Pressure-driven Microchannel Flow Research Articles

Pressure-driven diffusive gas flows in micro-channels: from the Knudsen to the continuum regimes

Despite the enormous scientific and technological importance of micro-channel gas flows, the understanding of these flows, by classical fluid mechanics, remains incomplete including the prediction of flow rates. In this paper, we revisit the problem of micro-channel compressible gas flows and show that the axial diffusion of mass engendered by the density (pressure) gradient becomes increasingly significant with increased Knudsen number compared to the pressure driven convection. The present theoretical treatment is based on a recently proposed modification (Durst et al. in Proceeding of the international symposium on turbulence, heat and mass transfer, Dubrovnik, 3-18 September, pp 25-29, 2006) of the Navier-Stokes equations that include the diffusion of mass caused by the density and temperature gradients. The theoretical predictions using the modified Navier-Stokes equations are found to be in good agreement with the available experimental data spanning the continuum, transition and free-molecular (Knudsen) flow regimes, without invoking the concept of Maxwellian wall-slip boundary condition. The simple theory also results in excellent agreement with the results of linearized Boltzmann equations and Direct Simulation Monte Carlo (DSMC) method. Finally, the theory explains the Knudsen minimum and suggests the design of future micro-channel flow experiments and their employment to complete the present days understanding of micro-channel flows.

Analysis of the electro-viscous effects on pressure-driven liquid flow in a two-section heterogeneous microchannel

In this paper, the electro-viscous effects on pressure-driven liquid flow through a microchannel which is composed of two heterogeneous sections are analyzed. The Poisson–Boltzmann equation, Navier–Stokes equations and a set of constrained equations are solved analytically to obtain the velocity profiles and the streaming potentials in each section. Effects of the zeta potential and length ratio of the two sections on the flow resistance are discussed by means of the apparent viscosity ratio and the Poiseuille number.

Streaming potential and electroviscous effects in periodical pressure-driven microchannel flow

An analytical solution for pressure-driven periodical electrokinetic flows in a two-dimensional uniform microchannel is presented based on the Poisson–Boltzmann equation for electrical double layer and the Navier–Stokes equations for incompressible viscous fluid. The analytical results indicate that the periodical streaming potential strongly depends on the periodical Reynolds number (Re=ωh2∕ν) which is a function of the frequency, the channel size, and the kinetic viscosity of fluids. For Re<1, the streaming potential behaves similarly to that of steady flow, whereas it decreases rapidly with Re as Re>1. In addition, the electroviscous force affects greatly both the periodical flow and streaming potential, particularly when the nondimensional electrokinetic diameter κh is small. The electroviscous force has been found to depend on three factors: first, the electroviscous parameter, which is defined as the ratio of the maximum electroviscous force to the pressure gradient; second, the distribution parameter describing the distribution of the electroviscous force over the cross section of the microchannel; third, the coupling coefficient, which is a function of both the periodical Reynolds number and electroviscous parameter, determining both the amplitude attenuation and phase offset of the electroviscous force.

Investigation of Combined Electro-Osmotic and Pressure-Driven Flow in Rough Microchannels

The present study is carried out to investigate the influence of surface roughness in combined electro-osmotic and pressure-driven flow in microchannel. Two-dimensional theoretical model is developed to predict the behavior of velocity profiles in rough microchannel. The concept of surface roughness-viscosity model is used to account the effect of surface roughness. The pluglike velocity profile for electro-osmotic flow and the parabolic velocity profile for pressure-driven flow with delay in attaining the centerline velocity are observed. It is found that for electro-osmotic flow, the deviation in velocity profile from a flow in a smooth channel occurs near the wall, whereas in pressure-driven flow, such deviation is dominant in the core region. A superposition of pluglike and parabolic velocity profiles is found in combined electro-osmotic and pressure-driven flow. It is also observed that in the case of combined flow, the deviation in velocity profile from the smooth channel case reduces gradually with the distance from the wall.

Semi-analytical solution of the extended Graetz problem for combined electroosmotically and pressure-driven microchannel flows with step-change in wall temperature

Analytical solutions are obtained for the temperature and Nusselt number distribution in the thermal entrance region of a parallel plate microchannel under the combined action of pressure-driven and electroosmotic transport mechanisms, by taking into account the effects of viscous dissipation, Joule heating and axial conduction simultaneously, in the framework of an extended Graetz problem. Step changes in wall temperature are considered to represent physically conceivable thermal entrance conditions. The solution of the temperature distributions at the various channel sections essentially involves the determination of a set of eigenvalues and eigenfunctions corresponding to a Sturm Liouiville problem with non self-adjoint operators. The resultant eigenfunctions are non orthogonal in nature, and are obtained in the forms of hypergeometric functions. Parametric variations on the effects of the relative strengths of the pressure gradients and the electric field, ratio of the rate of heat generation to the rate of wall heat transfer, and the Peclet number are analyzed in details, in terms of their influences on the temperature field as well as the Nusselt number distribution.

