A comprehensive theoretical model of capillary transport in rectangular microchannels

A detailed theoretical model of capillary transport in rectangular microchannels is proposed. Two important aspects of capillary transport are revisited, which are considered with simplified assumption in the literature. The capillary flow is assumed as a low Reynolds number flow and hence creeping flow assumptions are considered for majority of analyses. The velocity profile used with this assumption results into a steady state fully developed velocity profile. The capillary flow is inherently a transient process. In this study, the capillary flow analysis is performed with transient velocity profile. The pressure field expression at the entrance of the microchannel is another aspect which is not often accurately represented in the literature. The approximated pressure field expression at the entrance of the rectangular microchannel is widely used in the literature. An appropriate entrance pressure field expression for a rectangular microchannel is proposed. For both analyses, the governing equation of the capillary transport in rectangular microchannel is derived by applying the momentum equation to the fluid control volume along the microchannel. The non-dimensional governing equations are obtained, each for a transient velocity profile and a newly proposed pressure field, for analyzing the importance of such velocity profile and pressure field expression.     

Numerical simulation of flow and heat transfer in radially rotating microchannels

Investigation of fluid flow and heat transfer in rotating microchannels is important for centrifugal microfluidics, which has emerged as an advanced technique in biomedical applications and chemical separations. The centrifugal force and Coriolis force, arising as a consequence of the microchannel rotation, change the flow pattern significantly from the symmetric profile of a non-rotating channel. Successful design of microfluidic devices in centrifugal microfluidics depends on effectively regulating these forces in rotating microchannels. In this work, we have numerically investigated the flow and heat transfer in rotating rectangular microchannel with continuum assumption. A pressure-based finite-volume technique with a staggered grid was applied to solve the steady incompressible Navier–Stokes and energy equations. It was observed that the effect of Coriolis force was determined by the value of the non-dimensional rotational Reynolds number (Re _ω ). By comparing the root mean square deviation of the axial velocity profiles with the approximate analytical results of purely centrifugal flow for different aspect ratios (AR = width/height), a critical rotational Reynolds number (Re _ω,cr) was computed. Above this value of (Re _ω,cr), the effect of secondary flow becomes dominant. For aspect ratios of 0.25, 0.5, 1.0, 2.0, 4.0 and 9.09, this critical rotational Reynolds number (Re _ω,cr) was found to be 14.0, 5.5, 3.8, 4.7, 6.5 and 10.0, respectively.     

Design and mixing efficiency of rhombic micromixer with flat angles

In this paper, we used CFD-ACE software to investigate fluid mixing of the rhombic micromixer with flat angles. According to the results of the numerical simulations, this rhombic microchannel with flat angles showed high mixing efficiency compared to cross-shape straight microchannel. Over 95% mixing efficiency had been achieved at Re > 180 due to enhancement of vortices. In processing, CO₂ laser machining is used to fabricate the master mold easily instead of conventional photolithography process. From results of the mixing experiment, high Reynolds number resulted in better fluid mixing because of stronger Dean vortices and recirculation effect.     

Micromixing via recirculatory flow generated by an oscillatory microplate

Mixing in micro-environment has been explored in a number of studies. This study presents a unique approach of efficient mixing of two heterogeneous streams via two counter-rotating recirculatory streams induced by in-plane resonance of a rectangular microplate actuated via Lorentz force. The generated time-mean flow structure was interrogated for mixing efficacy over a range of excitation voltage, Reynolds number, and Pèclet number, along with numerical analysis to probe the time-mean flow physics. Results show that the recirculatory flow is generated at the plate’s edges due to local flow non-linearity, characteristic of acoustic streaming. The percentage of mixing, at one device length-scale downstream, attains 93% at a low Reynolds number of 0.0037 (based on mean velocity of 0.078 mm/s and channel height of 50 μm) at 8 V excitation. Further characterization via enhanced diffusivity shows a maximum of 80.7-fold increase. Comparison with other active mixers shows the current device achieves mixing in one of the shortest distances. The proposed approach is robust, tunable to attain desired mixing characteristics and essentially independent of the properties of the fluid medium, which should be useful in a number of microfluidic applications requiring fast mixing.     

