Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows

Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz-Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz-Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz-Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.     

Insulator-based dielectrophoretic focusing and trapping of particles in non-Newtonian fluids

Insulator-based dielectrophoretic (iDEP) microdevices have been limited to work with Newtonian fluids. We report an experimental study of the fluid rheological effects on iDEP focusing and trapping of polystyrene particles in polyethylene oxide, xanthan gum, and polyacrylamide solutions through a constricted microchannel. Particle focusing and trapping in the mildly viscoelastic polyethylene oxide solution are slightly weaker than in the Newtonian buffer. They are, however, significantly improved in the strongly viscoelastic and shear thinning polyacrylamide solution. These observed particle focusing behaviors exhibit a similar trend with respect to electric field, consistent with a revised theoretical analysis for iDEP focusing in non-Newtonian fluids. No apparent focusing of particles is achieved in the xanthan gum solution, though the iDEP trapping can take place under a much larger electric field than the other fluids. This is attributed to the strong shear thinning-induced influences on both the electroosmotic flow and electrokinetic/dielectrophoretic motions.     

Elastic instabilities in the electroosmotic flow of non-Newtonian fluids through T-shaped microchannels

Electroosmotic flow (EOF) has been widely used to transport fluids and samples in micro- and nanofluidic channels for lab-on-a-chip applications. This essentially surface-driven plug-like flow is, however, sensitive to both the fluid and wall properties, of which any inhomogeneity may draw disturbances to the flow and even instabilities. Existing studies on EOF instabilities have been focused primarily upon Newtonian fluids though many of the chemical and biological solutions are actually non-Newtonian. We carry out a systematic experimental investigation of the fluid rheological effects on the elastic instability in the EOF of phosphate buffer-based polymer solutions through T-shaped microchannels. We find that electro-elastic instabilities can be induced in shear thinning polyacrylamide (PAA) and xanthan gum (XG) solutions if the applied direct current voltage is above a threshold value. However, no instabilities are observed in Newtonian or weakly shear thinning viscoelastic fluids including polyethylene oxide (PEO), polyvinylpyrrolidone (PVP), and hyaluronic acid (HA) solutions. We also perform a quantitative analysis of the wave parameters for the observed elasto-elastic instabilities.     

Continuous and precise particle separation by electroosmotic flow control in microfluidic devices

A new scheme has been described for continuous particle separation using EOF in microfluidic devices. We have previously reported a method for particle separation, called "pinched flow fractionation (PFF)", in which size-dependent and continuous particle separation can be achieved by introducing pressure-driven flows with and without particles into a pinched microchannel. In this study, EOF was employed to transport fluid flows inside a microchannel. By controlling the applied voltage to electrodes inserted in each inlet/outlet port, the flow rates from both inlets, and flow rates distributed to each outlet could be accurately tuned, thus enabling more effective separation compared to the pressure-driven scheme. In the experiment, the particle behaviors were compared between EOF and pressure-driven flow schemes. In addition, micrometer- and submicrometer-sized particles were accurately separated and individually collected using a microchannel with multiple outlet branch channels, demonstrating the high efficiency of the presented scheme.     

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study.     

Electroosmotic flow of non‐Newtonian fluids in a constriction microchannel

Insulator‐based dielectrophoresis has to date been almost entirely restricted to Newtonian fluids despite the fact that many of the chemical and biological fluids exhibit non‐Newtonian characteristics. We present herein an experimental study of the fluid rheological effects on the electroosmotic flow of four types of polymer solutions, i.e., 2000 ppm xanthan gum (XG), 5% polyvinylpyrrolidone (PVP), 3000 ppm polyethylene oxide (PEO), and 200 ppm polyacrylamide (PAA) solutions, through a constriction microchannel under DC electric fields of up to 400 V/cm. We find using particle streakline imaging that the fluid elasticity does not change significantly the electroosmotic flow pattern of weakly shear‐thinning PVP and PEO solutions from that of a Newtonian solution. In contrast, the fluid shear‐thinning causes multiple pairs of flow circulations in the weakly elastic XG solution, leading to a central jet with a significantly enhanced speed from before to after the channel constriction. These flow vortices are, however, suppressed in the strongly viscoelastic and shear‐thinning PAA solution.     

Fluid rheological effects on streaming dielectrophoresis in a post-array microchannel

Recent studies have demonstrated the strong influences of fluid rheological properties on insulator-based dielectrophoresis (iDEP) in single-constriction microchannels. However, it is yet to be understood how iDEP in non-Newtonian fluids depends on the geometry of insulating structures. We report in this work an experimental study of fluid rheological effects on streaming DEP in a post-array microchannel that presents multiple contractions and expansions. The iDEP focusing and trapping of particles in a viscoelastic polyethylene oxide solution are comparable to those in a Newtonian buffer, which is consistent with the observations in a single-constriction microchannel. Similarly, the insignificant iDEP effects in a shear-thinning xanthan gum solution also agree with those in the single-constriction channel except that gel-like structures are observed to only form in the post-array microchannel under large DC electric fields. In contrast, the iDEP effects in both viscoelastic and shear-thinning polyacrylamide solution are significantly weaker than in the single-constriction channel. Moreover, instabilities occur in the electroosmotic flow and appear to be only dependent on the DC electric field. These phenomena may be associated with the dynamics of polymers as they are electrokinetically advected around and through the posts.     

