Abstract

Drop-on-demand inkjet printing is one of the most widespread applications of microfluidics. Within the printhead, ink continuously flows through multiple microchannels. Each microchannel contains a piezo-electric actuator on the top face and a nozzle on the opposite face. When the actuator pulses, a droplet is forced through the nozzle. Acoustic oscillations then reverberate within the microchannel until they are damped by viscous and thermal dissipation. If a droplet is ejected before the reverberations from the previous droplet have been sufficiently damped, its size is affected by the reverberations, which spoils the image being printed. In this study, we design open loop control of the actuator to eliminate these reverberations. First, we derive the governing equations of the thermoviscous acoustic flow by linearising the compressible Navier-Stokes equations. Then we derive the associated adjoint problem to obtain the gradient of the objective function (the acoustic energy after a given time) with respect to the actuator deformation. Finally we formulate an optimisation problem to find the actuator waveform that minimises the reverberations within a given time.

Abstract

 In this study, we find the optimal control boundary (i.e., actuator velocity) that cancels the acoustic reverberations inside drop-on-demand inkjet printheads at a specific time. We formulate an optimiza tion problem to minimize the total energy of the oscillating flow at a given time (i.e., the acoustic energy inside the microchannel and the surface energy of the droplet). We use the adjoint method to compute the gradient of the cost function with respect to the control boundary, and a gradient-based optimization algorithm to converge to the optimal solution. This methodology has been successfully applied to two generic inkjet printhead mechanisms: thin-film and bulk types. In both cases, the actu ator first reduces the surface energy of the system by extracting fluid from the nozzle. In this process, acoustic waves also propagate through the channel and reverberate at the ends, which increases the acoustic energy of the system. The actuator then sends additional acoustic waves that cancel these reverberations. Both mechanisms have been able to reduce the total energy of the system by a factor of over 100 in comparison with the uncontrolled cases.