Viscoelastic instabilities in temperature-dependent viscosity roll-over-web coating: An analytical study of the Johnson–Segalman model

In many industrial applications including battery manufacturing, pharmaceuticals, optical films, and polymer laminates, where obtaining a uniform coating is crucial, the roll-over-web coating method is essential. The non-isothermal roll-over-web coating of a viscoelastic fluid described by the Johnson–Segalman (JS) model is theoretically investigated in this work, with an emphasis on the impacts of temperature-dependent viscosity. Lubrication approximation theory (LAT) is used to simplify the governing conservation equations, and the Adomian decomposition method (ADM) is used to derive analytical solutions for the velocity, temperature, and pressure fields. To clarify the impact of Weissenberg number (We), Brinkman number (Br), slip parameter (α), variable viscosity parameter (β), and effective viscosity (ϕ) on important engineering quantities, such as separation points (xsep), coating thickness (λ), separation force (F), power input (P), Nusselt number (Nu), and shear stress (Sxy), a parametric analysis is carried out. The findings indicate slip, thermal, and elastic effects interact intricately. Due to strong viscous dissipation, increasing the Brinkman number from 0.1 to 0.9 raises the separation force by about 59%, whereas increasing slip parameter (α) from 0.95 to 1.15 lowers this force by around 33%. The model accurately predicts when spurt instabilities will occur, capturing the non-monotonic behavior of the Johnson–Segalman fluid. An increase in the We from 0.8 to 1.0 causes a sharp increase in coating thickness of almost 49% at high viscous dissipation (Br=0.9), indicating a crucial limit for steady functioning. The separation force increases 87% as β is increased, highlighting the considerable influence of temperature-dependent viscosity. Additionally, to measure the linear correlations between the rheological parameters and model outputs, a Pearson correlation analysis is performed. Significant couplings are found in this research, most notably a large positive connection between viscous dissipation and the thermal sensitivity parameter, which highlights their combined influence on the pressure and temperature fields. These results offer a quantitative foundation for managing complex fluid film development and preventing harmful instabilities in industrial coating applications. The impacts of JS fluid flow during the roll-over-web coating process under the influence of the temperature-dependent viscosity effect have not yet been studied. This work offers an innovative viewpoint on these intricate relationships, advancing the field of roll-over-web research.

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