The effect of asymmetry on micromixing in curvilinear microchannels

The necessity of microscale mixing processes has been tremendously increasing in most of the microsize chemical and biochemical devices during recent years, particularly in the design of lab-on-a-chip and micrototal analysis systems. Different approaches were implemented in the available micromixers in the literature for improving the mixing performance. Due to the absence of any external source, mixing by utilizing passive mixing techniques is more economical. In curvilinear microchannels, which offer effective passive mixing, chaotic advection results in continuous radial perforation of inter-diffusion layer between the fluid streams due to the transverse secondary flows. In this study, the effects of Dean vortices and secondary flows were investigated in asymmetrical polydimethylsiloxane curvilinear rectangular microchannels, which were fabricated by one-step lithography process and had repeated S-shape patterns with a curvature of 280° along the channel. Moreover, the effect of asymmetry was assessed by comparing the mixing results with symmetrical microchannels. Mixing performance was analyzed by using NaOH and phenolphthalein solutions as mixing fluids, which entered from the channel inlets. According to the results, the significant effects of stretching and contracting motion of Dean vortices revealed themselves above a certain Dean number value, thereby making the asymmetrical microchannel outperform the symmetrical channel in the mixing performance. Below this threshold, the symmetrical microchannel was observed to be superior to the asymmetrical microchannel.     

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.     

High-throughput,single-stream microparticle focusing using a microchannel with asymmetric sharp corners

A new microfluidic device for fast and high-throughput particle focusing is reported. The particle focusing is based on the combination of inertial lift force effect and centrifugal force effect generated in a microchannel with a series of repeated asymmetric sharp corners on one side of the channel wall. The inertial lift force induces two focused particle streams in the microchannel, and the centrifugal force generated at the sharp corner structures tends to drive the particles laterally away from the corner. With the use of a series of repeated asymmetric sharp corner structures, a single and highly focused particle stream was achieved near the straight channel wall at a wide range of flow rate. In comparison with other hydrodynamic particle focusing methods, this method is less sensitive to the flow rate and can work at a higher flow rate (up to 700 μL/min) and Reynolds number (Re = 129.5). With its simple structure and operation, and high throughput, this method can be potentially used in particle focusing processes in a variety of lab-on-a-chip applications.     

Effect of baffle height and Reynolds number on fluid mixing

In this paper, both numerical simulation and experiment were performed to investigate the mixing process within mixing chambers of the planar micromixer with three baffles at varied baffle height. The presence of three baffles causes the flow to separate and creates the recirculation and back flow within mixing chambers. The fluid mixing was greatly influenced by the baffle height and Reynolds number (Re) related to the size of recirculation zone. Larger baffle height or Re produces larger recirculation zone and convective mixing. The micromixer with 350 μm high baffles in 400 μm wide channel results in over 95% mixing at Re = 80 from the simulation results. The experiment results confirm the above simulation results qualitatively. This planar micromixer has the merits of simple design and easy fabrication as compared to the three-dimensional passive micromixers.     

Passive mixing in a three-dimensional serpentine microchannel

A three-dimensional serpentine microchannel design with a “C shaped” repeating unit is presented in this paper as a means of implementing chaotic advection to passively enhance fluid mixing. The device is fabricated in a silicon wafer using a double-sided KOH wet-etching technique to realize a three-dimensional channel geometry. Experiments using phenolphthalein and sodium hydroxide solutions demonstrate the ability of flow in this channel to mix faster and more uniformly than either pure molecular diffusion or flow in a “square-wave” channel for Reynolds numbers from 6 to 70. The mixing capability of the channel increases with increasing Reynolds number. At least 98% of the maximum intensity of reacted phenolphthalein is observed in the channel after five mixing segments for Reynolds numbers greater than 25. At a Reynolds number of 70, the serpentine channel produces 16 times more reacted phenolphthalein than a straight channel and 1.6 times more than the square-wave channel. Mixing rates in the serpentine channel at the higher Reynolds numbers are consistent with the occurrence of chaotic advection. Visualization of the interface formed in the channel between streams of water and ethyl alcohol indicates that the mixing is due to both diffusion and fluid stirring     

Influence of adjusting the inlet channel confluence angle on mixing behaviour in inertial microfluidic mixers

Recent drive for high-throughput microfluidic systems has triggered tremendous research effort to develop efficient, high-throughput microfluidic mixers. In particular, inducing a fluid–fluid collision at high flow rate in microfluidic channel has been suggested as an effective strategy to enhance mixing. However, previous studies using T-shaped microfluidic mixers showed that, in addition to fluid–fluid collision, the confluence angle of fluid stream in microfluidic channel also has a dramatic effect on mixing. This study suggests the possibility to enhance mixing by simply changing the inlet confluence angle of the streams. In this work, we assess the mixing behaviour of microfluidic mixers with variable inlet confluence angle with the Reynolds number (Re) range of 2.83–566. It is shown that the increase in inlet confluence angle enables the reduction of Re required for complete mixing. Simulation results demonstrate that increasing the confluence angle facilitates the interaction of vortices in mixers to induce an enhanced mixing. We further demonstrate that the increased interaction of vortices also prompts the turbulent emulsification where a significant reduction in emulsion size is observed for each mixer with increased inlet confluence angle at same Re.     