Highly productive droplet formation by anisotropic elongation of a thread flow in a microchannel

We developed a microfluidic device to form monodisperse droplets with high productivity by anisotropic elongation of a thread flow, defined as a threadlike flow of a dispersed liquid phase in a flow of an immiscible, continuous liquid phase. The thread flow was anisotropically elongated in the depth direction in a straight microchannel with a step, where the microchannel depth changed. Consequently, the elongated thread flow was given capillary instability (Rayleigh-Plateau instability) and was continuously transformed into monodisperse droplets at the downstream area of the step in the microchannel. We examined the effects of the flow rates of the dispersed phase and the continuous phase on the droplet formation behavior, including the droplet diameter and droplet formation frequency. The droplet diameter increased as the fraction of the dispersed-phase flow rate relative to the total flow rate increased and was independent of the total flow rate. The droplet formation frequency proportionally increased with the total flow rate at a constant dispersed-phase flow rate fraction. These results are explained in terms of a mechanism similar to that of droplet formation from a cylindrical liquid thread flow by Rayleigh-Plateau instability. The microfluidic device described was capable of forming monodisperse droplets with a 160-microm average diameter and 3-microm standard deviation at a droplet formation frequency of 350 droplets per second from a single thread flow. The highest total flow rate achieved was 6 mL/h using the present device composed of a straight microchannel with a step. We also demonstrated parallel droplet formation by anisotropic elongation of multiple thread flows; the process was applied to form W/O and O/W droplets. The highly productive droplet formation process presented in this study is expected to be useful for future industrial applications.     

Shear-thickening flow of nanoparticle suspensions flocculated by polymer bridging

The steady-shear viscosity, dynamic viscoelasticity, and stress relaxation behavior were measured for suspensions of silica nanoparticles dispersed in aqueous solutions of poly(ethylene oxide) (PEO). The suspensions of silica with diameters of 8-25 nm show striking shear-thickening profiles in steady shear and highly elastic responses under large strains in oscillatory shear. Since the silica particles are much smaller than the polymer coils, one molecule can extend through several particles by intrachain bridging. Each polymer coil may remain isolated as a floc unit and the silica particles hardly connect two flocs. Therefore, the flow of suspensions is Newtonian with low viscosity at low shear rates. When the polymer coils containing several nanoparticles are subjected to high shear fields, three-dimensional network is developed over the system. The shear-thickening flow may arise from the elastic forces of extended bridges. But, the polymer chain is easily detached from particle surface by thermal energy because of large curvature of particles. As a result, the network structures are reversibly broken down in a quiescent state and the suspensions behaves as viscoelastic fluids with the zero-shear viscosity.     

Gravity-induced convective flow in microfluidic systems: electrochemical characterization and application to enzyme-linked immunosorbent assay tests

A way of using gravity flow to induce a linear convection within a microfluidic system is presented. It is shown and mathematically supported that tilting a 1 cm long covered microchannel is enough to generate flow rates up to 1000 nL.min(-1), which represents a linear velocity of 2.4 mm.s(-1). This paper also presents a method to monitor the microfluidic events occurring in a covered microchannel when a difference of pressure is applied to force a solution to flow in said covered microchannel, thanks to electrodes inserted in the microfluidic device. Gravity-induced flow monitored electrochemically is applied to the performance of a parallel-microchannel enzyme-linked immunosorbent assay (ELISA) of the thyroid-stimulating hormone (TSH) with electrochemical detection. A simple method for generating and monitoring fluid flows is described, which can, for instance, be used for controlling parallel assays in microsystems.     

Flow behaviors of a viscoelastic polymer solution at 3D micro pore-throat structure

Polymers are abundantly used in oil production industry, especially in enhanced oil recovery process. The underground oil reservoir is a kind of porous media where complex microscopic geometries lead to strong shearing and extensional components. This research focuses on a novel method used to investigate the flow behaviors of hydrolyzed polyacrylamide solution at a micro pore-throat structure with a comparison with Newtonian flow of water. For polymer solution, the flow velocimetry revealed the viscoelastic flow has two main characters compared with Newtonian fluid. First, the instability or non-linearity of polymer flows led to bending and distorted streamlines. The instability of the flow is mainly caused by the growth of high stress generated in the viscoelastic polymer fluid as it accelerates and decelerates into and out from the narrow throat, respectively speaking. The second character is the back-streams at the outlet of the throat.     

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.     

