Liquid and gas flows in microchannels of varying cross section: a comparative analysis of the flow dynamics and design perspectives

This paper presents a comparative study of the flow of liquid and gases in microchannels of converging and diverging cross sections. Towards this, the static pressure across the microchannels is measured for different flow rates of the two fluids. The study includes both experimental and numerical investigations, thus providing several useful insights into the local information of flow parameters as well. Three different microchannels of varying angles of convergence/divergence (4°, 8° and 12°) are studied to understand the effect of the angle on flow properties such as pressure drop, Poiseuille number and diodicity. A comparison of the forces involved in liquid and gas flows shows their relative significance and effect on the flow structure. A diodic effect corresponds to a difference in the flow resistance in a microchannel of varying cross section, when the flow is subjected alternatively to converging and diverging orientations. In the present experiments, the diodic effect is observed for both liquid and gas as working fluids. The effect of governing parameters—Reynolds number and Knudsen number, on the diodicity is analysed. Based on these results, a comparison of design perspectives that may be useful in the design of converging/diverging microchannels for liquid and gas flows is provided.     

DSMC investigation of rarefied gas flow through diverging micro- and nanochannels

Direct simulation Monte Carlo (DSMC) method with simplified Bernoulli trials (SBT) collision scheme has been used to study the rarefied pressure-driven nitrogen flow through diverging micro- and nanochannels. The fluid behaviours flowing between two plates with different divergence angles ranging between 0° and 17° are described at different pressure ratios (1.5 ≤ Π ≤ 2.5) and Knudsen numbers (0.03 ≤ Kn ≤ 12.7). The primary flow field properties, including pressure, velocity, and temperature, are presented for divergent micro- and nanochannels and are compared with those of a micro- and nanochannel with a uniform cross section. The variations of the flow field properties in divergent micro- and nanochannels which are influenced by the area change, the channel pressure ratio, and the rarefication are discussed. The results show no flow separation in divergent micro- and nanochannels for all the range of simulation parameters studied in the present work. It has been found that a divergent channel can carry higher amounts of mass in comparison with an equivalent straight channel geometry. A correlation between the mass flow rate through micro- and nanochannels, the divergence angle, the pressure ratio, and the Knudsen number has been suggested. The present numerical findings prove the occurrence of Knudsen minimum phenomenon in micro- and nanochannels with non-uniform cross sections.     

Experimental investigation on the flow transition in different pin-fin arranged microchannels

The flow characteristics of water through the in-line and staggered pin-fin microchannels with length of 25 mm, width of 2.4 mm and height of 0.11 mm were studied experimentally. The flow transition was identified as a sudden increasing slope in both pressure drop versus mass flow rate curve and friction factor versus Reynolds number curve for in-line pin-fin microchannels, but it did not occur for staggered pin-fin microchannels. The effect of pin-fin arrangements on the flow transition was not reported in the previous literature. With the aid of microparticle image velocimetry (Micro-PIV) technology, the streamlines, velocity fields and velocity fluctuation fields of flow through the pin-fin microchannels were captured to explain the flow transition, and the effect of pin-fin arrangements on the flow transition was analyzed for the first time. It was found that at the critical Reynolds number where the flow transition occurred for the in-line pin-fin microchannels, the steady double-vortex wake flow changed to the unsteady vortex-shedding wake flow. The occurrence of vortex shedding caused an obvious change in main stream from straight flow to wavy flow and further induced significant increases of transversal velocity and velocity fluctuations, which induced strong flow disturbance in transversal directions and large additional pressure drop, and finally caused the flow transition in the in-line pin-fin microchannels. For the staggered pin-fin microchannels, the main stream through the pin-fin arrays was found to be already the wavy flow before the vortex shedding. Thus, the transversal velocity and velocity fluctuations induced by the vortex shedding were relatively small, and therefore, the flow transition with an abrupt pressure drop increase was not observed in the staggered pin-fin microchannels.     