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.     

A new model for Brownian force and the application to simulating nanofluid flow

A new expression is proposed to simulate Brownian force based on the experimental measurement results of Brownian motion, which follows white Gaussian noise process. As the time t → 0 and the particle density is equal to the fluid density, the new expression approaches the classical formula of the model used by many researchers. The modified model is validated by theoretical and experimental data. On the other hand, as it origins from the unbalanced force exerted by surrounding fluid molecules, the drag analogy force model is constructed describing the Brownian force, which depends on size-related statistical velocity. Thus, a different expression for the Langevin equation is presented. The present model is applied in simulating flow and heat transfer in a channel utilizing alumina–water nanofluid. Navier–Stokes equations with modified source terms for the continuous flow have been discretized using finite element method. The velocities and temperatures of nanoparticles are determined in the Lagrangian reference frame. The simulation results show that the distribution of nanoparticles inside the channel is obviously unsteady and nonuniform. The fluid velocity and temperature profiles show significant fluctuation feature at low Reynolds numbers (Re). The impact of Brownian motion on the fluid flow is analyzed quantitatively. We have found that for Re < 0.06, the affected intensity increases rapidly.     

Formation of recirculation zones in a sudden expansion microchannel with a rectangular block structure over a wide Reynolds number range

This article involves computational and experimental investigations into the flow of a Newtonian fluid through a sudden expansion microchannel consisting of a rectangular block. The results elucidate that the Reynolds number and aspect ratio has a significant impact on the sequence of vortex growth downstream of the expansion channel. The experimental flow visualization results are found to be in good agreement with the numerical predictions of the local fluid dynamics. The simulation results also draw the Re—γ (Reynolds number—aspect ratio) flow pattern map to classify how the flow structures vary with Reynolds number, for example, the resulting flow structures can be classified as five types progressively. The findings in this study provide designers with valuable guidelines for improving the design and operation of the proposed microfluidic rectifier.     

Investigations into mixing of fluids in microchannels with lateral obstructions

This work presents a study of a passive micromixer with lateral obstructions along a microchannel. The mixing process is simulated by solving the continuity, momentum and diffusion equations. The mixing performance is quantified in terms of a parameter called ‘mixing efficiency’. A comparison of mixing efficiencies with and without obstructions clearly indicates the benefit of having obstructions along the microchannel. The numerical model was validated by comparing simulation results with experimental results for a micromixer. An extensive parametric study was carried out to investigate the influence of the geometrical and operational parameters in terms of the mixing efficiency and pressure drop, which are two important criteria for the design of micromixers. A very interesting observation reveals that there exists a critical Reynolds number (Re _cr  ~ 100) below which the mixing process is diffusion dominated and thus the mixing efficiency is reduced with increase in Re and above which the mixing process is advection dominated and mixing efficiency increases with increase in Re. Microchannels with symmetric and staggered protrusion arrangements were studied and compared. The mixing performance of the staggered arrangement was comparable with that of symmetric arrangement but the pressure drop was lower in the case of staggered arrangements making it more suitable.     

Flow feature analysis of an eye shaped split and collision (ES-SAC) element based micromixer for lab-on-a-chip application

An eye shaped split and collision micromixer having low-pressure drop is proposed, which works on the concept of unbalanced splits and cross-collisions of fluid streams. The 3-D Navier–Stokes equations in combination with an advection–diffusion model were solved for the analysis with water and ethanol as working fluids. The in-depth analysis of the flow features and the mixing performance parameters viz. mixing index and pressure drop of the micromixer has been carried out. The micromixer model is composed of two sub-channels of equal/unequal widths which repeatedly undergo splitting and collision of fluid streams along the flow direction. The numerical study has been carried out on the micromixer at Reynolds numbers ranging from 0.1 to 45. The difference between the mass flow rates in the two sub-channels creates an unbalanced collision of the two fluid streams. Mixing enhancement is mainly due to the effect of unbalanced collisions of the fluid streams. The micromixers show exciting flow features for different ratios of the widths of the sub-channels. The ratios of a width of subchannels viz. 1, 1.4 and 2 are considered. The highest mixing performance has been observed for the width ratio of 2, whereas poor mixing performance has been observed for the width ratio of 1.

