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

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, i.e. Re∼ O(10 −2 -10 +1 ), fluid flow through a shallow deformable microchannel with ultra-low height-to-widthratios, i.e. O(10 −3 ). 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.

Theory of the flow-induced deformation of shallow compliant microchannels with thick walls

“…Our theory uncovers the physics hidden in the fitting parameter, α, of the widely used model (5.1), of which many ad hoc variations have been proposed [25,26,39]. The present analysis also provides a clear answer for why the previous plate-theory-based models [28,29,41] cannot be pushed to large-thickness regime (even qualitatively) by showing that the bending effects are trivial in the present model. The differences between these theories are also reflected by the different parameter dependencies of the dimensionless numbers quantifying compliance.…”

“…However, our configuration, based on the fabrication methods from, e.g. [21] and depicted in figure 1, is different from previous studies [16,28,29,[39][40][41] in which the top wall is modelled as a clamped membrane or plate with small thickness t w. Consequently, 1/(γ δ) 2 1 is not satisfied and the analysis above is inapplicable. Nevertheless, the plane strain assumption is still valid.…”

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

“…The hydrodynamic pressure within such conduits is affected by their deformation due to two‐way FSI. Extensive experimental work over the past decade has sought to understand FSI in microfluidics, specifically the effect of FSI on the flow rate–pressure drop relationship in a soft microchannel [22–25]. Specifically, for the case of steady, low Reynolds number flow in microchannels for which the ambient and outlet pressures are the same (no extramural pressure differences), the pressure drop across a soft microchannel is significantly smaller compared to the rigid case.…”

Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation

“…(32). Based on applying the hydrodynamic bulge test idea to simulation data from the present study, as well as previous simulations [35] and experiments [23] without pre-stress, is λ = 5, is λ = 2, and △ is λ = 1. All other quantities are as given in Table 1.…”

“…This problem, rather than the problem of the deflection of circular membranes typically studied in the bulge testing literature, is more relevant to microfluidics because PDMS microchannels' walls are generally not circular but rectangular [9,21]. A mathematical model of such FSI requires the use of the lubrication approximation to obtain the leading-order (with the flow-wise aspect ratio as the small parameter) fluid flow field, and then coupling it to a deformation profile obtained under an appropriate structural mechanics model (herein, a plate theory) [21,22,23]. The main result of the mathematical derivations in this work is the flow rate-pressure drop relationship for flow in a long and shallow rectangular microchannel with deformable top wall.…”