Deformable Microchannels Research Articles

Bendocapillary instability of liquid in a flexible-walled channel

We study the bendocapillary instability of a liquid droplet that part fills a flexible walled channel. Inspired by experiments in which a periodic pattern emerges as droplets of liquid are condensed slowly into deformable microchannels, we develop a mathematical model of this instability. We describe equilibria of the system, and use a combination of numerical methods and asymptotic analysis in the limit of small channel wall deflections, to elucidate the key features of this instability. We find that configurations are unstable to perturbations of sufficiently small wavenumber regardless of parameter values, that the growth rate of the instability is highly sensitive to the volume of liquid in the channel, and that both wetting and non-wetting configurations are susceptible to the instability in the same channel. Insight into novel interfacial instabilities opens the possibility for their control and thus exploitation in processes such as microfabrication.

Elastohydrodynamic Relaxation of Soft and Deformable Microchannels.

Hydrodynamic flows in compliant channels are of great interest in physiology and microfluidics. In these situations, elastohydrodynamic coupling leads to (i)a nonlinear pressure-vs-flow-rate relation, strongly affecting the hydraulic resistance; and (ii), because of the compliance-enabled volume storage, a finite relaxation time under a stepwise change in pressure. This latter effect remains relatively unexplored, even while the timescale can vary over a decade in typical situations. In this study we provide time-resolved measurements of the relaxation dynamics for thin and soft, rectangular microfluidic channels. We describe our data using a perturbative lubrication approximation of the Stokes equation coupled to linear elasticity, while taking into account the effect of compliance and resistance of the entrance. The modeling allows us to completely describe all of the experimental results. Our Letter is relevant for any microfluidic scenario wherein a time-dependent driving is applied and provides a first step in the dynamical description of compliant channel networks.

Enhancing particle transport in deformable micro-channels.

It is shown that the action of an oscillating force on particles moving through a deformable-walled channel causes them to travel greater distances than in the case of a rigid channel. This increase in the transport efficiency is due to an intensification of the stochastic resonance effect observed in corrugated rigid channels, for which the response to the force is maximal for an optimal value of the thermal noise. The distances traveled by the particles are even larger when the oscillation of the micro-channel is synchronized with that of an applied transverse force and also when a constant external force is considered. The phenomenon found could be observed in the transport of particles through elastic porous media, in drug delivery to cancerous tissues, and in the passage of substrates through transporters in biological membranes. Our results indicate that an appropriate channel design and a suitable choice of applied forces lead to optimal scenarios for particle transport.

Start-up flow in shallow deformable microchannels

Microfluidic systems are usually fabricated with soft materials that deform due to the fluid stresses. Recent experimental and theoretical studies on the steady flow in shallow deformable microchannels have shown that the flow rate is a nonlinear function of the pressure drop due to the deformation of the upper soft wall. Here, we extend the steady theory of Christov et al. (2018) by considering the start-up flow from rest, both in pressure-controlled and in flow-rate-controlled configurations. The characteristic scales and relevant parameters governing the transient flow are first identified, followed by the development of an unsteady lubrication theory assuming that the inertia of the fluid is negligible, and that the upper wall can be modeled as an elastic plate under pure bending satisfying the Kirchhoff-Love equation. The model is governed by two non-geometrical dimensionless numbers: a compliance parameter $\beta$, which compares the characteristic displacement of the upper wall with the undeformed channel height, and a parameter $\gamma$ that compares the inertia of the solid with its flexural rigidity. In the limit of negligible solid inertia, $\gamma \to 0$, a quasi-steady model is developed, whereby the fluid pressure satisfies a nonlinear diffusion equation, with $\beta$ as the only parameter, which admits a self-similar solution under pressure-controlled conditions. This simplified lubrication description is validated with coupled three-dimensional numerical simulations of the Navier equations for the elastic solid and the Navier-Stokes equations for the fluid. The agreement is very good when the hypotheses behind the model are satisfied. Unexpectedly, we find fair agreement even in cases where the solid and liquid inertia cannot be neglected.

Electroosmosis with Augmented Mixing in Rigid to Flexible Microchannels with Surface Patterns

We explore the salient features of electroosmotic flow inside patterned and deformable microchannels. A computational fluid dynamic simulator is developed to solve the coupled Poisson’s equation fo...