Self-organization in the flow of complex fluids (colloid and polymer systems). Part 2: Theoretical models

Flow induced transitions in complex fluids are usually accompanied by changes in the internal media structure and the flow symmetry. In this review paper, we discuss the theoretical models and approaches that have been used for the analysis of different types of flow instabilities and flow patterns. The main attention is focused on the basic fluid models which reveal vortex and banding flow structures at high shear rates. The Oldroyd-B fluid is one of such models. The Reynolds and the Weissenberg (or Deborah) numbers are the parameters governing its flow behavior. For this model, the secondary flow patterns arising in viscometric flows of different geometries at the bifurcation point are described. Complex fluids which are able to exist in multiple states can form coexisting bands of different structures with different rheological properties and flowing with different shear rates at the same shear stress. Shear banding is typical for fluids demonstrating non-monotonous flow curves described by such models as the diffusive Johnson-Segalman fluid model, for example. Recent progress in exploring this phenomenon is discussed.     

Residence time distribution for electrokinetic flow through a microchannel comprising a bundle of cylinders

The electrokinetic flow of an electrolyte solution through a microchannel that comprises a bundle of cylinders is investigated for the case of constant surface potential. The system under consideration is simulated by a unit cell model, and analytical expressions for the flow field and the corresponding residence time distribution under various conditions are derived. These results are readily applicable to the assessment of the performance of a microreactor such as that which comprises a bundle of optical fibers. Numerical simulations are conducted to investigate the influences of the key parameters, including the thickness of the double layer, the strength of the applied electric field, the magnitude of the applied pressure gradient, and the characteristic sizes of a microchannel, on the residence time distribution. We show that the following could result in a shorter residence time: thin double layer, strong applied electric field, large applied pressure gradient, and small number of cylinders. Based on the thickness of the double layer, criteria are proposed for whether the flow field can be treated as a laminar flow or as a plug flow, two basic limiting cases in reactor design.     

Flow of non‐newtonian fluids in porous media

The study of flow of non‐Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield‐stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non‐Newtonian fluids are generally classified into three main categories: time‐independent whose strain rate solely depends on the instantaneous stress, time‐dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article, the key aspects of these fluids are reviewed with particular emphasis on single‐phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore‐scale network modeling. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Oscillating laminar electrokinetic flow in infinitely extended rectangular microchannels

This paper has addressed analytically the problem of laminar flow in microchannels with rectangular cross-section subjected to a time-dependent sinusoidal pressure gradient and a sinusoidal electric field. The analytical solution has been determined based on the Debye-Hückel approximation of a low surface potential at the channel wall. We have demonstrated that Onsager's principle of reciprocity is valid for this problem. Parametric studies of streaming potential have shown the dependence of the electroviscous effect not only on the Debye length, but also on the oscillation frequency and the microchannel width. Parametric studies of electroosmosis demonstrate that the flow rate decreases due to an increase in frequency. The obtained solutions for both the streaming potential and electroosmotic flows become those for flow between two parallel plates in the limit of a large aspect ratio.     

Determination of the pressure coefficient and pressure effects in capillary flow

General expressions for determining the pressure coefficient and axial distribution of the viscosity and pressure in capillary flow are derived for Newtonian and shear-thinning fluids. The pressure-dependent viscosity model is obtained from the WLF equation as derived from Doolittle's free volume theory. The model has also been derived from Eyring's hole theory for viscosity. Poiseuille's equation is modified to correct for the pressure effect on viscosity. A Newtonian, low-molecular-weight polystyrene and a shear-thinning, high-molecular-weight polystyrene were tested in an Instron capillary rheometer. The axial velocity distribution was found to be negligibly affected by pressure whereas the viscosity was shown to increase markedly with a decrease in volume. The resulting pressure effects on the viscosity of both samples were analyzed by using the derived expressions.     

Multiphase microfluidics: from flow characteristics to chemical and materials synthesis

We review transport characteristics of pressure-driven, multiphase flows through microchannel networks tens of nanometres to several hundred of micrometres wide with emphasis on conditions resulting in enhanced mixing and reduced axial dispersion. Dimensionless scaling parameters useful in characterizing multiphase flows are summarized along with experimental flow visualization techniques. Static and dynamic stability considerations are also included along with methods for stabilizing multiphase flows through surface modifications. Observed gas-liquid and immiscible liquid-liquid flows are summarized in terms of flow regime diagrams and the different flows are related to applications in chemistry and materials synthesis. Means to completely separate multiphase flows on the microscale and guidelines for design of scalable multiphase systems are also discussed.     

Structural rationale of a non-Newtonian flow

The complex rheological behavior of structured systems, namely, suspensions, emulsions, polymer melts and solutions, micellar fluids, and liquid crystalline systems is analyzed. The behavior of such systems is characterized by the coexistence of different flow regimes in a wide range of shear rates. It is shown that the generalized flow equation (GFE) effectively describes plastic and pseudoplastic flow systems. The Newtonian and non-Newtonian behavior of structured flowable systems is explained within the structural microrheological model.