Pressure-driven Microchannel Research Articles

On the Enhancement of Heat Transfer and Reduction of Entropy Generation by Asymmetric Slip in Pressure-Driven Non-Newtonian Microflows

We study hydrodynamics, heat transfer, and entropy generation in pressure-driven microchannel flow of a power-law fluid. Specifically, we address the effect of asymmetry in the slip boundary condition at the channel walls. Constant, uniform but unequal heat fluxes are imposed at the walls in this thermally developed flow. The effect of asymmetric slip on the velocity profile, on the wall shear stress, on the temperature distribution, on the Bejan number profiles, and on the average entropy generation and the Nusselt number are established through the numerical evaluation of exact analytical expressions derived. Specifically, due to asymmetric slip, the fluid momentum flux and thermal energy flux are enhanced along the wall with larger slip, which, in turn, shifts the location of the velocity's maximum to an off-center location closer to the said wall. Asymmetric slip is also shown to redistribute the peaks and plateaus of the Bejan number profile across the microchannel, showing a sharp transition between entropy generation due to heat transfer and due to fluid flow at an off-center-line location. In the presence of asymmetric slip, the difference in the imposed heat fluxes leads to starkly different Bejan number profiles depending on which wall is hotter, and whether the fluid is shear-thinning or shear-thickening. Overall, slip is shown to promote uniformity in both the velocity field and the temperature field, thereby reducing irreversibility in this flow.

Pressure Work and Viscous Dissipation Effects on Heat Transfer in a Parallel–Plate Microchannel Gas Flow

ABSTRACTConvective heat transfer in a parallel plate microchannel gas flow is investigated analytically and numerically, considering the effects of viscous dissipation, pressure work, shear work, axial conduction and rarefaction. Analysis is performed with constant wall temperature and constant wall heat flux boundary conditions for both gas cooling and heating. The results presented demonstrate the significance of the combined effect of pressure work and viscous dissipation, shear work, rarefaction degree and axial conduction on microchannel convective heat transfer, in both the thermally developing and fully developed flow regions. Viscous dissipation and pressure work in a pressure-driven microchannel gas flow are of comparable magnitudes and may not be neglected from the energy equation. The shear work at the wall, which is effectively the combined effect of viscous dissipation and pressure work, needs to be included in the Nusselt number for better predictions of heat transfer.

Self-Organized Velocity Pulses of Dense Colloidal Suspensions in Microchannel Flow.

We present a numerical study of dense colloidal suspensions in a pressure-driven microchannel flow in two dimensions. The colloids are modeled as elastic and frictional spheres suspended in a Newtonian fluid, which we simulate using the method of multiparticle collision dynamics. The model reproduces periodic velocity and density pulse trains, traveling upstream in the microchannel, which are found in experiments conducted by Isa etal. [Phys. Rev. Lett. 102, 058302 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.058302]. We show that colloid-wall friction and the resultant force chains are crucial for the formation of these pulses. With an increasing colloid density, first solitary jams occur, which become periodic pulse trains at intermediate densities and unstable solitary pulses at high densities. We formulate a phenomenological continuum model and show how these spatiotemporal flow and density profiles can be understood as homoclinic and periodic orbits in traveling-wave equations.

A Rapid Capillary-Pressure Driven Micro-Channel to Demonstrate Newtonian Fluid Behavior of Zebrafish Blood at High Shear Rates

Blood viscosity provides the rheological basis to elucidate shear stress underlying developmental cardiac mechanics and physiology. Zebrafish is a high throughput model for developmental biology, forward-genetics, and drug discovery. The micro-scale posed an experimental challenge to measure blood viscosity. To address this challenge, a microfluidic viscometer driven by surface tension was developed to reduce the sample volume required (3μL) for rapid (<2 min) and continuous viscosity measurement. By fitting the power-law fluid model to the travel distance of blood through the micro-channel as a function of time and channel configuration, the experimentally acquired blood viscosity was compared with a vacuum-driven capillary viscometer at high shear rates (>500 s−1), at which the power law exponent (n) of zebrafish blood was nearly 1 behaving as a Newtonian fluid. The measured values of whole blood from the micro-channel (4.17cP) and the vacuum method (4.22cP) at 500 s−1 were closely correlated at 27 °C. A calibration curve was established for viscosity as a function of hematocrits to predict a rise and fall in viscosity during embryonic development. Thus, our rapid capillary pressure-driven micro-channel revealed the Newtonian fluid behavior of zebrafish blood at high shear rates and the dynamic viscosity during development.