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

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. $$Re \sim O(10^{-2}$$ – $$10^{+1})$$ , fluid flow through a shallow deformable microchannel with ultra-low height-to-width-ratios, 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.

A one-dimensional model for compressible fluid flows through deformable microchannels

Fluid-structure interactions in low-Reynolds-number flows have received an increasing interest due to emerging bio-applications of deformable microfluidics. We utilize the lubrication theory and wide-beam framework to develop a one-dimensional coupled fluid-solid-mechanics model for the prediction of the characteristic behavior of compressible fluid flows through deformable microchannels. An explicit relationship is extracted for the mass flow rate as a function of pressure difference across a microchannel, undeformed channel dimensions, and properties of channel’s ceiling such as thickness, modulus of elasticity, and Poisson’s ratio. The resulting fifth-order algebraic equation is also solved numerically to obtain the pressure distribution within the microchannel. As a special case for compressible fluid flows, the characteristics of ideal gas flows are extracted from the general model. Rigid and deformable microchannels are fabricated, and the mass flow rates of air through the channels are measured under various pressure differences across the channels. The proposed model predicts the mass flow rate with an acceptable accuracy. Our experimental and theoretical results highlight the importance of fluid compressibility and microchannel deformability, demonstrating that neglecting either of them under sufficiently large pressure differences can lead to erroneous results. To the best of the authors’ knowledge, this is the first theoretical model simultaneously addressing both fluid compressibility and microchannel deformability for an equilibrium pressure-driven compressible fluid flow in microscale.

Static response of deformable microchannels: a comparative modelling study

We present a comparative modelling study of fluid–structure interactions in microchannels. Through a mathematical analysis based on plate theory and the lubrication approximation for low-Reynolds-number flow, we derive models for the flow rate-pressure drop relation for long shallow microchannels with both thin and thick deformable top walls. These relations are tested against full three-dimensional two-way-coupled fluid–structure interaction simulations. Three types of microchannels, representing different elasticity regimes and having been experimentally characterized previously, are chosen as benchmarks for our theory and simulations. Good agreement is found in most cases for the predicted, simulated and measured flow rate-pressure drop relationships. The numerical simulations performed allow us to also carefully examine the deformation profile of the top wall of the microchannel in any cross section, showing good agreement with the theory. Specifically, the prediction that span-wise displacement in a long shallow microchannel decouples from the flow-wise deformation is confirmed, and the predicted scaling of the maximum displacement with the hydrodynamic pressure and the various material and geometric parameters is validated.

Hydrodynamics in deformable microchannels

We report experimental investigations into deformable rectangular microchannels using pressure drop, wall deformation and microparticle image velocimetry analysis. The available theoretical framework for the deformation of the wall is reviewed, and a physical explanation is obtained for the non-dimensional deformable parameter α through scaling analysis based on the thick-plate approximation. A new theoretical model based on the thick-plate approximation is developed and compared against the experimentally obtained values. The effect of the thickness of the microchannel on the deformation is also discussed. The bulging effects of the microchannel are probed along the length of the channel, and the reduction in the pressure drop is compared against a non-deforming channel. We observe a larger effect of the deformation near the microchannel inlet than that toward the end of the channel. Furthermore, we observe an upper limit to the maximum deformation of the microchannel walls, and the increased flow rate in the channel does not contribute to any further deformation and thus the reduction in the overall pressure drop. Overall, the observations from a multitude of experiments in the current study will aid in the development of microfluidic systems for Lab-on-Chip applications using soft lithography and also demonstrate the measures to be taken during the fabrication of any polydimethylsiloxane-based microfluidic systems.

Remote sensing of pressure inside deformable microchannels using light scattering in Scotch tape.

We present a simple but effective method to measure the pressure inside a deformable microchannel using laser scattering in a translucent Scotch tape. Our idea exploits the fact that the speckle pattern generated by a turbid layer is sensitive to the changes in the optical wavefront of an impinging beam. A change in the internal pressure of a channel deforms the elastic channel, which can be detected by measuring the speckle patterns of a coherent laser beam that has passed through the channel and the Scotch tape. We demonstrate that with a proper calibration, internal pressure can be remotely sensed with the resolution of 0.1 kPa within a pressure range of 0-3 kPa after calibration.