The sorting of biological cells using biological micro-electro-mechanical systems (BioMEMS) is of utmost importance in various biomedical applications. Here, we consider a new type of devices featuring surface acoustic wave (SAW) actuated cell sorting in microfluidic separation channels. The SAWs are generated by an interdigital transducer (IDT) and manipulate the fluid flow such that cells of different type leave the channel through designated outflow boundaries. The operation of the device can be formulated as an optimal control problem where the objective functional is of tracking type, the state equations describe the fluid-structure interaction between the carrier fluid and the cells, and the control is the electric power applied to the IDT
