Flow In Rectangular Microchannel Research Articles

Experimental and numerical study of droplets hydrodynamics in microchannels

AbstractThis article reports on numerical simulations and experimental determination of the hydrodynamics of liquid–liquid flow in rectangular microchannels. The numerical method is an interface‐capturing technique without any interface reconstruction. Microparticle image velocimetry (micro‐PIV) measurements are used to obtain experimental velocity fields inside droplets that are compared to simulations. Finally, injecting a passive tracer in the simulated droplets also helps to obtain a better understanding of the mixing phenomenon. These results allow interpreting mixing defaults during bleaching experiments inside microdroplets. Furthermore, this study leads to important results about interface deformation and velocity fields inside the droplets and in the continuous phase for mass‐ and heat‐transfer studies. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Numerical Simulation of Electrokinetic Flow and Heat Transfer in Microchannels with a Finite-Volume Method

ABSTRACT In this article, electrokinetic flow in rectangular microchannels is studied numerically with a finite-volume method. An externally applied electric field generates varying electromagnetic forces on the fluid, which can be manipulated to control heat exchange and fluid acceleration within the microchannel. Convective heat transfer is predicted on a staggered grid with a finite-volume formulation. The electromagnetic force is modeled as a linearized source term in a segregated solution of the axial momentum equation. Predictions of fluid velocity are compared successfully against past data. Constant wall temperature and constant wall heat flux cases are analyzed. The predicted results suggest that near-wall velocity and temperature gradients (constant wall temperature case) increase at larger Hartmann numbers, thereby leading to larger wall friction and convective heat transfer.

The effect of temperature distribution on the mass species transport in micro-channels driven by electroosmosis

The temperature-dependent Poisson- Boltzmann equation, momentum equation and the mass transport equation in a rectangular micro-channel flow driven by electroosmosis were derived firstly. Then these equations were solved numerically through the finite difference method. The effects of different temperature distributions on the axial velocity profile, the maximum of the species concentration, the symmetry of the species distribution and the width of sample band were analyzed. The results show that the maximum of the species concentration decreases with increasing of time for different uniform temperatures. The existence of lateral, radial and especially axial temperature gradient makes the species diffuse slowly, and narrows the sample band. The best way of making the sample band transport and separate effectively is forcing a temperature gradient along the axial direction.

Steady evaporating flow in rectangular microchannels

Analytical and numerical solutions are presented for steady evaporating flow in open microchannels having a rectangular cross section and a uniform depth. The flow, driven by the axial gradient of capillary pressure, generally consists of an entry region where the meniscus is attached to the top corners of the channel followed by a jump-like transition to a corner-flow region in which the meniscus progressively recedes into the bottom corners of the channel. Illustrative numerical solutions are used to guide the derivation of an easily applied analytical approximation for the maximum sustainable heat flux or capillary limit.

Interface motion of capillary-driven flow in rectangular microchannel.

In microchannel flow, gas-liquid interface behavior is important for developing a wide range of microfluidic applications, especially in passive microfluidic systems. This paper presents a discussion of interface motion driven by capillary action in a microchannel. We have extended the theory beyond the previous theory of capillary rise problem for a circular tube, to a rectangular microchannel. The same formula for the relation between nondimensional time and interface position is obtained as for a circular tube. We examined rectangular microchannels with several sizes (about 50 to 100 microm square) of glass capillaries and 85 x 68 microm and 75 x 45 microm polydimethylsiloxane (PDMS) microchannels fabricated by photolithography technique, respectively. We observed movement of the gas-liquid interface position and compared it to the dimensionless relation. We obtained the value of a dimensionless variable of driving force that is related to dynamic contact angles for glass-water, glass-ethanol, and PDMS-ethanol. Using this variable, interface motion can be predicted for any size of rectangular channels.

Two-Phase Flow and Heat Transfer in Rectangular Micro-Channels

Knowledge of flow pattern and flow pattern transitions is essential to the development of reliable predictive tools for pressure drop and heat transfer in two-phase micro-channel heat sinks. In the present study, experiments were conducted with adiabatic nitrogen-water two-phase flow in a rectangular micro-channel having a 0.406×2.032mm2 cross-section. Superficial velocities of nitrogen and water ranged from 0.08 to 81.92 m/s and 0.04 to 10.24 m/s, respectively. Flow patterns were first identified using high-speed video imaging, and still photos were then taken for representative patterns. Results reveal the dominant flow patterns are slug and annular, with bubbly flow occurring only occasionally; stratified and churn flow were never observed. A flow pattern map was constructed and compared with previous maps and predictions of flow pattern transition models. Features unique to two-phase micro-channel flow were identified and employed to validate key assumptions of an annular flow boiling model that was previously developed to predict pressure drop and heat transfer in two-phase micro-channel heat sinks. This earlier model was modified based on new findings from the adiabatic two-phase flow study. The modified model shows good agreement with experimental data for water-cooled heat sinks.

