Electroosmotically driven capillary transport of typical non-Newtonian biofluids in rectangular microchannels

In this paper, a detailed theoretical model is developed for studying the capillary filling dynamics of a non-Newtonian power-law obeying fluid in a microchannel subject to electrokinetic effects. Special attention is devoted to model the effects of the electroosmotic influences in the capillary advancement process, variable resistive forces acting over different flow regimes, and the dynamically evolving contact line forces, in mathematically closed forms. As an illustrative case study, in which the flow parameters are modeled as functions of the hematocrit fraction in the sample, the capillary dynamics of a blood sample are analyzed. Flow characteristics depicting advancement of the fluid within the microfluidic channel turn out to be typically non-linear, as per the relative instantaneous strengths of the capillary forces, electroosmotic forces and viscous resistances. Non-trivial implications of the blood hematocrit level and the imposed electric field on the progression of the capillary front are highlighted, which are expected to be of significant consequence towards the dynamics of electroosmotically aided capillary filling processes of biofluidic samples.     

Magnetohydrodynamic (MHD) flow of nanofluid with double stratification and slip conditions

This paper concerns with the analysis of double stratification in magnetohydrodynamic (MHD) flow of nanofluid by a stretching cylinder. Brownian motion and thermophoresis effects are present in the transport equations. The flow is subjected to velocity, thermal and solutal slip conditions. Non-linear ordinary differential equations are obtained from the governing non-linear partial differential equations after using appropriate transformations. The resulting non-linear ordinary differential equations are solved for the convergent series solutions. The velocity, temperature and concentration profiles are illustrated for different emerging parameters. Velocity distribution decays for higher estimation of velocity slip parameter. Furthermore, temperature decreases and concentration enhances for higher values of thermal stratification parameter and thermophoresis parameter, respectively. Numerical results for the skin friction, Nusselt number and Sherwood number are also presented and examined. Comparison between the published limiting solutions and present results is found in an excellent agreement.     

Electrically induced colloidal clusters for generating shear mixing and visualizing flow in microchannels

When aqueous suspensions of 1 μm, negatively charged polystyrene particles are subject to a 1 kHz alternating electric field of strength greater than 7 kV(rms) m(-1), dynamic elliptical clusters of particles spontaneously form. With potential applications in microchannel fluidics in mind, we characterize how cluster formation and particle circulation, driven by induced dipole-dipole interactions, is critically dependent on time, field strength, electrolyte concentration, and cell thickness. Logarithmic growth of cluster size is observed, and particle velocity within the clusters is found to be proportional to cluster length. Increasing cell thickness from 10 to 60 μm increases the projected cluster area but decreases cluster aspect ratio as the result of changing particle dispersal rates. Clusters are shown to generate significant fluid shear suitable for microchannel mixing applications. These clusters are observed to distort under transverse fluid flow and, above a critical flow rate, to undergo a transition to form regularly spaced particle streams, which may be suitable for two-dimensional visualization of fluid flow.     

Analytical study of Joule heating effects on electrokinetic transportation in capillary electrophoresis

Electric fields are often used to transport fluids (by electroosmosis) and separate charged samples (by electrophoresis) in microfluidic devices. However, there exists inevitable Joule heating when electric currents are passing through electrolyte solutions. Joule heating not only increases the fluid temperature, but also produces temperature gradients in cross-stream and axial directions. These temperature effects make fluid properties non-uniform, and hence alter the applied electric potential field and the flow field. The mass species transport is also influenced. In this paper we develop an analytical model to study Joule heating effects on the transport of heat, electricity, momentum and mass species in capillary-based electrophoresis. Close-form formulae are derived for the temperature, applied electrical potential, velocity, and pressure fields at steady state, and the transient concentration field as well. Also available are the compact formulae for the electric current and the volume flow rate through the capillary. It is shown that, due to the thermal end effect, sharp temperature drops appear close to capillary ends, where sharp rises of electric field are required to meet the current continuity. In order to satisfy the mass continuity, pressure gradients have to be induced along the capillary. The resultant curved fluid velocity profile and the increase of molecular diffusion both contribute to the dispersion of samples. However, Joule heating effects enhance the sample transport velocity, reducing the analysis time in capillary electrophoretic separations.     

