Shallow Microchannels Research Articles

Effect of elastic deformation on squeezing film lubrication properties of soft tribocontacts with microstructured surface

PurposeInspired by the high-friction performance of the soft toe pads of tree frogs, this study aims to investigate the effect of elastic deformation on the lubrication properties of squeezing films inside soft tribocontacts with microstructured surface under wet conditions.Design/methodology/approachA one-dimensional hydrodynamic extrusion model was used to study the film lubrication characteristics of conformal contact. The lubrication characteristics of the extruded film, including load-carrying capacity, liquid flow and surface elastic deformation, were obtained through the simultaneously iterative solution of the fluid-governing and deformation equations.FindingsThe results show that the hydrodynamic pressure is approximating parabolically and symmetrically distributed in the contact area, and the peak value appears in the center of the extrusion surface. Elastic deformation increases the thickness of the liquid film, weakens the bearing capacity and homogenizes the liquid flow rate of inside soft friction contact. The magnitude of this effect greatly increases as the initial liquid film thickness decreases. Moreover, the elastic deformation directly affects the average film thickness of the extrusion contact. Narrow and shallow microchannels are found to result in a more prominent elastic deformation on the microstructured soft surface.Originality/valueThese results present a design for soft tribocontacts suitable for submerged or wet environments involving high friction, such as wiper blades, in situ flexible electrons and underwater robots.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-02-2024-0049/

Reduced modelling and global instability of finite-Reynolds-number flow in compliant rectangular channels

Experiments have shown that flow in compliant microchannels can become unstable at a much lower Reynolds number than the corresponding flow in a rigid conduit. Therefore, it has been suggested that the wall's elastic compliance can be exploited towards new modalities of microscale mixing. While previous studies mainly focused on the local instability induced by the fluid–structure interactions (FSIs) in the system, we derive a one-dimensional (1-D) model to study the FSI's effect on the global instability. The proposed 1-D FSI model is tailored to long, shallow rectangular microchannels with a deformable top wall, similar to the experiments. Going beyond the usual lubrication flows analysed in these geometries, we include finite fluid inertia and couple the reduced flow equations to a novel reduced 1-D wall deformation equation. Although a quantitative comparison with previous experiments is difficult, the behaviours of the proposed model show, qualitatively, agreement with the experimental observations, and capture several key effects. Specifically, we find the critical conditions under which the inflated base state of the 1-D FSI model is linearly unstable to infinitesimal perturbations. The critical Reynolds numbers predicted are in agreement with experimental observations. The unstable modes are highly oscillatory, with frequencies close to the natural frequency of the wall, suggesting that the observed instabilities are resonance phenomena. Furthermore, during the start-up from an undeformed initial state, self-sustained oscillations can be triggered by FSI. Our modelling framework can be applied to other microfluidic systems with similar geometric scale separation under different operating conditions.

A depth-averaged model for Newtonian fluid flows in shallow microchannels

Pressure-driven flow has been widely used in microfluidic devices to pump fluids and particles through planar microchannels for various applications. The variation in channel geometry (e.g., contraction or expansion) may lead to complex flow phenomena (e.g., recirculations) useful for microfluidic sampling, such as fluid mixing and particle focusing. In this work, we develop a depth-averaged inertial flow model for Newtonian fluids in shallow microchannels based on an asymptotic analysis of the continuity and momentum equations. The validity and accuracy of this two-dimensional model are assessed through comparisons with the experimental measurements and three-dimensional numerical simulations for water flow through contraction–expansion microchannels of varying depths. Our proposed depth-averaged model provides the accuracy of three-dimensional modeling if the channel depth-to-width ratio remains small (specifically, at ∼0.1 or less).

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.

