Mathematical study of viscoelastic polymer during roll-over-web coating

Abstract

Roll-coating, also known as roll-to-roll coating or web coating is a continuous and high-speed method used in various industrial applications to apply a thin and uniform layer of material onto a substrate. This process is commonly employed in industries such as electronics, photovoltaic, printing, packaging, and other fields where precise and consistent coating is essential. Here we present an asymptotic analysis of forward roll coating over a rigid substrate for low Weissenberg number viscoelastic fluids. The analysis uses lubrication theory coupled with regular perturbation theory assuming a simplified Phan-Thien-Tanner (SPPT) constitutive equation and small values of the extensibility parameter ε. The analytical expressions of velocity fields, pressure gradient and pressure fields are obtained while the load carrying force, and power input are estimated by numerical solutions (4th order Runge-Kutta). Increases in both Wi and ε increases the pressure gradient in the nip region and increases in viscoelasticity reduce the overall force on the roll. Further, SPTT model predicts 14% lower pressure for [Formula: see text] in the nip region when compared to Newtonian model.

Applications of lubrication approximation theory in the analysis of the roll‐coating using a tangent hyperbolic fluid model

“…The engineering quantities are presented in Tables 1–3 for various $$We$$ and n . In Table 1, the separation point shifts forward to its Newtonian value of enhancing the value of $$We.$$ We also compared our results with reference [30] and noted that the coating thickness and the separation point increase and decrease for larger We in the current study and previous study respectively.…”

“…The required boundary conditions [2, 30] are: $$$$\begin{equation}\underline u = \underline U \,at\,\underline y = 0,\end{equation}$$$$ $$$$\begin{equation}\underline u = \underline U \,at\,\underline y = \underline h (\underline x ),\end{equation}$$$$ $$$$\begin{equation}\underline p = 0\,at\,\underline x = - {\underline x }_b,\end{equation}$$$$ $$$$\begin{equation}\underline p = 0\,at\,\underline x = {\underline x }_s.\end{equation}$$$$where $$$$\begin{equation}\underline h \left( {\underline u } \right) = {H}_0 + \underline R - {\left( {{{\underline R }}^2 - {{\underline x }}^2} \right)}^{\frac{1}{2}}.\end{equation}$$$$…”

“…Very recently, Atif et al. [29–30] presented a study of roll‐over‐web coating using the Robinowitsch and simplified Phan‐Thien‐Tanner models. The study of hybrid nanofluid flows over an exponentially stretching surface is reported by various researchers [31–34]…”

Temperature-Dependent Viscosity Analysis of Powell–Eyring Fluid Model during a Roll-over Web Coating Process

“…The research emphasizes the control mechanisms provided by these parameters for exit sheet thickness, power input, and separating force in the coating process. In light of this, several investigations have explored the utilization of reverse roll coating with various fluid types and are cited in [ 9 , 10 , 11 , 12 ].…”