     

Unsteady pulsating characteristics of the fluid flow through a sudden expansion microvalve

This paper investigates the unsteady characteristics of flow in a specific type of microvalve with sudden expansion shape. The resultant vortex structures cause different flow resistance in forward and backward flow directions. This may be used in applications such as a microvalve in micropump system and MEMS-based devices. A time-varying sinusoidal pressure was set at the inlet of the microchannel to produce unsteadiness and simulate the pumping action. The existence of block obstacle and expansion shoulders leads to various sizes of vortex structures in each flow direction. All simulation results are based on the numerical simulation of two-dimensional, unsteady, incompressible and laminar Navier–Stokes equations. Two fundamental parameters were varied to investigate the vortex growth throughout the time: the frequency of the inlet actuating mechanism (1 Hz ≤ f ≤ 1,000 Hz) and the amplitude of the inlet pressure. In this way, one can see the effect of actuation mechanism on the onset of separation and follow the size and duration of the vortex growth. In order to better understand the effect of geometry and frequency on flow field, the pressure and velocity distributions are studied through one cycle. Strouhal number is calculated for frequency, and a critical value of f = 250 Hz is found for St = 1. The obtained results provide a deep insight into the physics of unsteady flow in valveless micropumps and leads to better use of current design as a part of microfluidic system.     

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.     

Electrokinetic power generation of non-Newtonian fluids in a finite length microchannel

In order to examine the effects of the fluid type as the electrolyte solvent on the efficiency of electrokinetic energy conversion, a comparative numerical study among three different fluid types of a transient electrokinetic flow through a single circular finite length microchannel has been conducted. The system was initially at an equilibrium non-flow state, and a step change in flow was applied and the calculation proceeding until steady state was achieved. The analysis was based on non-dimensional transport governing equations that were scaled using Debye length as the characteristic length scale and diffusion time as characteristic time scale. The fluid types considered were shear thinning, Newtonian, and shear thickening, and a power law modeled them with the scaled flow behavior index having values of 0.2, 1.0, and 1.8. In order to isolate the electrokinetic effects of the different relationships between the shear strain rate and shear stress, the flow consistency index was adjusted so that in all the cases the flow rate and total pressure drop matched that of water at 25 °C. All other fluid and interfacial properties were the same for all cases. The key observational difference between the various fluid types was that their different axial velocity profile acted on essential the same free charge density profiles. Consequently, the convection current density (i.e., the radial distribution of charge being advected along the channel) was strongly affected by the fluid type. Integration of this quantity to calculate the convection current showed that for the particular fluid properties chosen the shear thinning fluid was 20 % higher than the Newtonian fluid, while the shear thickening fluid was only 4 % lower than the Newtonian fluid. Combined with the effects, these different currents have on the streaming potential, the shear thinning fluid was 50 % more effective in converting flow work to electrical work than the Newtonian fluid, while the shear thickening fluid was only 16 % lower than the Newtonian fluid.     

A chaotic mixer for magnetic bead-based micro cell sorter

An efficient magnetic force driven mixer with simple configuration is designed, fabricated, and tested. It is designed to facilitate the mixing of magnetic beads and biomolecules in a microchannel, where mixing is unavoidably inefficient due to its low Reynolds number. With appropriate temporal variations of the force field, chaotic mixing is achieved, hence the mixing becomes effective. The mixing device consists of embedded microconductors as a magnetic field source and a microchannel that guides the streams of working fluid. It is demonstrated that a pair of integrated micro conductors provides a local magnetic field strong enough to attract nearby magnetic beads. Mixing of magnetic beads is accomplished by applying a time-dependent control signal to a row of conductors, at the Reynolds number of as low as 10/sup -2/. Two-dimensional numerical simulation has been performed to design the configuration of the channel and electrodes, which creates chaotic motion of beads. It is found that a simple two-dimensional serpentine channel geometry with the transverse electrodes is able to create the stretching and folding of material lines, which is a manifestation of chaos. The mixing pattern predicted by the simulation has been confirmed by both flow visualization and PTV (particle tracking velocimetry) in the chaotic mixer fabricated, which should greatly increase the attachment of beads onto the target biomolecules. The optimum frequency of applied control signal is searched by evaluating the Lyapunov exponent in both numerical and experimental particle tracking. It is found that the range of optimum Strouhal number is 5相似文献   

Modeling, analysis and design of centrifugal force driven transient filling flow into rectangular microchannel

Recently, centrifugal pumping has been discovered to be an excellent alternative method for controlling the fluid flow inside microchannels. In this paper, we have developed the physical modeling and carried out the analysis for the centrifugal force driven transient filling flow into a rectangular microchannel. Two types of analytic solutions for the transient flow were obtained: (1) a pseudo-static approximate solution, and (2) an exact solution. Analytic solutions include expressions for flow front advancement, detailed velocity profile and pressure distribution. The obtained analytical results show that the filling flow driven by centrifugal force is affected by three dimensionless parameters which combine fluid properties, rectangular channel geometry and processing condition of rotational speed. Effects of inertia, viscous and centrifugal forces were also discussed based on the parametric study. Furthermore, we have also successfully provided a simple and convenient analytical design tool for such rectangular microchannels, demonstrating two design application examples.