Numerical simulation of the capillary flow in the meander microchannel

Pumping in microfluidic devices is an important issue in actuating fluid flow in microchannel, especially that capillary force has received more and more attractions due to the self-driven motion without external power input. However, less 2D simulation was done on the capillary flow in microchannel especially the meander microchannel which can be used for mixing and lab-on-a-chip (LOC) application. In this paper, the numerical simulation of the capillary flow in the meander microchannel has been studied using computer fluid dynamic simulation software CFD-ACE⁺. Different combinations of channel width in the X-direction denoted as W_x and Y-direction denoted as W_y were designed for simulating capillary flow behavior and pressure drop. The designed four types of meander microchannels (W_x × W_y) were 100 × 100 μm, 100 × 200 μm, 50 × 200 μm, and 50 × 400 μm. In this simulation results, it is found that the capillary pumping speed is highly depending on the channel width. The large speed change occurs at the turning angle of channel width change from W_x to W_y. The fastest pumping effect is found in the meander channel of 100 × 100 μm, which has an average pumping speed of 0.439 mm/s. The slowest average flow speed of 0.205 mm/s occurs in the meander channel of 50 × 400 μm. Changing the meander channel width may vary the capillary flow behavior including the pumping speed and the flow resistance as well as pressure drop which will be a good reference in designing the meander microchannels for microfluidic and LOC application.     

Superhydrophobic, hierarchical, plasma-nanotextured polymeric microchannels sustaining high-pressure flows

We fabricated superhydrophilic and superhydrophobic polymeric microfluidic devices with controlled hierarchical, random roughness, using plasma processing. We implemented a dye staining technique to visually demonstrate the persistence of the superhydrophobic state under flow for pressures in excess of 2.5 bar inside the microchannel. We further confirmed the stability of superhydrophobicity by pressure drop measurements, friction factor and slip length calculations under laminar flow conditions. We also compared identical rough superhydrophilic and superhydrophobic microchannels showing reduced pressure drop in the latter by as much as 22 %. Plasma etching and simultaneous nanotexturing (followed by optional fluorocarbon plasma deposition) are thus shown as an easy-to-implement method for attaining robust Cassie-state against high-pressure microchannel flows.     

Flow-induced deformation of compliant microchannels and its effect on pressure–flow characteristics

We report theoretical and experimental investigations of flow through compliant microchannels in which one of the walls is a thin PDMS membrane. A theoretical model is derived that provides an insight into the physics of the coupled fluid–structure interaction. For a fixed channel size, flow rate and fluid viscosity, a compliance parameter \(f_{\text{p}}\) is identified, which controls the pressure–flow characteristics. The pressure and deflection profiles and pressure–flow characteristics of the compliant microchannels are predicted using the model and compared with experimental data, which show good agreement. The pressure–flow characteristics of the compliant microchannel are compared with that obtained for an identical conventional (rigid) microchannel. For a fixed channel size and flow rate, the effect of fluid viscosity and compliance parameter \(f_{\text{p}}\) on the pressure drop is predicted using the theoretical model, which successfully confront experimental data. The pressure–flow characteristics of a non-Newtonian fluid (0.1 % polyethylene oxide solution) through the compliant and conventional (rigid) microchannels are experimentally measured and compared. The results reveal that for a given change in the flow rate, the corresponding modification in the viscosity due to the shear thinning effect determines the change in the pressure drop in such microchannels.     

A facile pressure drop measurement system and its applications to gas–liquid microflows

A system for measuring the pressure drop of a fluid in a microchannel was developed in this study with measurements ranging from 0 to 7 kPa and an accuracy of 1 Pa for constant pressure drop. This system utilizes commercial pressure sensors, self-made amplifiers and a vibration insulation platform to insure accuracy and reproducibility of the results. Pressure calibrations can be conveniently computed using the manufacturers’ datasheet. This measuring system was firstly tested with the pressure drop measurement of single-phase flow in microchannels and the results showed good agreement with theoretical computations. Oscillating pressure drops in the generation of bubbles in T-junction microchannel were studied using the pressure measurement system and their amplitude relatively to the change of working systems is carefully discussed with the comparison of theoretical models from literatures.     