Pressure drop of slug flow in microchannels with increasing void fraction: experiment and modeling

Pressure drop in a gas-liquid slug flow through a long microchannel of rectangular cross-section was investigated. Pressure measurements in a lengthy (～0.8 m) microchannel determined the pressure gradient to be constant in a flow where gas bubbles progressively expanded and the flow velocity increased due to a significant pressure drop. Most of the earlier studies of slug flow in microchannels considered systems where the expansion of the gas bubbles was negligible in the channel. In contrast, we investigated systems where the volume of the gas phase increased significantly due to a large pressure drop (up to 1811 kPa) along the channel. This expansion of the gas phase led to a significant increase in the void fraction, causing considerable flow acceleration. The pressure drop in the microchannel was studied for three gas-liquid systems; water-nitrogen, dodecane-nitrogen, and pentadecane-nitrogen. Inside the microchannel, local pressure was measured using a series of embedded membranes acting as pressure sensors. Our investigation of the pressure drop showed a linear trend over a wide range of void fractions and flow conditions in the two-phase flow. The lengths and the velocities of the liquid slugs and the gas bubbles were also studied along the microchannel by employing a video imaging technique. Furthermore, a model describing the gas-liquid slug flow in a long microchannel was developed to calculate the pressure drop under conditions similar to the experiments. An excellent agreement between the developed model and the experimental data was obtained.     

Internal flow in polymer solution droplets deposited on a lyophobic surface during a receding process

When a polymer solution droplet is deposited on a lyophobic surface, the contact line is moved back to some degree and subsequently pinned. An experimental setup is constructed to investigate not only the receding process but also an internal flow of polystyrene-acetophenone and -anisole solutions. As a result, the time variation of the evaporation rate per unit area during receding does not strongly depend on the initial solute concentration. The average solute concentration at the pinning of the contact line increases as the initial solute concentration increases. A convective circulation flow that is upward at the axis of symmetry is observed. This flow pattern is different from those of pure liquids such as water, acetone, benzene, and so forth, which have been previously reported. Furthermore, the observed flow is enhanced as the initial solute concentration increases, contrary to an increase in the fluid viscosity. To resolve these discrepancies, the mechanism of the flow is numerically investigated using a hemispherical droplet model considering the density and surface tension distributions. The numerical results demonstrate that the circulation flow that is experimentally observed is actually caused. It is also found that the solutal Rayleigh effect initially induces the internal flow, and subsequently the solutal Marangoni effect dominates the flow. Both effects are enhanced as the initial concentration increases because of the evaporative mass balance at the free surface.     

Finite sample effect in temperature gradient focusing

Temperature gradient focusing (TGF) is a new and promising equilibrium gradient focusing method which can provide high concentration factors for improved detection limits in combination with high-resolution separation. In this technique, temperature-dependent buffer chemistry is employed to generate a gradient in the analyte electrophoretic velocity. By the application of a convective counter-flow, a zero-velocity point is created within a microchannel, at which location the ionic analytes accumulate or focus. In general, the analyte concentration is small when compared with buffer ion concentrations, such that the focusing mechanism works in the ideal, linearized regime. However, this presumption may at times be violated due to significant sample concentration growth or the use of a low-concentration buffer. Under these situations the sample concentration becomes non-negligible and can induce strong nonlinear interactions with buffer ions, which eventually lead to peak shifting and distortion, and the loss of detectability and resolution. In this work we combine theory, simulation, and experimental data to present a detailed study on nonlinear sample-buffer interactions in TGF. One of the key results is the derivation of a generalized Kohlrausch regulating function (KRF) that is valid for systems in which the electrophoretic mobilities are not constant but vary spatially. This generalized KRF greatly facilitates analysis, allowing reduction of the problem to a single equation describing sample concentration evolution, and is applicable to other problems with heterogeneous electrophoretic mobilities. Using this sample evolution equation we have derived an understanding of the nonlinear peak deformation phenomenon observed experimentally in TGF. We have used numerical simulations to validate our theory and to quantitatively predict TGF. Our simulation results demonstrate excellent agreement with experimental data, and also indicate that the proper inclusion of Taylor dispersion is important for the accurate modeling of TGF. This work is an important first step towards the understanding and prediction of the more complex, nonlinear, and multi-species interactions which often occur in on-chip electrophoretic assays such as TGF.     

High-throughput microfluidics: improved sample treatment and washing over standard wells

Fluid flow in microchannels is used to treat or wash samples and can be incorporated into high-throughput applications such as drug screening, which currently use standard microtiter wells for performing assays. This paper provides theoretical and experimental data comparing microchannels and standard wells on the metrics of sample washing and experimental error in treatment concentrations. It is shown numerically and experimentally that microchannel concentration can be approximated with an inverse linear relationship to input volume. The experimentally supported mathematical approximation and error propagation methods are used to compare the accuracy and precision of treatments in microchannels vs. standard wells. Mathematical results suggest microchannels can provide 10 or more times the treatment precision of standard wells for volume ratios typical of high-throughput screening. Passive-pumping and diffusion are utilized to improve microchannel accuracy and precision even further in a treat-wait-treat method. The advantages of microchannels outlined here can have large-scale effects on cost and accuracy in screening applications.     

