Optimal control in ink-jet printing via instantaneous control

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.

Optimal Control of Droplets on a Solid Surface Using Distributed Contact Angles

“…In general, we can apply every model which provides the dynamic position and shape of the droplet in sufficient accuracy as well as the gradient for the optimization to calculate optimal controls. Droplets and curved interfaces in the relevant physical sizes of nanometers to millimeters are most often described by either the lattice Boltzmann model − or continuum models based on the Navier–Stokes (NS) equations ,, or simplifications, i.e., thin-film equations. The models can contain expansions to cope with additional difficulties such as contact angle hysteresis or electrostatics .…”

“…Yet only very few articles describe optimal control within the scope of droplet-based microfluidics. This includes the control of the footprint and shape of a static droplet 25 , the position of a moving droplet and its shape in absence of gravity 26 , and the position of the gas-liquid interface of rising liquid in a capillary 27 . However, the simultaneous and precise control of both the shape and position of a droplet to fulfill a target in a mathematically optimal way is absent.…”

Optimal Control of Sliding Droplets using the Contact Angle Distribution

“…The position of a moving droplet and its shape without the influence of gravity is considered in [13]. Results on the position of the gas-liquid interface of rising liquid in a capillary are provided in [25].…”