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

Long, shallow microchannels embedded in thick, soft materials are widely used in microfluidic devices for lab-on-a-chip applications. However, the bulging effect caused by fluid-structure interactions between the internal viscous flow and the soft walls has not been completely understood. Previous models either contain a fitting parameter or are specialized to channels with plate-like walls. This work is a theoretical study of the steady-state response of a compliant microchannel with a thick wall. Using lubrication theory for low-Reynolds-number flows and the theory for linearly elastic isotropic solids, we obtain perturbative solutions for the flow and deformation. Specifically, only the channel's top wall deformation is considered, and the ratio between its thickness t and width w is assumed to be (t/w)2≫1. We show that the deformation at each stream-wise cross section can be considered independently, and that the top wall can be regarded as a simply supported rectangle subject to uniform pressure at its bottom. The stress and displacement fields are found using Fourier series, based on which the channel shape and the hydrodynamic resistance are calculated, yielding a new flow rate-pressure drop relation without fitting parameters. Our results agree favourably with, and thus rationalize, previous experiments.

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.

Investigation on critical heat flux of flow boiling in parallel microchannels with large aspect ratio: Experimental and theoretical analysis

Critical heat flux (CHF) for microchannel heat sink makes significant sense to industrial applications in preventing thermal safety accidents and avoiding facility burnout. Nevertheless, the fundamentals of CHF in confined microchannels are lack of clear comprehension, and related visualization experimental data about CHF also needs complement. The present work explores flow boiling CHF in parallel shallow microchannel heat sink with visualization experiments, aiming to provide new CHF data for microchannels with large aspect ratio (AR = W/H = 5). Two test configurations (S1: H = 400 μm, W = 2000 μm, S2: H = 300 μm, W = 1500 μm) and two kinds of working fluids (ethanol and acetone) are adopted. By capturing bubble behaviors with high speed photography, the characteristics and mechanism of CHF for such shallow microchannels are revealed. It is found out that the boiling curve keeps a linear growth with the wall superheating degree after the local dry-out, where the dominate heat transfer mechanism directly transits to the film boiling without experiencing the transition boiling. Meanwhile, the effect of mass flux, working fluid, and hydraulic diameter of channel on the CHF is also studied respectively. The experimental results illustrate that the CHF in the microchannels with large AR is significantly influenced by flow instability and presents a third order polynomial increasing trend with G. Besides, statistic analysis on the CHF data with some well-known correlations is conducted to find out the suitable theoretical mode for the shallow microchannels. A new CHF correlation that can especially fit for the microchannels with aspect ratio heavily deviated from 1 is proposed, where 116 data points involving 8 different working fluids and 9 types of microchannels are verified with MAE of 7.3%.

Transient response of nonideal ion-selective microchannel-nanochannel devices.

We report evidence of variation in ion selectivity of a fabricated microchannel-nanochannel device resulting in the appearance of a distinct local maximum in the overlimiting chronopotentiometric response. In this system consisting of shallow microchannels joined by a nanochannel, viscous shear at the microchannel walls suppresses the electro-osmotic instability and prevents any associated contribution to the nonmonotonic response. Thus, this response is primarily electrodiffusive. Numerical simulations indicate that concentration polarization develops not only within the microchannel but also within the nanochannel itself, with a local voltage maximum in the chronopotentiometric response correlated with interfacial depletion and having the classic i^{-2} Sands time dependence. Furthermore, the occurrence of the local maxima is correlated with the change in selectivity due to internal concentration polarization. Understanding the transient nonideal permselective response is essential for obtaining fundamental insight and for optimizing efficient operation of practical fabricated nanofluidic and membrane devices.

A two-step sealing-and-reinforcement SU8 bonding paradigm for the fabrication of shallow microchannels

