Noninvasive Measurement of the Pressure Distribution in a Deformable Micro-Channel

Abstract

Direct and noninvasive 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 micro-channel under flow. Our method is based on a measurement of the channel deflection profile as a function of applied \emph{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 \emph{hydrodynamic} pressure distribution. The method is validated by measurements on planar micro-fluidic 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, ${\zeta }_{\max }/2h_0=\mathcal{O}(1)$, 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.

References in corpus (1)

• A Universality in Oscillating Flows

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