Simplified model for operability window of slot coating without vacuum

Slot coatings are widely used to fabricate films with highly uniform thicknesses. Stable operating conditions are critical for achieving desired thickness uniformity. When the slot coating is operated with a vacuum chamber to produce thin films of a Newtonian fluid, the visco-capillary model of Higgins and Scriven (1980) has been successfully used to predict the operability window, i.e., the range of stable operating conditions. The model assumes a channel flow under the slot-die and describes the pressure balance inside the channel to determine the operability window, particularly for the vacuum pressure range. Currently, battery electrodes and membrane coatings require relatively thick films that can be processed without a vacuum. Such operating conditions are compatible with high aspect ratio channels. We show that the model describes the downstream pressure jump contribution as having a negligible magnitude compared to the total pressure drop inside the channel. Consequently, a simplified model can be obtained by omitting the downstream contribution from the visco-capillary model. The simplified model is consistent with the experimental results for a thick film production of a high viscosity Newtonian liquid. Furthermore, because the simplified model is expressed as an explicit function of the operating conditions, it enables straightforward estimation of the operability window and the solution of inverse problems, such as predicting the desired viscosity range from the target operating condition.