This finding is reversed at higher extensional viscosity levels (e < 0.5). This trend reveals qualitative agreement with theoretical studies. Noting flow behaviour under EPTT solution, increasing the peak level of strain hardening/softening is found to stimulate vortex activity around the nip region, with a corresponding increase in peak pressure and lift values.