Adhesive bonding is a key technique to create microfluidic devices when two separate substrates are used to form microchannels. Among many adhesives explored in microchannel fabrication, SU8 has been widely used as an adhesive layer for sealing the microchannel sidewalls. The majority of the available SU8-based bonding methods, however, suffer from the difficulties associated with sealing of two important types of the microchannel architecture: (1) shallow microchannels with small patterns on a large area, and (2) microchannels with ultra-low aspect ratios (e.g. 6 mm in width and m in height). In this paper, a new bonding paradigm based upon the low-temperature and low-pressure SU8 bonding, consisting of two steps of sealing using a thin-SU8-coated PET film and bonding reinforcement using a SU8-coated glass slide, is proposed to resolve the aforementioned difficulties. Since it does not need complicated instruments such as a wafer bonding machine and a lamination device, the developed bonding paradigm is convenient and economical. We successfully demonstrate the compatibility of the proposed bonding paradigm with the two microchannel fabrication approaches based on the glass wet etching and the SU8 photo-lithography, where small microchannels with the innermost surfaces fully made of SU8 are obtained. A theoretical model is employed to better investigate the flow characteristics and the structural behavior of the microchannel including the PET film deformation, strain and von Mises stress distributions, bonding strength, etc. Moreover, we demonstrate the fabrication of the multi-height deep–shallow microchannel sidewalls and their sealing using the SU8-coated PET film. Finally, as a proof-of-concept device, a microfluidic filter consisting of the double-height deep–shallow microchannel is fabricated for separation of 3 µm and 10 µm particles.

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.

Induced charge effects on electrokinetic entry flow

Electrokinetic flow, due to a nearly plug-like velocity profile, is the preferred mode for transport of fluids (by electroosmosis) and species (by electrophoresis if charged) in microfluidic devices. Thus far there have been numerous studies on electrokinetic flow within a variety of microchannel structures. However, the fluid and species behaviors at the interface of the inlet reservoir (i.e., the well that supplies the fluid and species) and microchannel are still largely unexplored. This work presents a fundamental investigation of the induced charge effects on electrokinetic entry flow due to the polarization of dielectric corners at the inlet reservoir-microchannel junction. We use small tracing particles suspended in a low ionic concentration fluid to visualize the electrokinetic flow pattern in the absence of Joule heating effects. Particles are found to get trapped and concentrated inside a pair of counter-rotating fluid circulations near the corners of the channel entrance. We also develop a depth-averaged numerical model to understand the induced charge on the corner surfaces and simulate the resultant induced charge electroosmosis (ICEO) in the horizontal plane of the microchannel. The particle streaklines predicted from this model are compared with the experimental images of tracing particles, which shows a significantly better agreement than those from a regular two-dimensional model. This study indicates the strong influences of the top/bottom walls on ICEO in shallow microchannels, which have been neglected in previous two-dimensional models.

Electrokinetic instability in microchannel ferrofluid/water co-flows

Electrokinetic instability refers to unstable electric field-driven disturbance to fluid flows, which can be harnessed to promote mixing for various electrokinetic microfluidic applications. This work presents a combined numerical and experimental study of electrokinetic ferrofluid/water co-flows in microchannels of various depths. Instability waves are observed at the ferrofluid and water interface when the applied DC electric field is beyond a threshold value. They are generated by the electric body force that acts on the free charge induced by the mismatch of ferrofluid and water electric conductivities. A nonlinear depth-averaged numerical model is developed to understand and simulate the interfacial electrokinetic behaviors. It considers the top and bottom channel walls’ stabilizing effects on electrokinetic flow through the depth averaging of three-dimensional transport equations in a second-order asymptotic analysis. This model is found accurate to predict both the observed electrokinetic instability patterns and the measured threshold electric fields for ferrofluids of different concentrations in shallow microchannels.

Use of a CD laser pickup head to fabricate microelectrodes in polymethylmethacrylate substrates for biosensing applications.

In this work, we report a simple fabrication method for microelectrodes on a polymethylmethacrylate substrate, using a low-cost laser platform based on a CD-DVD unit for direct rapid-prototyping. We used this laser microfabrication technique to etch any desired design on polymethylmethacrylate substrates to produce microchannels with controlled geometry, with a highly repeatable micron-scale resolution. Those shallow microchannels were then filled with a conductive paste of material of our choice that was converted into microelectrodes of desired shapes and geometries after drying. To validate our process, different geometries, sizes and materials were used as electrodes, and then tested for amperometry and impedance measurements. Development of these microelectrodes is motivated by their potential application in sensors and biosensors, such as glucose and cell counting, as demonstrated in this paper.