Velocity amplification in pressure-driven flows between superhydrophobic gratings of small solid fraction.

With diminishing fraction of their solid portion, compound gas-solid superhydrophobic surfaces exhibit a large amount of slip which allows for appreciable velocity amplification in pressure-driven microchannel flows. We address this small solid-fraction limit in the context of a grating-like configuration, where superhydrophobicity is provided by a periodic array of flat-meniscus bubbles which are trapped in a Cassie state within the grooved channel walls. Asymptotic analysis for both longitudinal and transverse flows reveals a logarithmic scaling of the effective slip length in the solid fraction of the compound boundaries, thus refuting earlier claims of an algebraic singularity. The logarithmic scaling in the longitudinal problem is explained using an analogy between the unidirectional velocity and the velocity potential in two-dimensional irrotational flows. In the transverse problem it has to do with the Stokes paradox. The mechanisms identified herein explain the absence of slip-length singularity in the comparable asymmetric configuration, where only one of the channel walls is superhydrophobic.

Combined Effects of EDL and Boundary Slip on the Stability of Liquid-Liquid Viscosity-Stratified Flow in Microchannels

AbstractThe stability of pressure-driven liquid-liquid viscosity-stratified microchannel flow is investigated by considering the combined effects of electrical double layer (EDL) and boundary slip. The electrical streaming currents determined by the Streaming Electrical Current Balance (ECB) and the boundary slip are considered by Navier slip assumption. The stability of flow is studied by the small disturbance theory. Numerical results indicate that the effect of boundary slip on the flow stability is strongly depended on the EDL. The boundary slip stables the flow when EDL effect is weak and destabilizes the flow when EDL effect is strong. The effects of boundary slip and EDL on flow stability is also determined by viscosity ratio, the height of channel, interface position and conductivity ratio.

Solitary and transitional waves in pressure-driven two-layer microchannel flow

Similar to the case of the gravity-driven flow (Sisoev and Bennett 2013 Fluid Dyn. Res. 45 015503) we use the integral method to derive evolution equations modeling a pressure-driven two-layer flow of immiscible viscous fluids in a plane microchannel. It is shown that the system possesses a vast set of steady-traveling solitary and transitional waves. Analysis of the phase trajectories of the relevant dynamical system indicates the existence of families of steady-traveling periodic waves.

Filter-matrix lattice Boltzmann model for microchannel gas flows

The lattice Boltzmann method has been shown to be successful for microscale gas flows, and it has attracted significant research interest. In this paper, the recently proposed filter-matrix lattice Boltzmann (FMLB) model is first applied to study the microchannel gas flows, in which a Bosanquet-type effective viscosity is used to capture the flow behaviors in the transition regime. A kinetic boundary condition, the combined bounce-back and specular-reflection scheme with the second-order slip scheme, is also designed for the FMLB model. By analyzing a unidirectional flow, the slip velocity and the discrete effects related to the boundary condition are derived within the FMLB model, and a revised scheme is presented to overcome such effects, which have also been validated through numerical simulations. To gain an accurate simulation in a wide range of Knudsen numbers, covering the slip and the entire transition flow regimes, a set of slip coefficients with an introduced fitting function is adopted in the revised second-order slip boundary condition. The periodic and pressure-driven microchannel flows have been investigated by the present model in this study. The numerical results, including the velocity profile and the mass flow rate, as well as the nonlinear pressure distribution along the channel, agree fairly well with the solutions of the linearized Boltzmann equation, the direct simulation Monte Carlo results, the experimental data, and the previous results of the multiple effective relaxation lattice Boltzmann model. Also, the present results of the velocity profile and the mass flow rate show that the present model with the fitting function can yield improved predictions for the microchannel gas flow with higher Knudsen numbers in the transition flow regime.