Combination of large‐volume sample stacking with an electroosmotic flow pump with field‐amplified sample injection on cross‐channel chips

A combination of two online sample concentration techniques, large‐volume sample stacking with an electroosmotic flow (EOF) pump (LVSEP) and field‐amplified sample injection (FASI), was investigated in microchip electrophoresis (MCE) to achieve highly sensitive analysis. By applying reversed‐polarity voltages on a cross‐channel microchip, anionic analytes injected throughout a microchannel were first concentrated on the basis of LVSEP, followed by the electrokinetic stacking injection of the analytes from a sample reservoir by the FASI mechanism. As well as the voltage application, a pressure was also applied to the sample reservoir in LVSEP‐FASI. The applied pressure generated a counter‐flow against the EOF to reduce the migration velocity of the stacked analytes, especially around the cross section of the microchannel, which facilitated the FASI concentration. At the hydrodynamic pressure of 15 Pa, 4520‐fold sensitivity increase was obtained in the LVSEP‐FASI analysis of a standard dye, which was 33‐times higher than that obtained with a normal LVSEP. Furthermore, the use of the sharper channel was effective for enhancing the sensitivity, e.g., 29 100‐fold sensitivity increase was achieved with the 75‐μm wide channel. The developed method was applied to the chiral analysis of amino acids in MCE, resulting in the sensitivity enhancement factor of 2920 for the separated d ‐leucine.     

Schmidt number effects in dissipative particle dynamics simulation of polymers

Simulation studies for dilute polymeric systems are presented using the dissipative particle dynamics method. By employing two different thermostats, the velocity-Verlet and Lowe's scheme, we show that the Schmidt number (S(c)) of the solvent strongly affects nonequilibrium polymeric quantities. The fractional extension of wormlike chains subjected to steady shear is obtained as a function of S(c). Poiseuille flow in microchannels for fixed polymer concentration and varying number of repeated units within a chain is simulated. The nonuniform concentration profiles and their dependence on S(c) are computed. We show the effect of the bounce-forward wall boundary condition on the depletion layer thickness. A power law fit of the velocity profile in stratified Poiseuille flow in a microchannel yields wall viscosities different from bulk values derived from uniform, steady plane Couette flow. The form of the velocity profiles indicates that the slip flow model is not useful for the conditions of these calculations.     

Mechanism of hydrodynamic separation of biological objects in microchannel devices

In this study, the separation mechanism employed in hydrodynamic chromatography in microchannel devices is analyzed. The main purpose of this work is to provide a methodology to develop a predictive model for hydrodynamic chromatography for biological macromolecules in microchannels and to assess the importance of various phenomenological coefficients. A theoretical model for the hydrodynamic chromatography of particles in a microchannel is investigated herein. A fully developed concentration profile for non-reactive particles in a microchannel was obtained to elucidate the hydrodynamic chromatography of these particles. The external forces acting on the particles considered in this model include the van der Waals attractive force, double-layer force as well as the gravitational force. The surface forces, such as van der Waals attractive force as well as the double-layer repulsive force, can either enhance or hinder the average velocity of the macromolecular particles. The average velocity of the particles decreases with the molecular radius because the van der Waals attractive force increases the concentration of the particles near the channel surface, which is the low-velocity region. The transport velocity of the particles is dominated by the gravity and the higher density enlarges the effect caused by gravity.     

Influence of the three-dimensional heterogeneous roughness on electrokinetic transport in microchannels

Surface roughness has been considered as a passive means of enhancing species mixing in electroosmotic flow through microfluidic systems. It is highly desirable to understand the synergetic effect of three-dimensional (3D) roughness and surface heterogeneity on the electrokinetic flow through microchannels. In this study, we developed a three-dimensional finite-volume-based numerical model to simulate electroosmotic transport in a slit microchannel (formed between two parallel plates) with numerous heterogeneous prismatic roughness elements arranged symmetrically and asymmetrically on the microchannel walls. We consider that all 3D prismatic rough elements have the same surface charge or zeta potential, the substrate (the microchannel wall) surface has a different zeta potential. The results showed that the rough channel's geometry and the electroosmotic mobility ratio of the roughness elements' surface to that of the substrate, epsilon(mu), have a dramatic influence on the induced-pressure field, the electroosmotic flow patterns, and the electroosmotic flow rate in the heterogeneous rough microchannels. The associated sample-species transport presents a tidal-wave-like concentration field at the intersection between four neighboring rough elements under low epsilon(mu) values and has a concentration field similar to that of the smooth channels under high epsilon(mu) values.     