Liquid film thickness measurement underneath a gas slug with miniaturized sensor matrix in a microchannel

Measurement of liquid film thickness is essential for understanding the dynamics of two-phase flow in microchannels. In this work, a miniaturized sensor matrix with impedance measurement and MEMS technology to measure the thin liquid film underneath a bubble in the air–water flow in a horizontal microchannel has been developed. This miniaturized sensor matrix consists of 5 × 5 sensors where each sensor is comprised of a transmitter and a receiver electrode concentrically. The dimension and performance of the sensor electrodes were optimized with simulation results. The maximum diameter of the sensor ring is 310 µm, allowing a measurable range of liquid film thickness up to 83 µm. These sensors were distributed on the surface of a wafer with photolithography technology, covering a total length of 8 mm and a width of 2 mm. A spatial resolution of 0.5 × 2.0 mm² and a temporal resolution of 5 kHz were achieved for this sensor matrix with a measurement accuracy of 0.5 µm. A series of microchannels with different heights were used in the calibration in order to achieve the signal-to-thickness characteristics of each sensor. This delicate sensor matrix can provide detailed information on the variation of film thickness underneath gas–water slug directly, accurately and dynamically.     

Pressure drop of three-phase liquid–liquid–gas slug flow in round microchannels

In this paper we present a model for the calculation of pressure drop of three-phase liquid–liquid–gas slug flow in microcapillaries of a circular cross section. Introduced models consist of terms attributing for frictional and interfacial pressure drop, incorporating the presence of a stagnant thin film at the wall of the channel. Different formulations of the interfacial pressure drop equation were employed, using expressions developed by Bretherton (J Fluid Mech 10:166–188, 1961), Warnier et al. (Microfluid Nanofluid 8:33–45, 2010) or Ratulowski and Chang (Phys Fluids A 1:1642–1655, 1989). Models were validated experimentally using oleic acid–water–nitrogen and heptane–water–nitrogen three-phase flows in round Teflon or Radel R microchannels of 254- and 508-µm nominal inner diameter, for capillary numbers Ca _b between 10^?4 and 4.9 × 10^?1 and Reynolds numbers Re between 0.095 and 300. Best agreement between measured and calculated values of pressure drop, with relative error between ?22 and 19 % or ?20 and 16 %, is reached for Warnier’s or Ratulowski and Chang’s interfacial pressure drop equation, respectively. The results prove that three-phase slug flow pressure drop can be successfully predicted by extending existing two-phase slug flow correlations. Good agreement of Bretherton’s equation was reached only at lower Ca numbers, indicating that an extension of the interfacial pressure drop equation as performed by Warnier et al. (Microfluid Nanofluid 8:33–45, 2010) or Ratulowski and Chang (Phys Fluids A 1:1642–1655, 1989) for higher capillary numbers is necessary. Additionally it was demonstrated that pressure drop increases substantially if dry slug flow occurs or if microchannels with significant surface roughness are employed. Those influences were not accounted for in the models presented.     

Effects of interface curvature on Poiseuille flow through microchannels and microtubes containing superhydrophobic surfaces with transverse grooves and ribs

This paper presents numerical results pertaining to the effects of interface curvature on the effective slip behavior of Poiseuille flow through microchannels and microtubes containing superhydrophobic surfaces with transverse ribs and grooves. The effects of interface curvature are systematically investigated for different normalized channel heights or tube diameters, shear-free fractions, and flow Reynolds numbers. The numerical results show that in the low Reynolds number Stokes flow regime, when the channel height or tube diameter (normalized using the groove–rib spacing) is sufficiently large, the critical interface protrusion angle at which the effective slip length becomes zero is θ _c ≈ 62°–65°, which is independent of the shear-free fraction, flow geometry (channel and tube), and flow driving mechanism. As the normalized channel height or tube diameter is reduced, for a given shear-free fraction, the critical interface protrusion angle θ _c decreases. As inertial effects become increasingly dominant corresponding to an increase in Reynolds number, the effective slip length decreases, with the tube flow exhibiting a more pronounced reduction than the channel flow. In addition, for the same corresponding values of shear-free fraction, normalized groove–rib spacing, and interface protrusion angle, longitudinal grooves are found to be consistently superior to transverse grooves in terms of effective slip performance.     