Dynamic aspects of electroosmotic flow in rectangular microchannels

The study presents an analysis of the dynamic aspects of the electroosmotic flow in rectangular microchannels. An analytical solution for electrical potential distribution in the channel is obtained by solving the linearized Poisson–Boltzmann equation under the Debye–Hückel approximation. Dynamic electroosmotic flow field driven by an alternating electric field is solved analytically by using the Green's function method. Parametric studies are carried out to examine the time evolution of the electroosmotic flow under the effects of the channel size, ionic concentration, and zeta potential. Specifically, the effect of frequency-dependent AC electric field on the oscillating electroosmotic flow is discussed. In addition, the solution of the slip velocity approximation based on the Stokes second problem is presented for comparison with the results obtained from the analytical scheme developed in this study.

An experimental study of electro-osmotic flow in rectangular microchannels

Experimental studies were carried out on fully developed and steady electro-osmotic flow in a rectangular channel where the channel height $h$ is comparable to its width and the thickness of the electric double layer characterized by the Debye length is much less than $h$ . The nano-particle image velocimetry technique was used to measure the two components of the velocity field parallel to and within about 100 nm of the channel wall for $h\,{\leq}\,25\,\umu$ m. The mobility of the particle tracers was calculated from averaged velocity data for various electric field strengths. The experimentally determined mobility values are compared with analytical predictions for dilute aqueous solutions of sodium tetraborate.

Validation of a Second-Order Slip Flow Model in Rectangular Microchannels

An analytical slip-flow model based on second-order boundary conditions was proposed for gaseous flow in rectangular microchannels. An experimental setup has been designed for the measurement of gaseous micro flow rates under controlled temperature and pressure conditions. Data relative to nitrogen and helium flows through rectangular microchannels, from 4.5 to 0.5 μm in depth and with aspect ratios from 1–9%, are presented and analyzed. A method is proposed to eliminate the main source of uncertainty, which is the imprecision when measuring the dimensions of the microchannel cross-section. It is shown that in rectangular microchannels, the proposed second-order model is valid for Knudsen numbers up to about 0.25, whereas the first-order model is no longer accurate for values higher than 0.05. The best fit is found for a tangential momentum accommodation coefficient σ = 0.93, both with helium and nitrogen.

Analytical treatment of electrokinetic microfluidics in hydrophobic microchannels

Microfluidics in microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) devices is complex due to the large surface area to volume ratio. Thus, surface properties play an important role in flow behavior. In this paper, we summarize the effects of electric double layer and surface hydrophobicity of rectangular microchannels on time-dependent electrokinetic flow. Theoretically, we have shown that flow resistance can, in principal, be significantly reduced so that a larger flow rate can be obtained for pressure-driven flow or electric-field-driven flow. This relies on the ability to change surface charges and surface hydrophobicity independently. Our theoretical results provide guidelines for the design and operation of microfluidic flow in rectangular microchannels. Because of liquid slippage, zeta potential determination by traditional method could be overestimated. Taking into account the effect of hydrophobicity, a modified method is proposed to determine the zeta potential and slip coefficient for parallel-plate microchannels with hydrophobic surfaces.

Numerical solution of electro-osmotic flow in a “flow field effect transistor”

Recently, a general applicable numerical model for the simulation of steady electro-osmotic flow in rectangular micro-channels has been presented and evaluated based on available analytical solutions [Anal. Chem. 74 (19) (2002) 4919]. This model combines the steady multi-ion transport model and the Navier–Stokes equations, and has been implemented in a finite element code. The model includes the ion distribution in the Helmholtz double layer and considers only one single electrical potential field variable throughout the domain. In this paper, the model is further evaluated through comparison with experimental data obtained in a so-called flow field effect transistor or FlowFET [Science 286 (1999) 942]. It has been found that the numerical solutions are in very good agreement with the experimental data and with the commonly used slip boundary condition model.

Acceleration Schemes of the Discrete Velocity Method: Gaseous Flows in Rectangular Microchannels

The convergence rate of the discrete velocity method (DVM), which has been applied extensively in the area of rarefied gas dynamics, is studied via a Fourier stability analysis. The spectral radius of the continuum form of the iteration map is found to be equal to one, which justifies the slow convergence rate of the method. Next the efficiency of the DVM is improved by introducing various acceleration schemes. The new synthetic-type schemes speed up significantly the iterative convergence rate. The spectral radius of the acceleration schemes is also studied and the so-called H1 acceleration method is found to be the optimum one. Finally, the two-dimensional flow problem of a gas through a rectangular microchannel is solved using the new fast iterative DVM. The number of required iterations and the overall computational time are significantly reduced, providing experimental evidence of the analytic formulation. The whole approach is demonstrated using the BGK and S kinetic models.