Sodium silicate based sol–gel structures for generating pressure-driven flow in microfluidic channels

In this article, we report the design of a microchip based hydraulic pump that employs a sodium silicate derived sol–gel structure for generating pressure-driven flow within a microfluidic network. The reported sol–gel structure was fabricated in a chosen location of our device by selectively retaining sodium silicate solution within a sub-micrometer deep segment via capillary forces, and then providing the precursor material appropriate thermal treatment. It was shown that while the molecular weight cut-off for these membranes is at least an order of magnitude smaller than their photo-polymerized counterparts, their electrical conductance is significant. Moreover, unlike their polymeric counterparts these structures were found to be capable of blocking electroosmotic flow, thereby generating a pressure-gradient around their interface with an open microchannel upon application of an electric field across the microchannel–membrane junction. In this work, a fraction of the resulting hydrodynamic flow was successfully guided to an electric field-free analysis channel to implement a pressure-driven assay. Our experiments show that the pressure-driven velocity produced in the analysis channel of our device varied linearly with the voltage applied across the sol–gel membrane and was nearly independent of the cross-sectional dimensions of the membrane and the microfluidic channels. With our current design pressure-driven velocities up to 1.7 mm/s were generated for an applied voltage of 2 kV, which easily covers the range of flow speeds that can minimize the plate height in most microfluidic separations. Finally, the functionality of our device was demonstrated by implementing a reverse phase chromatographic separation in the analysis channel of our device using the pressure-driven flow generated on-chip.     

The bis(p-sulfonatophenyl)phenylphosphine-assisted synthesis and phase transfer of ultrafine gold nanoclusters

The behavior of Couette flow of nanofluids composed of negatively-charged nanoparticles dispersed in aqueous NaCl solutions is studied theoretically. The equation for calculating the Couette flow velocity profiles is derived. The induced electric fields and velocity profiles are calculated as a function of key parameters including nanoparticle size and volume fraction. We have found for the first time that the velocity profile of nanofluids containing charged nanoparticles deviates significantly from the classical linear velocity profile for Couette flow. This previously unseen flow phenomenon is attributed to the dominance of the electric field strength induced by the flow of charged nanoparticles. This new mechanism of nanoparticle-induced microfluidic transport could lead to novel microfluidic and tribological applications.     

Electroosmotic transport through rectangular channels with small zeta potentials

In this article, we analyze the electroosmotic transport of neutral samples through rectangular channels having a small zeta potential at their walls. Exact analytical expressions have been derived for quantifying the solute velocity in such conduits and the Taylor-Aris dispersivity in large-aspect-ratio rectangular geometries. In addition, a semianalytical theory has been presented for estimating the solutal spreading rate in rectangular profiles of all aspect ratios by decoupling the effects of vertical and horizontal velocity gradients in the system. Finally, the predictions made by this theory have been compared with the results from numerical simulations in which all assumptions were relaxed. Our analysis shows that while the sidewalls in a rectangular conduit modify the fluid velocity only to a moderate extent, they can increase the hydrodynamic dispersion of sample slugs as much as by a factor of 8 under strong Debye-layer overlap conditions. In the opposite limit of thin Debye layers, however, the increase in dispersion due to the side regions is only by a factor of 2 and remains nearly unaffected by the aspect ratio of the channel, in agreement with the prediction by [E.K. Zholkovskij, J.H. Masliyah, J. Czarnecki, Anal. Chem. 75 (2003) 901].     

A microfluidic device for separating erythrocytes polluted by lead (II) from a continuous bloodstream flow

To sort and separate erythrocytes contaminated by lead (II) from whole bloodstream flow, the first step is to use a microchannel to transport the blood cells into a microdevice. Within the device, polluted erythrocytes can be separated from the bloodstream by applying local dielectrophoretic (DEP) forces. Exploiting the fact that Pb(2+) ions attach to the membranes of the erythrocytes, we utilize the microfluidic DEP device to perform property-based fractionation of the blood samples and to separate the polluted erythrocytes from the continuous bloodstream flow. Atomic absorption spectrometer analysis reveals that, to remove lead-polluted erythrocytes, the most effective driving velocity was less than 0.1 cm/s through our microfluidic DEP device, based on an applied power of 10 V(peak-peak) and a frequency of 15.5 MHz AC field. We were able to remove 80% of the polluted erythrocytes. Using gentle DEP manipulating techniques to efficiently sort unique cells within a complex biological sample may potentially allow biological sorting to be performed outside of hospitals, in facilities without biological analyzing equipment.     