Analysis and experiment of transient filling flow into a rectangular microchannel on a rotating disk

In order to predict the time-dependent behaviors of the moving front in lab-on-a-CD systems or centrifugal pumping, an analytical expression and experimental methods of centrifugal-force-driven transient filling flow into a rectangular microchannel in centrifugal microfluidics are presented in this paper. Considering the effect of surface tension, and neglecting the effect of Coriolis force, the velocity profile, flow rate, the moving front displacement and the pressure distribution along the microchannel are characterized. Experiments are carried out using the image-capturing unit to measure the shift of the flow in rectangular microchannels. The flow characteristics in rectangular microchannels with different cross-sectional dimensions (200, 300 and 400 μm in width and 140, 240 and 300 μm in depth) and length (18 and 25 mm) under different rotational speed are investigated. According to the experimental data, the model can be more reasonable to predict the flow displacement with time, and the errors between theoretical and the experimental will decrease with increasing the cross-section size of the microchannel.     

Flow characteristics of polar liquids in microfluidic immunosensors

There is an interest in microfluidic devices for disease detection. In microfluidic immunosensors, the microchannel surfaces are functionalized with a stack of intermediate linker molecules to the specific antibodies. The efficiency of these immunosensors depends on the effective capture of antigens flowing in the carrier fluid by the surface-immobilized antibodies. The diffusion of these antigens to these antibody-immobilized surfaces is governed by the velocity profile, which in turn is governed by the interaction of the carrier fluid molecules with the surface antibodies. We report a systematic study to characterize fluid flow of different polar liquids (water, methanol and isopropyl alcohol) in trapezoidal Si microchannels, of about 100 μm hydraulic diameter, functionalized with intermediate molecular layers along with three different antibodies immobilized via these molecular layers. The friction constants were calculated from the pressure drop measurements. We attempted to understand the solid–liquid interactions in terms of the friction constants as a function of the solid surface free energies of the terminal antibody layers (which are affected by the energetics of the underlying layers) immobilized on to the microchannels, and the polarities of the liquids flowing through these microchannels. Correlations of liquid polarities with the friction constants were seen for almost all the functionalized surfaces. A reasonable correlation of the surface energies with the friction constants was seen for most of the surfaces studied. Possible reasons for the behaviors are discussed. The measured friction constants and the knowledge of the solid–liquid interactions could facilitate improved designs of microfluidic immunosensors.     

Design and simulation of passive micromixers based on capillary

Three-dimensional passive micromixers made by clamping capillaries in different directions and angles are presented in this paper. This type of mixers is easier to fabricate than the multi-layer passive mixers, and is the firstly proposed capillary-based micromixer. Simulations have been conducted for the flow and mass transport through the 3D-twisted compression–expansion microchannels. The simulations show that, compared to the T-mixer with the same cross-sectional perimeter, the 3D capillary mixers proposed in this paper can significantly enhance mixing. The 3D-twisted compression–expansion mixers with different clamping angles are analyzed. The results show that capillaries with clamping angle of 90°, 45–90° and 45° exhibit different mixing mechanism. The 45-mixer presents the best mixing enhancement by reducing 90.8?% of the mixing length with only 57?%extra pressure drop in transporting the liquids to those of the T-mixer when the clamping cross-section of 0.6?mm?×?0.2?mm, clamping interval of 1?mm, and the Peclet number of 3,000 are applied to all designed mixers.     

Measurement of pressure drop and flow resistance in microchannels with integrated micropillars

In the present study, we investigate single phase fluid flow through microchannels with integrated micropillars to calculate the pressure drop and flow resistance. The microchannels, which contain micropillars arranged in square and staggered arrangement, are fabricated in silicon substrate using standard photolithography and deep reactive ion etching (DRIE) techniques. The DRIE technique results in precise and accurate fabrication with smooth and vertical wall profiles. Pressure drop measurements are performed on microchannels with integrated micropillars under creeping flow regime over a range of water flow rates from 50 to 600 μl/min. It is observed that the pressure drop varies linearly with increasing flow rates. Flow resistance ( $\Updelta P/Q$ ) is calculated using the pressure drop values and is found to be decreasing as the Darcy number ( $\sqrt{K/h^2}$ ) increases. In general, the square arrangement of pillars offers higher resistance to flow than their staggered counterparts. It is observed that the existing theoretical models fail to accurately predict the permeability of the microchannel with integrated micro-pillars, particularly for cases where the micropillars have smooth and accurate geometric conformity, as obtained in the microfabricated structures used in the present study.     

