Finite Element Computation of Blade Coating via a Partitioned Approach
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Shear flow-based coatings are widely used in industry to deposit uniform thin liquid films onto solid substrates. Blade coating, where the film is formed by flow in a narrow channel between a blade and a substrate, is one of the simplest variants of this technique. Computational modeling of blade coating systems is challenging due to their multiphysics nature, which requires the simultaneous solution of fluid flow and mesh displacement fields. Although a previous study applied a monolithic finite element method to solve this coupled system in two dimensions, this approach generates a massive linear system. Consequently, it can become computationally prohibitive when expanded to three dimensions or when incorporating additional physical variables. This work employs a partitioned approach, solving each field alternatively via a staggered iterative scheme. The primary challenge lies in imposing coupled boundary conditions, such as the contact angle. To address this, an indirect method for enforcing contact angles is proposed. Furthermore, the study investigates the evaluation of surface tension in three dimensions, particularly at the truncated outlet boundary. The two-dimensional results exhibit trends consistent with the prior study while maintaining a reasonable number of coupling iterations per timestep. The three-dimensional results demonstrate the validity of the proposed surface tension treatment for the truncated outlet. Furthermore, transverse flow, flow across the substrate width, is analyzed to distinguish the main flow characteristics between two-dimensional and three-dimensional models. Ultimately, this framework offers a basis for improving film quality control in industrial coating processes.
