Elisabeth Diehl

The correct choice of the doctor blade angle is essential in rotogravure printing to achieve efficient removal of excess ink and entrained air for optimal filling of gravure cells. An improper doctor blade angle can lead to the entrapment of air bubbles within or significant underfilling of the engraved cells, which can result in print defects such as voids, streaks, and ink splatter. In this paper, we propose a numerical setup that allows to calculate the optimal doctor blade angle for a given gravure cell shape and ink properties. The doctor blade angle optimization procedure utilizes the Gauss-Newton method while the ink acquisition and doctor blading process is simulated using the Computational Fluid Dynamics (CFD) software OpenFOAM. Moreover, the numerical setup involves a fully automatized geometry generation and meshing procedure which makes the whole setup very flexible and enables its use for further optimization studies. The findings presented in this paper provide insights into the role of the doctor blade angle in rotogravure printing and show a global trend of smaller angles leading to improved air removal. This result can potentially be exploited to optimize the printing process and reduce print defects.

We analyze optimal control problems for two-phase Navier-Stokes equations with surface tension. Based on $L_p$-maximal regularity of the underlying linear problem and recent well-posedness results of the problem for sufficiently small data we show the differentiability of the solution with respect to initial and distributed controls for appropriate spaces resulting form the $L_p$-maximal regularity setting. We consider first a formulation where the interface is transformed to a hyperplane. Then we deduce differentiability results for the solution in the physical coordinates. Finally, we state an equivalent Volume-of-Fluid type formulation and use the obtained differentiability results to derive rigorosly the corresponding sensitivity equations of the Volume-of-Fluid type formulation. For objective functionals involving the velocity field or the discontinuous pressure or phase indciator field we derive differentiability results with respect to controls and state formulas for the derivative. The results of the paper form an analytical foundation for stating optimality conditions, justifying the application of derivative based optimization methods and for studying the convergence of discrete sensitivity schemes based on Volume-of-Fluid discretizations for optimal control of two-phase Navier-Stokes equations.