Perturbation-based simplified models for unsteady incompressible microchannel flows

• A simplified model for unsteady liquid flows in micro channels is presented.
• The model relies on a perturbation analysis of the Navier–Stokes equations.
• Channels considered have a small aspect ratio and a slowly varying cross-section.
• The model is accurate for Re  < = 1 and all values of Strouhal number.
• The model is up to 2 orders of magnitude faster than CFD simulations.

A fast simplified model for a pressure-driven, unsteady and incompressible flow in two dimensional microchannels with a variable cross section is presented. The model relies on a perturbation analysis of the equations of mass and momentum under the assumptions that the channels have a small aspect ratio of height to length and that they have a slowly varying cross-section. A key advantage of this model is that it provides (quasi-) analytic expressions for the velocity, pressure distribution and mass flow rate in terms of the pressure drop along the channel, which makes the evaluation of such expressions very fast, compared to simulating the full Navier–Stokes equations. This is especially important in applications where the flow rate-pressure drop relation can be cast into a circuit, to be potentially integrated in a more complex system. The model turns out to be fairly accurate for a wide range of non-negligible Reynolds and Strouhal numbers and a fairly large class of channels. Furthermore, the model offers a speed factor of at least 500 over classical CFD simulations.