Non-invasive measurement of the pressure distribution in a deformable micro-channel

Direct and non-invasive measurement of the pressure distribution in test sections of a micro-channel is a challenging, if not an impossible, task. Here, we present an analytical method for extracting the pressure distribution in a deformable microchannel under flow. Our method is based on a measurement of the channel deflection profile as a function of applied hydrostatic pressure; this initial measurement generates 'constitutive curves' for the deformable channel. The deflection profile under flow is then matched to the constitutive curves, providing the hydrodynamic pressure distribution. The method is validated by measurements on planar microfluidic channels against analytic and numerical models. The accuracy here is independent of the nature of the wall deformations and is not degraded even in the limit of large deflections, zeta(max)/2h(0) = O(1), with zeta(max) and 2h(0) being the maximum deflection and the unperturbed height of the channel, respectively. We discuss possible applications of the method in characterizing micro-flows, including those in biological systems.