Thermal effects on mixed electro-osmotic and pressure-driven flows in triangle microchannels

A numerical investigation on the mixed electro-osmotic and pressure-driven flows in triangle microchannels with constant wall temperature is reported in the present study. The Galerkin method is employed to solve the Poisson equation, energy equation and Navier–Stokes equations for the flow driven by electro-osmotic and pressure gradient synchronously under the conditions of favorable pressure gradients and backpressure gradients. The physical properties of the electrolyte solution are considered to be varying with the temperature, and the dimensionless velocity profile, dimensionless temperature profile as well as dimensionless mass flux of the electrolyte solution are obtained. Furthermore, the parameters studies including pressure gradient, length ratio and Joule heating on mass flux of the electro-osmotic flows are performed, respectively. The numerical results show that a large Joule number leads to large dimensionless mass flux and dimensionless temperature of the electrolytic solution in the triangular microchannels for both conditions. For the electro-osmotic flows under the favorable pressure gradient, the increase in dimensionless mass flux resulted from Joule heating is enlarged with increasing pressure gradient and length ratio. However, for the electro-osmotic flows under the backpressure gradient, Joule heating results in a reverse flow in the channel, and the dimensionless mass flux of the reverse flow increases with increasing backward pressure gradient and decreasing length ratio. It is further found that the Joule heating induces a more significant increase in the dimensionless mass flux under favorable pressure gradient compared with that under backpressure gradient.

Free-surface microfluidic control of surface-enhanced Raman spectroscopy for the optimized detection of airborne molecules

We present a microfluidic technique for sensitive, real-time, optimized detection of airborne water-soluble molecules by surface-enhanced Raman spectroscopy (SERS). The method is based on a free-surface fluidic device in which a pressure-driven liquid microchannel flow is constrained by surface tension. A colloidal suspension of silver nanoparticles flowing through the microchannel that is open to the atmosphere absorbs gas-phase 4-aminobenzenethiol (4-ABT) from the surrounding environment. As surface ions adsorbed on the colloid nanoparticles are substituted by 4-ABT, the colloid aggregates, forming SERS "hot spots" whose concentrations vary predictably along the microchannel flow. 4-ABT confined in these hot spots produces SERS spectra of very great intensity. An aggregation model is used to account quantitatively for the extent of colloid aggregation as determined from the variation of the SERS intensity measured as a function of the streamwise position along the microchannel, which also corresponds to nanoparticle exposure time. This allows us to monitor simultaneously the nanoparticle aggregation process and to determine the location at which the SERS signal is optimized.

Streaming potential and electroviscous effect in heterogeneous microchannels

This communication presents a theoretical analysis of the streaming potential and the electroviscous effect on pressure-driven flow in heterogeneous microchannels. Compact formulae in terms of phenomenological coefficients are derived for the streaming potential and the apparent viscosity ratio in channels with surface charge variations perpendicular and parallel to the applied pressure gradient. In the latter case, the streaming potential per unit liquid flow in a multi-section channel is found to be simply the summation of that in each homogeneous section. The apparent viscosity ratio is a weighted average of each section where the hydrodynamic resistance serves as the weighting factor. The phenomenological coefficients are specified using electrokinetic flow analysis, through which the streaming potential and electroviscous effect in a two-section slit channel are examined. It is found that they both depend on the arrangement of surface heterogeneity in small microchannels. This dependence, however, gets weak in large microchannels, which is consistent with the prediction of thin double layer approximation.

Direct Flow Visualization of Colloidal Gels in Microfluidic Channels

The behavior of colloidal gels under pressure-driven flow in square microchannels is quantified by microscopic particle image velocimetry (muPIV) and compared to predictions of available rheological models. The gels consist of hydrophobically modified silica microspheres (phi = 0.15-0.33) suspended in a refractive index-matched fluid along with fluorescent tracers to aid visualization. Measured velocity flow profiles show a transition from plug flow to more fluid-like behavior with increasing volumetric flow rate (Q) at all phi. This transition is not captured by theoretical predictions of the flow profile based on the Herschel-Bulkley model. Rather, a model that accounts for gel breakup into a suspension of clusters at elevated shear rates by assuming a finite viscosity at infinite shear is needed to accurately predict the flow behavior of colloidal gels at large Q.

Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation

A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuum flow regimes can be presented on the basis of the kinetic Boltzmann–Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integration method can be developed and adopted to attack complex flows with different Mach numbers. HPF parallel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarily with massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuille- channel flow and pressure-driven gas flows in two-dimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of micro-scale gas flows occuring in the Micro-Electro-Mechanical System (MEMS).

Electro-osmotic control of the interface position of two-liquid flow through a microchannel

This paper presents theoretical and experimental investigations of the pressure-driven two-liquid flow in microchannels with the AN electro-osmosis effect. For fully developed, steady state, laminar flow of two liquids under the combined effects of pressure gradient, electro-osmosis and surface charges at the liquid–liquid interface, we have derived analytical solutions that relate the velocity profiles and flow rates to the liquid holdup, the aspect ratio of the microchannel, the viscosity ratio of the two liquids and the externally applied electric field. It was shown that adjusting the externally applied electric field could control the fluid interface position precisely. The prediction from the proposed model compares very well with measured data.

Towards a generalized representation of surface effects on pressure-driven liquid flow in microchannels

This letter postulates a generalized fundamental formulation to model the influence of surface characteristics on pressure-driven liquid transport through microchannels. Probabilistic effects pertaining to the influence of roughness elements and uncertainties in wall conditions due to the presence of a random distribution of nanobubbles are represented spectrally by employing a stochastic version of the Navier-Stokes equations. A generalized mathematical expression is eventually arrived at, by normalizing these characteristics, which can act as a fundamental scientific guideline towards the design of microfluidic channels.

Integrated electrochemical velocimetry for microfluidic devices

We present a new electrochemical velocimetry approach with direct electrical output that is capable of complete device-level integration. The steady reduction rate of a reversible redox species at an embedded microband working electrode is monitored amperometrically. Only one working electrode of arbitrary width is required; all three electrodes, including counter and reference electrodes, are integrated on-chip for complete miniaturization of the sensor. Experimental results are complemented by a theoretical framework including a full 3D electrochemical model as well as empirical mass transfer correlations and scaling laws. When the sensor is operated in the convective/diffusive transport controlled mode, the output signal becomes a predictable function of velocity in two distinct regimes: (i) in the low velocity regime, the signal is directly proportional to flow rate, and (ii) in the high velocity regime, the signal scales as the cube root of the mean velocity. The proposed velocimetry technique is applicable to all practicable pressure-driven laminar flows in microchannels with known cross-sectional geometry.

Modeling electroosmotic and pressure-driven flows in porous microfluidic devices: Zeta potential and porosity changes near the channel walls

This work presents analytical solutions for both pressure-driven and electroosmotic flows in microchannels incorporating porous media. Solutions are based on a volume-averaged flow model using a scaling of the Navier-Stokes equations for fluid flow. The general model allows analysis of fluid flow in channels with porous regions bordering open regions and includes viscous forces, permitting consideration of porosity and zeta potential variations near channel walls. To obtain analytical solutions problems are constrained to the linearized Poisson-Boltzmann equation and a variation of Brinkman's equation [Appl. Sci. Res., Sect. A 1, 27 (1947); 1, 81 (1947)]. Cases include one continuous porous medium, two adjacent regions of different porosities, or one open channel adjacent to a porous region, and the porous material may have a different zeta potential than that of the channel walls. Solutions are described for two geometries, including flow between two parallel plates or in a cylinder. The model illustrates the relative importance of porosity and zeta potential in different regions of each channel.

Lattice Boltzmann study of three-dimensional gas microchannel flows

The compressibility and rarefaction of three-dimensional (3D) pressure-driven gas microchannel flow is studied by the lattice Boltzmann equation method. The method employs a modified particle distribution function and a Knudsen-number–relaxation-time relation without use of any ad hoc treatment at the wall for the slip velocity. The effects of the aspect ratio of the channel width to height, Ar, and the outlet Knudsen number, Kno, on pressure nonlinearity, slip velocity and mass flow rate are investigated. As Ar increases, the slip velocity decreases. As a consequence, the nonlinearity of pressure increases. Their distributions, as expected, get closer to some two-dimensional (2D) limit lines. With Ar being greater than 1, one of the most interesting phenomena is the variation of the slip velocity along the wall due to variation in shear rate. As Kno decreases, the differences between slip velocities Us-z at the bottom and top walls and Us-y at the side walls decrease. The mass flow rate is also calculated and compared with 2D analytical solution. The results show that the mass flow rate through the gas microchannel decreases with decreasing Ar. On the other hand, as Ar increases, the computed mass flow rate gets closer to 2D analytical solution.The page numbers of this article were corrected on 24 July 2006. The corrected electronic version is identical to the print version.