Development of a nanofluidic preconcentrator with precise sample positioning and multi-channel preconcentration

A nanofluidic preconcentrator with the capability of rapidly preconcentrating and precisely positioning protein bands in multiple microchannels has been developed for highly sensitive detection of biomolecules. A novel electrical resistive network model is developed to guide the design of the nanofluidic preconcentrator which consists of a PDMS slab bonded with a glass slide. In the prototype design, two microchannels (23 mm long, 25–50 μm wide, and 5–15 μm deep), one preconcentration microchannel and one ground microchannel are connected in the middle via 16 nanochannels (25–50 μm long, 25 μm wide, and 50–80 nm deep). With two sets of optimal voltage settings applied on the opposite ends of the nanofluidic chip, the ion depletion region and electrokinetic trapping were generated to carry out the preconcentration. With the optimal voltage settings (30–30 V) predicted by the model, the ionic current of the nanochannel in our optimized preconcentrator was adjusted to be greater than the threshold value (3.9 nA) needed for the occurrence of the preconcentration, and a preconcentration factor >10⁵ was achieved in 5 min. The sample positioning capability of the preconcentrator was demonstrated by adjusting the applied voltages and moving the preconcentrated protein bands to multiple sites by a distance from several micrometers to several millimeters in the preconcentration channel. The multi-channel preconcentration capability was also demonstrated by preconcentrating two protein bands in two separate microchannels. In this work, the resistive network model was developed and validated to optimize nanofluidic preconcentrators for rapid, high throughput and highly sensitive sensing of low abundance analytes.     

Seed bubbles trigger boiling heat transfer in silicon microchannels

The smooth channel surface of microsystems delays boiling incipience in heated microchannels. In this paper, we use seed bubbles to trigger boiling heat transfer and control thermal non-equilibrium of liquid and vapor phases in parallel microchannels. The test section consisted of a top glass cover and a silicon substrate. Microheater array was integrated at the top glass cover surface and driven by a pulse voltage signal to generate seed bubbles in time sequence. Each microheater corresponds to a specific microchannel and is located in the microchannel upstream. Five triangular microchannels with a hydraulic diameter of 100 μm and a length of 12.0 mm were etched in the silicon substrate. A thin platinum film was deposited at the back surface of silicon chip with an effective heating area of 4,500 × 1,366 μm, acting as the main heater for the heat transfer system. Acetone liquid was used. With the data range reported here, boiling incipience was not initiated if wall superheats are smaller than 15°C without seed bubbles assisted. Injection seed bubbles triggers boiling incipience and controls thermal non-equilibrium between liquid and vapor phases successfully. Four modes of flow and heat transfer are identified. Modes 1, 2, and 4 are the stable ones without apparent oscillations of pressure drops and heating surface temperatures, and mode 3 displays flow instabilities with apparent amplitudes and long periods of these parameters. The four modes are divided based on the four types of flow patterns observed in microchannels. Seed bubble frequency is a key factor to influence the heat transfer. The higher the seed bubble frequency, the more decreased non-equilibrium between two phases and heating surface temperatures are. The seed bubble frequency can reach a saturation value, at which heat transfer enhancement attains the maximum degree, inferring that a complete thermal equilibrium of two phases is approached. The saturation frequency is about a couple of thousand Hertz in this study.     

A level set-based topology optimization method for optimal manifold designs with flow uniformity in plate-type microchannel reactors

This paper proposes an optimal design method for plate-type microchannel reactor manifolds, using a level set-based topology optimization method that targets flow uniformity among the microchannels. For plate-type microchannel reactors, manifold designs must consider both the uniformity of flow among the microchannels and minimization of pressure drop in the device. To address these design requirements, the pressure drop in the device is defined as the objective functional to be minimized under a flow rate inequality constraint, defined as the deviation in flow rate among the microchannels during the optimization. In addition, we propose a comparably simple and stable augmented Lagrangian method using an exponential function, to determine the Lagrange multiplier that acts to satisfy the flow rate inequality constraint. To demonstrate the utility of our proposed method, two-dimensional Z-type and U-type manifold design problems are presented in the numerical examples.     

