The Correct Treatment of Harmonic Pressure-Flow Behavior in Microchannels

Advances in microfluidic technology give great potential for integrated systems with many components. Because continuum modeling is difficult even for simple systems, low-order modeling is essential to their design. Unsteady flow in microfluidic components such as channels and valves may require special treatment to achieve accurate low-order models of entire systems. One example is the fixed-valve micropump, in which the interaction between mechanical, electrical, and fluidic components produces maximum pump output at a resonant frequency near the corner frequency of the valves. In this frequency range the commonly-used value for fluid impedance was found to be in error by 30%, causing errors in predictions of pump membrane motion by as much as 300%. Proper treatment of the pressure-flow relations based on the exact solution of the Navier-Stokes equations for oscillatory flow corrected these deficiencies.