Numerical solution of a multi-ion one-potential model for electroosmotic flow in two-dimensional rectangular microchannels.

A new more general numerical model for the simulation of electrokinetic flow in rectangular microchannels is presented. The model is based on the dilute solution model and the Navier-Stokes equations and has been implemented in a finite-element-based C++ code. The model includes the ion distribution in the Helmholtz double layer and considers only one single electrical' potential field variable throughout the domain. On a charged surface(s) the surface charge density, which is proportional to the local electrical field, is imposed. The zeta potential results, then, from this boundary condition and depends on concentrations, temperature, ion valence, molecular diffusion coefficients, and geometric conditions. Validation cases show that the model predicts accurately known analytical results, also for geometries having dimensions comparable to the Debye length. As a final study, the electro-osmotic flow in a controlled cross channel is investigated.

Liquid transport in rectangular microchannels by electroosmotic pumping

The characteristics of electroosmotic flow in rectangular microchannels were investigated in this paper. A 2D Poisson–Boltzmann equation and the 2D momentum equation were used to model the electric double layer field and the flow field. The numerical solutions show significant influences of the channel cross-section geometry (i.e. the aspect ratio) on the velocity field and the volumetric flow rate. Also, the numerical simulation of the electroosmotic flow reveals how the velocity field and the volumetric flow rate depend on the ionic concentration, zeta potential, channel size and the applied electrical field strength.

Analysis of electrokinetic effects on the liquid flow in rectangular microchannels

The effects of the electrical double layer near the solid/liquid interface on liquid flow through a rectangular microchannel are analyzed in this work. Based on the Debye–Hückel approximation, a linear solution of a two-dimensional Poisson–Boltzmann equation governing the electrical potential distribution in the cross-section of rectangular channels is presented to describe the electrical double-layer field near the solid/liquid interface. An additional body force originating from the presence of the electrical double layer is considered to modify the conventional Navier–Stokes equation. By using the Green's function formula, an exact solution to this modified Navier–Stokes equation in rectangular microchannels is obtained. The effects of the electrical double-layer field, channel size and the electrical static charge on the fluid velocity distribution, streaming potential, volume flow rate, friction coefficient and apparent viscosity have been discussed. The results show that, for diluted liquid, the liquid flow in rectangular microchannels is influenced significantly by the electrical double layer and hence deviates from the flow characteristics described by classical fluid mechanics.

Unsteady gaseous flows in rectangular microchannels: frequency response of one or two pneumatic lines connected in series

This paper represents an initial analysis of unsteady gaseous flows in a rectangular microchannel under usual pressure and temperature conditions. The effect of depth and aspect ratios of the cross-section is investigated. With most fluid-based mechanical microsystems of small internal dimensions and subject to normal pressure and temperature conditions, flow is rarefied with slip at the walls. This flow is then modeled by the Navier-Stokes equations combined with slip and temperature jump conditions at the walls. These conditions are represented by Maxwell-Smoluchowski first order equations. By concentrating essentially on the pulsed sinusoidal regime, it is shown that the instantaneous flow rate amplitude, as well as the band pass of the microchannel are underestimated when slip at the walls is not taken into account. The frequency response of two microchannels connected in series with different cross-sectional areas is also studied. Finally, the proposed model can serve as a tool giving information about the current feasibilities of pressure sensors for the measurement of the dynamic characteristics of gaseous flows in microchannels.

Electrokinetic Effects on Pressure-Driven Liquid Flows in Rectangular Microchannels

The effects of the electrical double layer near the solid-liquid interface and the induced electrokinetic field on the pressure-driven liquid flow through a rectangular microchannel are analyzed in this work. A nonlinear, two-dimensional Poisson–Boltzmann equation governing the electrical double layer field in the cross section of rectangular channels is numerically solved with the use of a finite-difference scheme. A body force caused by the electrical double field and the flow-induced electrokinetic field is considered in the equation of motion. An exact solution to this equation of motion in rectangular microchannels is obtained by employing the Green function formulation. The effects of the ionic concentration of the liquid, the zeta potential of the solid surface, and the size and the shape of microchannels on the fluid velocity distribution, streaming potential, volumetric flow rate, friction coefficient, and apparent viscosity are discussed. The results clearly show that for a liquid solution of low ionic concentration and a solid surface of high zeta potential the liquid flow in rectangular microchannels is significantly influenced by the presence of the electrical double layer field and hence deviates from the flow characteristics described by classical fluid mechanics.