Adjoint-based optimization of open-loop control for microfluidics of an inkjet printhead.

We find the optimal actuator velocity profile that cancels acoustic reverberations inside drop-on-demand inkjet printheads and ensures a certain meniscus state at a specific time after ejection. We formulate an optimization problem to minimize the total energy of the three-dimensional oscillating flow in the microchannel at a given time. The total energy comprises the acoustic energy inside the microchannel and the surface energy of the droplet. We use an adjoint method to compute efficiently the gradient of the cost function with respect to the control boundary and a gradient-based optimization algorithm to converge to the optimal solution. We apply this methodology to two generic inkjet printhead mechanisms: one that forces the faces adjacent to the nozzle face and the other that forces the face opposite the nozzle face. In both cases, the actuator first reduces the surface energy of the system by extracting fluid from the nozzle. This causes acoustic waves to propagate through the channel and reflect off the junction with the manifolds, increasing the acoustic energy of the system. The actuator then sends additional acoustic waves that cancel these reverberations. Both mechanisms reduce the total energy of the system by a factor of over 100 compared with uncontrolled cases.