Fabrication of shallow microchannels for highly uniform blood smear preparation

Polydimethylsiloxane (PDMS) based microfluidic channels for blood cell analysis were fabricated using etched glass as the master for soft lithography. The design consisted of shallow microchannels with uniformly spaced micropillars that aid in the formation of thin blood films (smear) through capillary filling of the microchannels. The concentration of hydrofluoric acid (HF) and the time duration of etching were varied and conditions optimized for fabrication of microstructures of different depths. Morphological analysis revealed the structure and dimension of the microstructures to be highly consistent. It was also noted that the micropillars formed during soft lithography prevented the roof of the PDMS microchannel from collapsing, a common phenomena observed while using shallow microfluidic channels. The fabricated prototype was used for blood cell analysis and the blood smear formed due to capillary flow was found to eliminate the drawbacks associated with manual smear preparation. Thus, a novel cost effective microfluidic device for cell analysis using glass etching was successfully developed and tested.

Interaction forces between microfluidic droplets in a Hele-Shaw cell

Various microfluidic systems, such as chemical and biological lab-on-a-chip devices, involve motion of multiple droplets within an immersing fluid in shallow microchannels. Modelling the dynamics of such systems requires calculation of the forces of interaction between the moving droplets. These forces are commonly approximated by superposition of dipole solutions, which requires an assumption of sufficiently large distance between the droplets. In this work we obtain exact solutions (in the Hele-Shaw limit) for two moving droplets, and a droplet within a droplet, located within a moving immersing fluid, without limitation on the distance between the droplets. This is achieved by solution of the pressure field in a bipolar coordinate system and calculation of the force in Cartesian coordinates. Our results are compared with numerical computations, experimental data and the existing dipole-based models. We utilize the results to calculate the dynamics of a droplet within a droplet, and of two close droplets, located within an immersing fluid with oscillating speed. Overall, the obtained results establish the solid base for the rather important future extensions for modelling the complex, long-range interdroplet interactions in the limit of dense droplet media.

Theory of multi-species electrophoresis in the presence of surface conduction

Electrophoresis techniques are characterized by concentration disturbances (or waves) propagating under the effect of an electric field. These techniques are usually performed in microchannels where surface conduction through the electric double layer (EDL) at channel walls is negligible compared with bulk conduction. However, when electrophoresis techniques are integrated in nanochannels, shallow microchannels or charged porous media, surface conduction can alter bulk electrophoretic transport. The existing mathematical models for electrophoretic transport in multi-species electrolytes do not account for the competing effects of surface and bulk conduction. We present a mathematical model of multi-species electrophoretic transport incorporating the effects of surface conduction on bulk ion-transport and provide a methodology to derive analytical solutions using the method of characteristics. Based on the analytical solutions, we elucidate the propagation of nonlinear concentration waves, such as shock and rarefaction waves, and provide the necessary and sufficient conditions for their existence. Our results show that the presence of surface conduction alters the propagation speed of nonlinear concentration waves and the composition of various zones. Importantly, we highlight the role of surface conduction in formation of additional shock and rarefaction waves which are otherwise not present in conventional electrophoresis.

Boundary elements method for microfluidic two-phase flows in shallow channels

In the following work we apply the boundary element method to two-phase flows in shallow microchannels, where one phase is dispersed and does not wet the channel walls. These kinds of flows are often encountered in microfluidic Lab-On-A-Chip devices and characterized by low Reynolds and low capillary numbers.Assuming that these channels are homogeneous in height and have a large aspect ratio, we use depth-averaged equations to describe these two-phase flows using the Brinkman equation, which constitutes a refinement of Darcy’s law. These partial differential equations are discretized and solved numerically using the boundary element method, where a stabilization scheme is applied to the surface tension terms, allowing for a less restrictive time step at low capillary numbers. The convergence of the numerical algorithm is checked against a static analytical solution and on a dynamic test case. Finally the algorithm is applied to the non-linear development of the Saffman–Taylor instability and compared to experimental studies of droplet deformation in expanding flows.

