Experimental and theoretical investigation of a low-Reynolds-number flow through deformable shallow microchannels with ultra-low height-to-width aspect ratios

TL;DR

This study combines experimental and theoretical approaches to analyze low-Reynolds-number flow in ultra-low aspect ratio deformable microchannels, revealing how geometry and pressure influence flow regimes and fluid-solid interactions.

Contribution

It introduces a lumped flexibility parameter and a master curve to predict flow behavior in shallow deformable microchannels with ultra-low aspect ratios, extending previous research.

Findings

Flow regimes depend on the flexibility parameter and pressure difference.

A master curve relates flow rate and deformation across different geometries.

Criteria are proposed for when coupled fluid-solid mechanics are necessary.

Abstract

The emerging field of deformable microfluidics widely employed in the Lab-on-a-Chip and MEMS communities offers an opportunity to study a relatively under-examined physics. The main objective of this work is to provide a deeper insight into the underlying coupled fluid-solid interactions of a low-Reynolds-number fluid flow through a shallow deformable microchannel with ultra-low height-to-width ratios. The fabricated deformable microchannels of several microns in height and few millimeters in width, whose aspect ratio is about two orders of magnitude smaller than that of the previous reports, allow us to investigate the fluid flow characteristics spanning a variety of distinct regimes from small wall deflections, where the deformable microchannel resembles its corresponding rigid one, to wall deflections much larger than the original height, where the height-independent characteristic behavior emerges. The effects of the microchannel geometry, membrane properties, and pressure difference across the channel are represented by a lumped variable called flexibility parameter. Under the same pressure drop across different channels, any difference in their geometries is reflected into the flexibility parameter of the channels, which can potentially cause the devices to operate under distinct regimes of the fluid-solid characteristics. For a fabricated microchannel with given membrane properties and channel geometry, on the other hand, a sufficiently large change in the applied pressure difference can alter the flow-structure behavior from one characteristic regime to another. By appropriately introducing the flexibility parameter and the dimensionless volumetric flow rate, a master curve is found for the fluid flow through any long and shallow deformable microchannel. A criterion is also suggested for determining whether the coupled or decoupled fluid-solid mechanics should be considered.