Modular approach to fabrication of three-dimensional microchannel systems in PDMS-application to sheath flow microchips

A modular approach to fabrication of three-dimensional microchannel systems in polydimethylsiloxane (PDMS) is presented. It is based on building blocks with microstructuring on up to three faces. The assembled 3D-microchip consists of three building blocks in two layers. For assembly of the bottom layer two building blocks are joined horizontally, whereby the side structuring of the first is sealed against the flat side surface of the other. This results in the formation of a vertical interconnection opening between the building blocks to supplement the microstructuring on the lower faces. The 3D microchannel system is completed by placing a third building block, with microstructuring only on its lower face, on top of the assembled layer. While plasma assisted bonding is used between the two building blocks of the bottom layer, inherent adhesion is sufficient between the layers and for attaching the assembled 3D-microchip to a substrate. This modular approach was applied to the fabrication of a 3D-sheath flow microchip. It comprises a 20 microm deep microchannel system with sample inlet, open sensing area and outlet in the bottom layer and sheath flow inlet in the top layer. 100 microM fluorescein at 6 microL min(-1) was used as sample flow and water at increasing flow rates as sheath flow. With ratios of sheath to sample flow up to 20:1 sample layers down to 1 microm thickness could be generated. Sample layer thickness was determined via volume detection on an epi-fluorescence microscope followed by image analysis.     

Diffusioosmosis of electrolyte solutions along a charged plane wall

The steady diffusioosmotic flow of an electrolyte solution along a dielectric plane wall caused by an imposed tangential concentration gradient is analytically examined. The plane wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by the Poisson-Boltzmann equation. The macroscopic electric field along the tangential direction induced by the imposed electrolyte concentration gradient is obtained as a function of the lateral position. A closed-form formula for the fluid velocity profile is derived as the solution of a modified Navier-Stokes equation. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential of the wall and the properties of the electrolyte solution. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field in the double layer on the diffusioosmotic flow is found to be very significant and cannot be ignored.     

A parametric study of human fibroblasts culture in a microchannel bioreactor

The culture of cells in a microbioreactor can be highly beneficial for cell biology studies and tissue engineering applications. The present work provides new insights into the relationship between cell growth, cell morphology, perfusion rate, and design parameters in microchannel bioreactors. We demonstrate the long-term culture of mammalian (human foreskin fibroblasts, HFF) cells in a microbioreactor under constant perfusion in a straightforward simple manner. A perfusion system was used to culture human cells for more than two weeks in a plain microchannel (130 microm x 1 mm x 2 cm). At static conditions and at high flow rates (>0.3 ml h(-1)), the cells did not grow in the microchannel for more than a few days. For low flow rates (<0.2 ml h(-1)), the cells grew well and a confluent layer was obtained. We show that the culture of cells in microchannels under perfusion, even at low rates, affects cell growth kinetics as well as cell morphology. The oxygen level in the microchannel was evaluated using a mass transport model and the maximum cell density measured in the microchannel at steady state. The maximum shear stress, which corresponds to the maximum flow rate used for long term culture, was 20 mPa, which is significantly lower than the shear stress cells may endure under physiological conditions. The effect of channel size and cell type on long term cell culture were also examined and were found to be significant. The presented results demonstrate the importance of understanding the relationship between design parameters and cell behavior in microscale culture system, which vary from physiological and traditional culture conditions.     

Detection of ferricyanide as a probe for the effect of hematocrit in whole blood biosensors.

Measurement of the concentration of an analyte in whole blood can be influenced by a range of factors; the red cell content or hematocrit (Hct) of the sample, the distribution and rate of movement of analyte between red cells and plasma, the amount of protein in solution, the viscosity of the sample and fouling of the sensor. The effect of the red cells is the major factor that must be taken into account. Using the analyte molality rather than the analyte molarity, the theoretical response for a range of analytes which are found in plasma and in the red cells can be calculated. For an analyte which is found in plasma alone, the effect of hematocrit is significant, with a bias of -1% per %Hct; if the analyte can freely and rapidly diffuse between the red cells and plasma, this bias is reduced to zero. Using ferrocyanide as a model analyte, the effects of fouling and reduced sample viscosity were measured to be -0.2% per %Hct, giving an overall bias of -1.2% per %Hct, a level of bias which is not clinically acceptable. This bias can be negated by measuring the hematocrit separately and incorporating it into the measurement algorithm. Such a correction is essential for the correct measurement of the concentration of an analyte in whole blood.