Adjoint-based optimization of the control boundaries of a microfluidic acoustic flow

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.

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