Dynamics of step-emulsification: From a single to a collection of emulsion droplet generators

Microfluidics has proven to be an efficient tool for making fine and calibrated emulsion droplets. The parallelization of drop makers is required for producing large amounts. Here, we investigate the generation of emulsion drops along a series of shallow microchannels emerging in a deep one, in other words the step-emulsification process. The dynamics of a single drop maker is first characterized as a function of interfacial tension and viscosities of both phases. The characteristic time scale of drop formation, namely, the necking time that finally sets drop size, is shown to be principally governed by the outer phase viscosity to interfacial tension ratio with a minor correction linked to the viscosity ratio. The step emulsification process experiences a transition of fragmentation regime where both the necking time and drop size suddenly raise. This transition, that corresponds to a critical period of drop formation and thus defines a maximum production rate of small droplets, is observed to be ruled by the viscosity ratio of the two phases. When drops are produced along an array of microchannels with a cross flow of the continuous phase, a configuration comparable to a one-dimensional membrane having rectangular pores, a drop boundary layer develops along the drop generators. In the small drop regime, the local dynamics of drop formation is shown to be independent on the emulsion cross flow. Moreover, we note that the development of the drop boundary layer is even beneficial to homogenize drop size along the production line. On the other hand, in the large drop regime, drop collision can trigger fragmentation and thus lead to size polydispersity.

Pressure-driven deformation with soft polydimethylsiloxane (PDMS) by a regular syringe pump: challenge to the classical fluid dynamics by comparison of experimental and theoretical results

Pressure-driven flows through optically transparent polydimethylsiloxane (PDMS) microfluidic channels using a syringe pump are common in many experimental applications. However, because of small changes, the pressure-induced deformations due to soft materials and shapes and patterns in the microchannels, which generate untargeted flow velocity and pressure drop, have been easily ignored. In this paper, we present a simple experimental investigation with circular-shaped, periodically arranged objects of three different characteristic dimensions, as well as various channel heights ranging from 15 μm to 200 μm. The resultant CCD images and pressure data were used to determine the extent of the start-up transients and evaluate the establishment of quasi-steady flow conditions. Channel deformation, measured by fluorescence intensity difference, was severe in shallow microchannels that had characteristically large obstacles. In addition, PDMS microchannel bulging effects in shallow microchannels exerted a greater deleterious effect on (ΔP/Δx)QS values than upon VQS for the experiments using a volumetrically controlled syringe pump. The discrepancy between experimental and theoretical (ΔP/Δx) increased with decreasing microchannel height. This means that the severe PDMS bulging observed in shallow microchannels using a syringe pump can generate large deviations from the desired experimental result. As a result, the slope of Darcy friction factors plotted against the Reynolds number indicates that the slope was strongly dependent on microfluidic channel height and the degree of PDMS bulging. The microfluidic channel with the greatest height exhibited the smallest bulging effect and was shown to be in relatively good agreement with predicted values, while the slope became much steeper than −1 as channel heights decreased.

Foil assisted replica molding for fabrication of microfluidic devices and their application in vitro.

We present a simple, rapid, benchtop, Foil Assisted Rapid Molding (FARM) method for the fabrication of microfluidic devices. This novel technique involves the use of aluminium foil, pen and an X-Y plotter to create semi-circular or plano-concave, shallow microchannels. It is an easy do-it-yourself (DIY) technique for creating a microfluidic device in three simple steps: (1) create a channel design using the CAD software, (2) plot the patterns on aluminium foil and (3) use the reverse of the engraved foil as a mold to create microfluidic devices. In this report, we present a detailed study of the proposed method by varying a range of parameters such as foil thickness, tip material, and tip sizes and by investigating their effect on the creation of channels with varying geometry. Furthermore, we demonstrated the cytocompatibility of these devices in vitro.