Lateral migration of particles suspended in viscoelastic fluids in a microchannel flow

In this work, we investigated the lateral migration of microparticles suspended in two different viscoelastic fluids with or without the second normal stress difference. For the viscoelastic fluid without the second normal stress difference, competing forces existed between microfluidic inertia and the first normal stress difference (N ₁), which resulted in a synergetic effect of particle focusing. For the fluid with the second normal stress difference (N ₂), particles were greatly affected by a N ₂-induced secondary flow, and the competition among the inertia, N ₁, and N ₂ determined the lateral migration trajectories of the particles. The obtained results were delineated with the blockage ratio, which showed good agreement with the results of a recent numerical study (Villone et al. in J Non Newton Fluid Mech 195:1–8, 2013). The present study also examined the possibility of particle separation in a size-dependent manner using the N ₂-induced secondary flow in microchannel flow.     

Analysis of electroosmotic flow in a microchannel packed with microspheres

The electroosmotic flow in a microchannel packed with microspheres under both direct and alternating electric fields is analyzed. In the case of the steady DC electroosmosis in a packed microchannel, the so-called capillary model is used, in which it is assumed that a porous medium is equivalent to a series of intertwined tubules. The interstitial tubular velocity is obtained by analytically solving the Navier–Stokes equation and the complete Poisson–Boltzmann equation. Then, using the volume-averaging method, the solution for the electroosmotic flow in a single charged cylindrical tubule is applied to estimate the electroosmosis in the overall porous media by introducing the porosity and tortuosity. Assuming uniform porosity, an exact solution accounting for the electrokinetic wall effect is obtained by solving the modified Brinkman momentum equation. For the electroosmotic flow under alternating electric fields in a cylindrical microchannel packed with microspheres of uniform size, two different conditions regarding the openness of the channel ends are considered. Based on the capillary model, the time-periodic oscillating electroosmotic flow in an open-ended microchannel in response to the application of an alternating electric field is obtained using the Greens function approach to the Navier–Stokes equation. When the two ends of the channel are closed, a backpressure is induced to generate a counter flow, resulting in a new zero flow rate. Such induced backpressure associated with the counter flow in a closed-end microchannel is obtained analytically by solving the transient modified Brinkman momentum equation.     

Efficient mixing of viscoelastic fluids in a microchannel at low Reynolds number

In this paper, we examined mixing of various two-fluid flows in a silicon/glass microchannel based on the competition of dominant forces in a flow field, namely viscous/elastic, viscous/viscous and viscous/inertial. Experiments were performed over a range of Deborah and Reynolds numbers (0.36 < De < 278, 0.005 < Re < 24.2). Fluorescent dye and microshperes were used to characterize the flow kinematics. Employing abrupt convergent/divergent channel geometry, we achieved efficient mixing of two-dissimilar viscoelastic fluids at very low Reynolds number. Enhanced mixing was achieved through elastically induced flow instability at negligible diffusion and inertial effects (i.e. enormous Peclet and Elasticity numbers). This viscoelastic mixing was achieved over a short effective mixing length and relatively fast flow velocities.     

Transient electroosmotic slip flow of fractional Oldroyd-B fluids

The electroosmotic flow of a fractional Oldroyd-B fluid in a circular microchannel is studied. The linear Navier slip velocity model is used as the chosen slip boundary condition. Exact solutions for the electric potential and transient velocity are established by means of Laplace and finite Hankel transforms. And the velocity was presented as a sum of the steady part and the unsteady one. The corresponding solutions for the fractional Maxwell fluid, fractional second grade fluid, and Newtonian fluid can also be obtained from our results. Finally, numerical results for the fluid flow are obtained and some useful conclusions are drawn. Our results may be useful for the prediction of the flow behavior of viscoelastic fluids in microchannels and can benefit the design of microfluidic devices.     

PIV measurements of flow within plugs in a microchannel

The use of two-phase flow in lab-on-chip devices, where chemical and biological reagents are enclosed within plugs separated from each other by an immiscible fluid, offers significant advantages for the development of devices with high throughput of individual heterogeneous samples. Lab-on-chip devices designed to perform the polymerase chain reaction (PCR) are a prime example of such developments. The internal circulation within the plugs used to transport the reagents affects the efficiency of the chemical reaction within the plug, due to the degree of mixing induced on the reagents by the flow regime. It has been hypothesised in the literature that all plug flows produce internal circulation. This work demonstrates experimentally that this is false. The particle image velocimetry (PIV) technique offers a powerful non-intrusive tool to study such flow fields. This paper presents micro-PIV experiments carried out to study the internal circulation of aqueous plugs in two phase flow within 762 μm internal diameter FEP Teflon tubing with FC-40 as the segmenting fluid. Experiments have been performed and the results are presented for plugs ranging in length from 1 to 13 mm with a bulk mean flow velocity ranging from 0.3 to 50 mm/s. The results demonstrate for the first time that circulation within the plugs is not always present and requires fluidic design considerations to ensure their generation.     

