Simulation of slot-coating of nanocellulosic material subject to a wall-stress dependent slip-velocity at die-walls

Bio-based nanocellulosic materials are non-toxic, renewable, exhibit excellent barrier properties, and are suitable candidates for sustainable food packaging applications. Sizing and designing coating parameters for slot-coating process using nanocellulose suspensions is challenging due to complex shear-thinning rheology and the presence of a water-rich boundary layer, effecting significant apparent slip at the wall. Previous studies have shown that the flow inside the coating bead can be complex, with occasional stagnation regions and a rheological model incorporating yield stress which should be considered while analyzing slot coating of nanocellulosic flows. This work extends earlier investigations by including the effects of the particle depleted water-rich boundary layer. The suspension is modeled as a Casson fluid with a shear-thinning viscosity, and the particle depletion at the wall is represented by an infinitely thin layer modeled as a local shear-dependent nonlinear slip law. The resulting two-phase flow equations are solved using a Finite Volume Method (FVM) coupled with the Volume of Fluid (VoF) method for tracking the free surface interface. It is observed that slip alters the flow’s dynamics in the coating bead, and the effect of slip cannot be ignored, especially at high shear rates. For thin films, the presence of slip enhances the flow, leading to more material coated on the substrate. In contrast, for thicker coatings, apparent slip leads to an augmentation in stagnant, non-yielded regions, potentially generating uneven surfaces.

Coating Flow Near Channel Exit. A Theoretical Perspective

The planar flow of a steady moving-wall free-surface jet is examined theoretically for moderate inertia and surface tension. The method of matched asymptotic expansion and singular perturbation is used to explore the rich dynamics near the stress singularity. A thin-film approach is also proposed to capture the flow further downstream where the flow becomes of the boundary-layer type. We exploit the similarity character of the flow to circumvent the presence of the singularity. The study is of close relevance to slot and blade coating. The jet is found to always contract near the channel exit, but presents a mild expansion further downstream for a thick coating film. We predict that separation occurs upstream of the exit for slot coating, essentially for any coating thickness near the moving substrate, and for a thin film near the die. For capillary number of order one, the jet profile is not affected by surface tension but the normal stress along the free surface exhibits a maximum that strengthens with surface tension. In contrast to existing numerical findings, we predict the existence of upstream influence as indicated by the nonlinear pressure dependence on upstream distance and the pressure undershoot (overshoot) in blade (slot) coating at the exit.