Superhydrophobic,passive microvalves with controllable opening threshold: exploiting plasma nanotextured microfluidics for a programmable flow switchboard

Plasma processing is used to create passive superhydrophobic on–off valves with tailored opening pressure inside microfluidic devices. First, anisotropic O₂ plasma etching on polymeric microchannels is utilized to controllably roughen (nanotexture) the bottom of the microchannel. Second, the nanotextured surfaces are hydrophobized by means of a C₄F₈ plasma deposition step through a stencil mask creating superhydrophobic stripes or patches. The superhydrophobic patches play the role of on/off valves with predesigned opening pressure threshold (in the range 40–110 mbar), determined by the microchannel dimensions and the size of the nanotexture on the patch. These valves are integrated inside microchannel networks paving the way to autonomous microfluidic devices. To this aim, we present a novel preprogrammable flow switchboard that can split and control the liquid flow for multiple analysis purposes. The proposed valves present an example of how effectively plasma nanoscience and nanotechnology can be applied to microfluidics/nanofluidics and analytical chemistry.     

Role of interface shape on the laminar flow through an array of superhydrophobic pillars

In this study, measurements of the pressure drop and the velocity vector fields through a regular array of superhydrophobic pillars were systematically taken to investigate the role of air–water interface shape on laminar drag reduction. A polydimethylsiloxane microfluidic channel was created with a regular array of apple-core-shaped and circular pillars bridging across the entire channel. Due to the shape and hydrophobicity of the apple-core-shaped pillars, air was trapped on the side of the pillars after filling the microchannel with water. The measurements were taken at a capillary number of Ca = 6.6 × 10^?5. The shape of the air–water interface trapped within the superhydrophobic apple-core-shaped pillars was systematically modified from concave to convex by changing the static pressure within the microchannel. The pressure drop through the microchannel containing the superhydrophobic apple-core-shaped pillars was found to be sensitive to the shape of the air–water interface. For static pressures which resulted in the apple-core-shaped superhydrophobic pillars having a circular cross section, D/D ₀ = 1, a drag reduction of 7% was measured as a result of slip along the air–water interface. At large static pressures, the interface was driven into the apple-core-shaped pillars, resulting in decrease in the effective size of the pillars and an increase in the effective spacing between pillars. When combined with a slip velocity measured to be 10% of the average velocity between the pillars, the result was a pressure drop reduction of 18% compared to the circular pillars at a non-dimensional interface diameter of D/D ₀ = 0.8. At low static pressures, the pressure drop increased significantly as the expanded air–water interface constricted flow through the array of pillars even as large interfacial slip velocity was maintained. At D/D ₀ = 1.1, for example, the pressure drop increased by 17% compared to the circular pillar. This drag increase was the result of an increased form drag due to a decrease in porosity and permeability of the pillar array and a decrease in the skin friction drag due to the presence of the air–water interface. For D/D ₀ = 1.1, the slip velocity was measured to be 45% of the average streamwise velocity between the pillars. When compared to no-slip pillars of similar shape, the drag reduction was found to increase from 6 to 9% with increasing convex curvature of the air–water interface.     

Microcapillary electrophoresis chip with a bypass channel for autonomous compensation of hydrostatic pressure flow

The application of chip-based microcapillary electrophoresis (µCE) to determine the electrophoretic mobility of molecules and particles has been intensively studied in the last two decades. Balancing the hydrostatic pressure between both ends of the microchannel is essential for free-zone electrophoresis and highly accurate measurement. This balancing operation appears simple on a macroscale (e.g., >?10^?3 m); however, on a microscale (e.g., 10^?6–10^?3 m), it is not straightforward because of the complexity of the interface dynamics at the meniscus. The hydrostatic pressure flow is unstable because of the small size of the microchannel, which is smaller than a single droplet of water. In this study, a µCE chip design was proposed by adding an extra bypass channel to balance the fluid level of the two open reservoirs and inhibit the generation of hydrostatic pressure flow within the microchannel. The fluid behaviors in the microchannel and current and voltage (I–V) characterization were experimentally studied. In addition, a numerical simulation of the electroosmotic flow and hydrostatic flow in the µCE chip was performed. The comparison between the µCE chip with and without the bypass channel showed that the bypass channel did not produce a disturbance in the microchannel for the electrophoretic measurement. The simple microchannel design enabled autonomous compensation of the hydrostatic pressure from the instability of the meniscus, and thus improved the usability of the chip-based µCE chip and the accuracy in the electrophoretic measurement.