Analysis and measurements of mixing in pressure-driven microchannel flow

The mixing phenomena for two fluid streams in pressure-driven rectangular microchannels are analyzed and directly compared with the measurements of mixing intensity for a wide range of aspect ratio (width/depth = 1–20). In the analysis, the three-dimensional transport equation for species mixing was solved using the spectral method in a dimensionless fashion covering a large regime of the normalized downstream distance. The analysis reveals the details of non-uniform mixing process, which originates from the top and bottom walls of the channel and stretches out toward the center of the channel, and its transition to uniformity. Employing different length scales for the non-uniform and uniform mixing regimes, the growth of mixing intensity can be expressed in a simple relationship for various aspect ratios in the large range. The mixing experiments were carried out on silicon- and poly(methyl methacrylate) (PMMA)-based T-type micromixers utilizing fluids of pH indicator (in silicon channel) and fluorescent dye (in PMMA channel) to evaluate the mixing intensity based on flow visualization images. Using conventional microscopes, the experiments demonstrate the mixing intensity as a power law of the stream velocity for all the microfluidic channels tested. The variations of measured mixing intensity with the normalized downstream distance are found in favorable agreement with the numerical simulations. The comparison between the experiments and simulations tells the capabilities and limitations on the use of conventional microscopes to measure the mixing performance.

Theoretical investigation of two-fluid electroosmotic flow in microchannels

This paper presents theoretical investigations of the pressure-driven two-liquid flow in microchannels with electroosmosis effect. For a fully developed, steady state, laminar flow of two liquids combined the pressure gradient and the electroosmotic effects, we have derived analytical solutions that relate the velocity profiles and flow rates to the liquid holdup, the aspect ratio of the microchannel, the viscosity ratio of the two liquids and the externally applied electric field.

NUMERICAL SIMULATION OF ISOTHERMAL MICRO FLOWS BY LATTICE BOLTZMANN METHOD AND THEORETICAL ANALYSIS OF THE DIFFUSE SCATTERING BOUNDARY CONDITION

A Lattice Boltzmann model for simulating micro flows has been proposed by us recently (Europhysics Letters, 67(4), 600–606 (2004)). In this paper, we will present a further theoretical and numerical validation of the model. In this regards, a theoretical analysis of the diffuse-scattering boundary condition for a simple flow is carried out and the result is consistent with the conventional slip velocity boundary condition. Numerical validation is highlighted by simulating the two-dimensional isothermal pressure-driven micro-channel flows and the thin-film gas bearing lubrication problems, and comparing the simulation results with available experimental data and analytical predictions.

Interface control of pressure-driven two-fluid flow in microchannels using electroosmosis

This paper presents an experimental investigation of the pressure-driven two-fluid flow in microchannels with electroosmosis effect. Two fluids, aqueous NaCl solution and aqueous glycerol, were introduced by syringe pumps to flow side by side in a straight microchannel. The external electric field was applied on the NaCl side. Under the same inlet volumetric flowrate condition, the applied electric field was varied. The interface position between the two fluids with the electroosmosis effect was studied in the first part of the experiment using the fluorescence imaging technique. In the second part, the velocity field was measured using the micro-PIV technique. The parameters, flowrate and electric field which affect the interface position and velocity field were investigated. The measured velocity field from the experiment agrees well with that of theoretical analysis.

Intrinsic Viscosity of Polymers and Biopolymers Measured by Microchip

Intrinsic viscosity provides insight to molecular structure and interactions in solution. A new microchip method is described for fast and accurate measurements of viscosity and intrinsic viscosity of polymer and biopolymer solutions. Polymer samples are diluted with solvent in the microfluidic chip by imposing pressure gradients across the channel network. The concentration and flow dilutions of the polymer sample are calculated from the fluorescent signals recorded over a range of dilutions. The viscosities at various polymer dilutions are evaluated using mass and momentum balances in the pressure-driven microchannel flow. The technique is particularly important to many chemical, biological, and medical applications where sample is available in very small quantities. The intrinsic viscosity experiments were performed for three classes of polymer solutions: (a) poly(ethylene glycol), polymers with linear hydrocarbon chains; (b) bovine serum albumin, biopolymer chains with hydrophobic and hydrophilic amino acids, and (c) DNA fragments, biological macromolecules with double-stranded polymeric chains. The measured values of intrinsic viscosity agree remarkably well with the available data obtained using different methods. The data exhibit power law behavior for molecular weight as described by the Mark-Houwink-Sakurada equation. Experiments were performed to understand the effect of solvent quality and salt concentration on molecular conformations and the intrinsic viscosity of the polymers. This method offers a new way to study the conformational changes in proteins and DNA solutions in various buffer conditions such as pH, ionic strength, and surfactants. The effects of shear rate in the microchannel and mixing time on the accuracy and limitation of the measurement method are discussed.