Hydrodynamic dispersion in long microchannels under conditions of electroosmotic circulation: II. Electrolytes

This work describes the steady-state transport of an electrolyte due to a stationary concentration difference in straight long channels under conditions of electroosmotic circulation. The electroosmotic flow is induced due to the slip produced at the charged channel walls. This flow is assumed to be compensated by a pressure-driven counterflow so that the net volume flow through the channel is exactly zero. Owing to the concentration dependence of electroosmotic slip, there is an involved coupling between the solute transfer, hydrodynamic flow and charge conservation. Nevertheless, for such a system the Taylor–Aris dispersion (TAD) theory is shown to be approximately applicable locally within an inner part of the channel for a wide range of Péclet numbers (Pe) irrespective of the concentration difference. Numerical simulations reveal only small deviations from analytical solutions for the inner part of the channel. The breakdown of TAD theory occurs within boundary regions near the channel ends and is related to the variation of the dispersion mechanism from the purely molecular diffusion at the channel ends to the hydrodynamic dispersion within the inner part of the channel. This boundary region is larger at the lower-concentration channel edge and its size increases nearly linearly with Pe number. It is possible to derive a simple analytical approximation for the inner profile of cross-section-averaged electrolyte concentration in terms of only few parameters, determined numerically. Such analytical approximations can be useful for experimental studies of concentration polarization phenomena in long microchannels.     

Suppression of electroosmotic flow by polyampholyte brush

Molecular dynamics simulations are conducted to investigate the suppression of electroosmotic flow by grafting polyampholyte brushes onto two parallel channel walls. The effects of grafting density and charge distribution of polyampholyte brushes on the electroosmotic flow velocity, salt ion distribution, and conformational characteristics of grafted brushes are studied in detail. Simulation results indicate that increasing the grafting density induces a stronger suppression of electroosmotic flow. The flow velocity is significantly influenced by the different charge distributions of polyampholyte brushes. In addition, an important flow phenomenon we have found is that the flow velocity profile shows a valley at the center of the channel. These results reveal that the flow velocity is dependent not only on the conformation of the polyampholyte brushes but also on the anion and cation distributions. The hierarchical distribution of salt ions is caused by the special properties of polyampholyte brushes.     

AC electroosmotic flow in a DNA concentrator

Experimental velocity measurements are conducted in an AC electrokinetic DNA concentrator. The DNA concentrator is based upon Wong et al. (Transducers 2003, Boston, pp 20–23, 2003a; Anal Chem 76(23):6908–6914, 2004)and consists of two concentric electrodes that generate AC electroosmotic flow to stir the fluid, and dielectrophoretic and electrophoretic force fields that trap DNA near the centre of the inside electrode. A two-colour micro-PIV technique is used to measure the fluid velocity without a priori knowledge of the electric field in the device or the electrical properties of the particles. The device is also simulated computationally. The results indicate that the numerical simulations agree with experimental data in predicting the velocity field structure, except that the velocity scale is an order of magnitude higher for the simulations. Simulation of the dielectrophoretic forces allows the motion of the DNA within the device to be studied. It is suggested that the simulations can be used to study the phenomena occurring in the device, but that experimental data is required to determine the practical conditions under which these phenomena occur.     

Blood flow driven by surface tension in a microchannel

This study aims to identify distinct blood flow characteristics in a microchannel at different sloping angles. The channel is determined by a bottom hydrophilic stripe on a glass substrate and a fully covered hydrophobic glass substrate. The channel has a height of 3 μm, and a width of 100 μm. It is observed that increasing the sloping angle from −90° (downward flow) to 90° (upward flow) increases the blood flow rate monotonically. These peculiar behaviors on the micro scale are explained by a dynamic model that establishes the balance among the inertial, surface tension, gravitational, and frictional forces. The frictional force is further related to the effective hematocrit. The model is used to calculate the frictional force, and thus the corresponding hematocrit, which is smaller when the blood flows upward, reducing the frictional force.     

Broadening of neutral analyte band in electroosmotic flow through slit channel with different zeta potentials of the walls

The study is concerned with addressing hydrodynamic dispersion of an electroneutral non-adsorbed solute being transported by electroosmotic flow through a slit channel formed by walls with different zeta potentials. The analysis is conducted in terms of the plate height which, using the Van Deemter equation, can be expressed through the cross-sectional mean flow velocity, the solute molecular diffusion coefficient and a length scale parameter having meaning of the minimum achievable plate height and depending on the velocity distribution within the channel cross-section. The minimum plate height is determined by substituting distribution of electroosmotic velocity into the preliminary derived integral expression that is valid for any given velocity distribution within a slit channel cross-section. The electroosmotic velocity distribution within the slit channel cross-section is obtained by solving one-dimensional version of the Stokes equation accounting for electric force exerted on the local equilibrium electric space charge. The major obtained result is an analytical expression which represents the minimum plate height normalized by half of channel width as a function of two dimensionless parameters, namely, half of channel width normalized by the Debye length, and the ratio of the wall zeta potentials. The obtained result reveals a substantial increase in the minimum plate height compared with the case of equal wall zeta potentials. Different limiting cases of the obtained relationships are analyzed and possible applications are discussed.     