Modeling of Asphaltene Transport and Separation in the Presence of Finite Aggregation Effects in Pressure-Driven Microchannel Flow

In this paper, we present a perturbation-based theoretical model on the asphatene transport and aggregation in a pressure-driven microchannel flow. The aggregation effect is captured by a first-order reaction kinetics quantified by the appropriate Damköhler number. We find that the rate of average transport, quantified by the corresponding band velocity of a traveling asphaltene plug, is lowered by an increase in the Damköhler number, suggesting that the aggregation event lowers the flow rate of an asphaltene sample. Also, the average spread of the channel centerline concentration, described by a Gaussian profile and dictated primarily by the axial dispersion (and not Taylor dispersion, in light of the small Peclet number) increases with the Damköhler number. The net effect is a distinctly noticeable separation of asphaltene molecules having different rates of aggregate formation.

Ionic liquid-based aqueous two-phase extraction within a microchannel system

Ionic liquid-based aqueous two-phase systems (IL-ATPSs) are great candidates for the replacement of volatile organic solvents in liquid–liquid extractions. Besides, microfluidic separation techniques are a promising alternative to conventional systems since they provide continuous operation, better performance and easier capacity increase by a numbering-up approach. Herein, the advantages of IL-ATPSs and microfluidic continuous separation were combined within a microfluidic device with parallel flow allowing for the separation of the two phases at the exit of the microchannel. An aqueous solution of [C4mim] [BF4] and d-fructose was used as an IL-ATPS and compared with a conventional ATPS consisted of polyethylene glycol/salt solution. Based on the evaluated partitioning coefficient of a model substance, namely bovine serum albumin, the ionic liquid concentration and pH value of the IL-ATPS have been selected for the use within a pressure-driven microchannel system with y-shaped inlet and outlet. Furthermore, a three-dimensional model considering convection in the flow direction and diffusion in all spatial directions at steady-state conditions was developed, validated by experimental results and used to assess the feasibility of micro-scale parallel flow extraction in a wide range of flow rates. The chosen IL-ATPS was shown to be much more efficient media for continuous microfluidic extraction as compared to conventional ATPS, primarily due to much lower dynamic viscosity of IL-rich phase related to PEG-rich phase.

Microfluidic diffusion measurements: The optimal H-cell

This article reports the optimal design and measurement conditions for microfluidic diffusion experiments. For this purpose, we conducted and experimentally validated the model-based Optimal Experimental Design (OED) of a pressure-driven H-cell microchannel for diffusion measurements in liquids. While earlier work employed low Fourier numbers (i.e., low contact times), our results show the existence of an optimal finite Fourier number for which the measurement sensitivity increases drastically. For the optimal contact times (Fo=0.30…0.39), the accuracy of diffusion measurements is improved by orders of magnitude compared to the previously used sub-optimal low Fourier region (Fo<0.01). A general design rule for optimal H-cell diffusion experiments is derived. To demonstrate the utility of the optimized microfluidic method, diffusion coefficients are measured for a variety of binary mixtures. We show that H-cell measurements designed and operated according to the identified principles lead to a fast, efficient and cheap method for high-throughput diffusion analysis.

Discussion on the Gaseous Slip Model Based on Langmuir Adsorption Isotherm

Abstract Different from the Maxwell slip model, the gaseous slip model based on the Langmuir adsorption isotherm, i.e. the Langmuir slip model, takes into account the interfacial interaction between the gas molecules and the wall surface. For pressure-driven micro-channel gas flow, both slip models are adopted and the velocity formulae of gas flow are derived analytically. The result indicates that the velocity formulae for the gas flow are the same except that one parameter which could be inferred from experiment data or theoretical prediction. In Maxwell slip model, the parameter is related with the surface accommodation coefficient; On the other hand, the parameter is related with the gas particle interaction potential and the heat of adsorption in Langmuir slip model. Therefore, the Langmuir slip model still has the same difficulty in determining the value of the parameter as the Maxwell slip model.

On the competition between streaming potential effect and hydrodynamic slip effect in pressure-driven microchannel flows

The competition between streaming potential effect and hydrodynamic slip effect in pressure-driven microchannel flows is elucidated. The treatment is performed analytically in the framework of the Debye–Hückel linear approximation and the Navier slip boundary condition. As compared with pressure-driven flows in nonslip microchannels, pressure-driven flows in microchannels with hydrodynamic slippage are found to experience severer flow reduction (streaming potential effect). An apparent viscosity ratio is also defined to identify the competition between streaming potential effect and hydrodynamic slip effect in pressure-driven microchannel flows. It is shown that the streaming potential effect predominates when this ratio is larger than unity and the slip effect predominates when this ratio is smaller than unity. More importantly, we derive a formula for the critical slip length which provides a guideline for designing hydrophobic surfaces over which the effect of hydrodynamic slip exactly counteracts that of streaming potential.

