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In this work, we derive a governing equation for web tension in a span by employing a Neo-Hookean material model that is applicable for transport of web materials under both small and large strains. This governing equation may be employed to study the evolution of tension within a span as well as propagation of tension variations from span to span as the web is transported in the machine. First, we find the stretch in a web span and relate it to web tension via a Neo-Hookean material model; the Neo-Hookean model is linear for small strain and nonlinear otherwise. Second, we conduct a dimensional analysis by defining several key coefficients that aid in grouping the machine and web material parameters separately in order to obtain a compact system of governing equations; this representation may be utilized to efficiently study the impact of web and roller properties on transport behavior. 

Based on a model developed for the roll-to-roll imprinting process, this paper describes the relative importance of the processing, material properties, and transport parameters in Roll-to-Roll Nanoimprint Lithography (R2RNIL). In particular, the model is utilized to investigate the effect of web speed, fluid film thickness, viscosity, stress relaxation time, mold pattern geometry and size on mold filling. Based on a typical imprint roller configuration, kinematic analysis, and the conservation laws from classical mechanics, the behavior of the squeezing of a viscoelastic fluid film into a rigid mold cavity is described. Further, the effect of web speed, fluid film thickness and key rheological parameters, namely the Weissenberg and Deborah numbers, are discussed. These dimensionless numbers are typically employed to quantify viscoelastic effects in fluid flow problems. The effect of other scale-sensitive and geometric parameters, such as the capillary number and pattern width-to-height ratio, on the imprint process is also discussed. Numerical simulations are provided to corroborate the discussions and to quantify the relative importance of the parameters.