Liquid flow through a diverging microchannel

In this work, experiments and three-dimensional numerical calculations of fluid flow through diverging microchannels were carried out with the aim of bringing out differences between flow in uniform and nonuniform passages. Deionized water was used as the working fluid in the experiments where the effects of mass flow rate (8.33 × 10^?6 to 8.33 × 10^?5 kg/s), microchannel hydraulic diameter (118–177 µm), length (10–30 mm) and divergence angle (4°–16°) on pressure drop were studied. The results are analyzed in detail with the help of numerical data. The pressure drop exhibits a linear dependence on the mass flow rate, whereas it is inversely proportional to the divergence angle and square of the hydraulic diameter. The pressure drop increases anomalously at 16°, suggesting that flow reversal occurs between 12° and 16°, which agrees with the corresponding value at the conventional scale. For the purpose of predicting pressure drop using straight microchannel theory, an equivalent hydraulic diameter was defined. It is observed that the equivalent hydraulic diameter, located at one-third of the diverging microchannel length from the inlet, becomes mostly independent of the mass flow rate, microchannel hydraulic diameter, length and divergence angle. The pressure drop for a diverging microchannel becomes equal to an equivalent hydraulic diameter uniform cross-section microchannel, suggesting that conventional correlations for straight microchannels can also be applied to diverging microchannels. The data presented in this work are of fundamental importance and can help in optimization of diffuser design used for example in valveless micropumps.     

Dynamic aspects of electroosmotic flow

This article presents an analysis of the frequency and time dependent electroosmotic flow in open-end and closed-end microchannels of arbitrary cross-section shape. In the numerical model, the modified Navier–Stokes equation governing the AC electroosmotic flow is solved using the control volume method. The iterative approach is used to determine the induced backpressure gradient. The potential distribution of the EDL in the channel is obtained by solving the non-linear 2D Poisson–Blotzmann equation. The comparison between the control volume formulation and the Green’s function method for the case of a rectangular microchannel shows a good agreement. The time evolution of the electroosmotic flow and the effect of a frequency-dependent AC electric field on the oscillating electroosmotic flow are also examined. The effect of the induced backpressure gradient with the frequency of the applied electric field is also shown.     

Improved particle concentration by cascade AC electroosmotic flow

The importance of electrokinetics in microfluidic technology has been growing owing to its versatility and simplicity in fabrication, implementation, and handling. Alternating-current electroosmosis (ACEO), which is the motion of fluid due to the ion movement by an interaction between AC electric field and an electrical double layer on the electrode surface, has a potential for a particle concentration method to detecti rare samples flowing in a microchannel. This study investigates an improved ACEO-based particle concentration by cascade electrokinetic approach. Flow field induced by ACEO and accumulation behavior of particles were parametrically measured to discuss the concentrating mechanism. The accumulation of particles by ACEO can be explained by a balance between the attenuating electroosmotic flow to transport particles and the inherent diffusive motion of the particles, which is hindered due to the near-wall location. Although a parallel double-gap electrode geometry enables particles to be collected at the center of electrode very sharply, it has scattering zones with accumulated particles at sidewalls of the channel. This drawback can be overcome by applying sheath flow or introducing cascade electrode pattern upstream of the focusing zone. As a result, total concentration efficiency was 98.4 % for all the particles flowing in the cascade device. The resultant concentrated particles exist on the electrode surface within 5 μm, and three-dimensional concentration of particle with the concentration factor as large as 700 is possible using a monolithic channel, co-planar electrode, and sheathless solution feeding. This cascade electrokinetic method provides a new and effective preconcentrator for ultra-sensitive detection of rare samples.     

Controlling electroosmotic flow by polymer coating: a dissipative particle dynamics study

We have performed dissipative particle dynamics (DPDs) simulations of electroosmotic flow (EOF) through a polymer-grafted nanopore. In this model, charged particles including salt ions and counterions are not included explicitly, and EOF is created using an effective boundary condition. The screening effect of polymer layer on EOF is investigated in detail under different solvent qualities and boundary electroosmotic velocities. Results show that the solvent quality has a significant effect on the conformational properties of polymer chains and the flow characteristics of the solvent. The polymer layer undergoes a collapsed transition when decreasing the solvent quality from good to poor. Under different solvent qualities, enhancing the EOF leads to a different variation tendency of the layer thickness. The solvent-induced permeability change is inconsistent with the steady velocity away from the surface. The minimum value of the solvent permeability occurs at an intermediate solvent quality. However, the layer thickness drops gradually to a smallest value (corresponding to the largest effective pore radius) in the poor solvent condition. It is also found that the polymer inclination and stretching length exhibit a complex behavior under the combined effect of solvent quality and electroosmosis-induced shear.     