Mechanical behaviour of DNA molecules—Elasticity and migration

A novel multi-scale simulation method developed to describe mesoscale phenomena occurring in biofluidic devices is presented. The approach combines the macro-scale modelling of the carrier fluid and the micro-scale description of the transported macromolecules or compounds. Application of the approach is demonstrated through mesoscale simulations of DNA molecules. The investigated phenomena include elastic relaxation of dsDNA molecules and migration of ssDNA molecules in a microchannel flow. The results of the first study demonstrate that the elastic behaviour of the DNA molecules can be captured sucessfully. The second study proves that the migration of ssDNA in pressure-driven microchannel flows can be explained by the hydrodynamic interaction with the carrier liquid.

Effect of electrical double layer on electric conductivity and pressure drop in a pressure-driven microchannel flow

The effect of an electrical double layer (EDL) on microchannel flow has been studied widely, and a constant bulk electric conductivity is often used in calculations of flow rate or pressure drop. In our experimental study of pressure-driven micropipette flows, the pipette diameter is on the same order of magnitude as the Debye length. The overlapping EDL resulted in a much higher electric conductivity, lower streaming potential, and lower electroviscous effect. To elucidate the effect of overlapping EDL, this paper developed a simple model for water flow without salts or dissolved gases (such as CO(2)) inside a two-dimensional microchannel. The governing equations for the flow, the Poisson, and Nernst equations for the electric potential and ion concentrations and the charge continuity equation were solved. The effects of overlapping EDL on the electric conductivity, velocity distribution, and overall pressure drop in the microchannel were quantified. The results showed that the average electric conductivity of electrolyte inside the channel increased significantly as the EDL overlaps. With the modified mean electric conductivity, the pressure drop for the pressure-driven flow was smaller than that without the influence of the EDL on conductivity. The results of this study provide a physical explanation for the observed decrease in electroviscous effect for microchannels when the EDL layers from opposing walls overlap.

Structure and rheology ofSiO2nanoparticle suspensions under very high shear rates

High shear rate experiments have been performed with capillary microviscometers onto SiO2 nanoparticles dispersed in alcohol (so-called nanofluids). The aim of these experiments was to investigate the processes of aggregation and dislocation of the nanoparticles in a shear flow under perikinetic and orthokinetic conditions. Shear rates as high as 2x10(5) s-1 were obtained in pressure-driven microchannels laminar flows. All the nanofluids under test have displayed a Newtonian behavior but with a strong enhanced viscosity, that is, the consequence of an effective volume concentration higher than the real one. It was possible to determine the average size of the aggregates and to find a correlation between their structure and the range of the hydrodynamic Peclet number at which experiments were performed. These results display a strong evidence of the role of aggregates and support the recent conclusions about the controversy of the thermal properties of nanofluids.

Electroosmotically enhanced microchannel heat sinks

The present study investigates the microchannel heat sink for pure electroosmotic, pressure-driven, and mixed (electroosmotic and pressure-driven) flows. A three-dimensional numerical analysis is performed for electroosmotic and mixed flows. Electroosmotic flow (EOF) induced in an ionic solution in the presence of surface charge and electric field is investigated with hydrodynamic pressure-driven flow (PDF) to enhance heat removal through the microchannel heat sink. In a pressure-driven microchannel heat sink, the application of an external electric field increases the flow rate that consequently reduces the thermal resistance. The effects of ionic concentration represented by the zeta potential and Debye thickness are studied with the various steps of externally applied electric potential. A higher value of zeta potential leads to higher flow rate and lower thermal resistance, which consequently reduce the temperature of the microprocessor chip and load of the micropump used to supply coolant to the microchannels.

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&amp;lt;1, the streaming potential behaves similarly to that of steady flow, whereas it decreases rapidly with Re as Re&amp;gt;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.

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.

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.