Optimal control in ink-jet printing via instantaneous control

TL;DR

This paper develops an efficient instantaneous control method for free surface flow in ink-jet printing, effectively damping oscillations and reducing transient times by discretizing the flow with finite element methods and applying optimal control techniques.

Contribution

It introduces a novel instantaneous control approach for free surface flow with moving contact lines, incorporating surface tension and wall friction effects, and demonstrates its efficiency through numerical tests.

Findings

Control method effectively dampens nozzle oscillations

Reduces transient duration significantly

Computational approach is highly efficient

Abstract

This paper concerns the optimal control of a free surface flow with moving contact line, inspired by an application in ink-jet printing. Surface tension, contact angle and wall friction are taken into account by means of the generalized Navier boundary condition. The time-dependent differential system is discretized by an arbitrary Lagrangian-Eulerian finite element method, and a control problem is addressed by an instantaneous control approach, based on the time discretization of the flow equations. The resulting control procedure is computationally highly efficient and its assessment by numerical tests show its effectiveness in deadening the natural oscillations that occur inside the nozzle and reducing significantly the duration of the transient preceding the attainment of the equilibrium configuration.