Effects of applied electric field and microchannel wetted perimeter on electroosmotic velocity

Parameters which affect electroosmotic flow (EOF) behavior need to be determined for characterizing flow in miniature biological and chemical experimental processes. Several parameters like buffer pH, ionic concentration, applied electric field and channel dimensions influence the magnitude of the electroosmotic flow. We conducted numerical and experimental investigations to determine the impact of electric field strength and wetted microchannel perimeter on EOF in straight microchannels of rectangular cross-section. Deviation from theoretical behavior was also investigated. In the numerical model, we solved the continuity and Navier–Stokes equations for the fluid flow and the Gauss law equation for the electric field. Computational results were validated against experimental data for PDMS-glass channels of different wetted perimeters over a range of applied electric fields. Results show that increasing the applied electric field at constant wetted perimeter caused the electroosmotic mobility, the ratio of electroosmotic velocity to applied electric field, to increase nonlinearly. It was also found that increasing the wetted perimeter at constant applied electric field decreased the electroosmotic flow. These findings will be useful in determining the optimum value of the electric field required to produce a desired electroosmotic flow rate in a channel of a particular dimension. Alternately, these will also be useful in determining the optimum channel dimensions to provide a desired electroosmotic flow rate at a specified value of the electric field.     

Electrokinetic power generation of non-Newtonian fluids in a finite length microchannel

In order to examine the effects of the fluid type as the electrolyte solvent on the efficiency of electrokinetic energy conversion, a comparative numerical study among three different fluid types of a transient electrokinetic flow through a single circular finite length microchannel has been conducted. The system was initially at an equilibrium non-flow state, and a step change in flow was applied and the calculation proceeding until steady state was achieved. The analysis was based on non-dimensional transport governing equations that were scaled using Debye length as the characteristic length scale and diffusion time as characteristic time scale. The fluid types considered were shear thinning, Newtonian, and shear thickening, and a power law modeled them with the scaled flow behavior index having values of 0.2, 1.0, and 1.8. In order to isolate the electrokinetic effects of the different relationships between the shear strain rate and shear stress, the flow consistency index was adjusted so that in all the cases the flow rate and total pressure drop matched that of water at 25 °C. All other fluid and interfacial properties were the same for all cases. The key observational difference between the various fluid types was that their different axial velocity profile acted on essential the same free charge density profiles. Consequently, the convection current density (i.e., the radial distribution of charge being advected along the channel) was strongly affected by the fluid type. Integration of this quantity to calculate the convection current showed that for the particular fluid properties chosen the shear thinning fluid was 20 % higher than the Newtonian fluid, while the shear thickening fluid was only 4 % lower than the Newtonian fluid. Combined with the effects, these different currents have on the streaming potential, the shear thinning fluid was 50 % more effective in converting flow work to electrical work than the Newtonian fluid, while the shear thickening fluid was only 16 % lower than the Newtonian fluid.     

Electrokinetic and aspect ratio effects on secondary flow of viscoelastic fluids in rectangular microchannels

The secondary flow of PTT fluids in rectangular cross-sectional plane of microchannels under combined effects of electroosmotic and pressure driving forces is the subject of the present study. Employing second-order central finite difference method in a very refined grid network, we investigate the effect of electrokinetic and geometric parameters on the pattern, strength and the average of the secondary flow. In this regard, we try to illustrate the deformations of recirculating vortices due to change in the dimensionless Debye–Hückel and zeta potential parameters as well as channel aspect ratio. We demonstrate that, in the presence of thick electric double layers, significant alteration occurs in the secondary flow pattern by transition from favorable to adverse pressure gradients. Moreover, it is found that for polymer-electrolyte solutions with large Debye lengths, the secondary flow pattern and the shape of vortices are generally dependent upon the width-to-height ratio of the channel cross section. Also, the inspections of strength and average of secondary flow reveal that the sensitivity of these quantities with respect to the electrokinetic, geometric and rheological parameters increases by increasing the absolute value of velocity scale ratio. In this regard, utilizing the curve fitting of the results, several empirical expressions are presented for the strength and average of the secondary flow under various parametric conditions. The obtained relations with the other predictions for secondary flow are of high practical importance when dealing with the design of microfluidic devices that manipulate viscoelastic fluids.     

Mixing and flow regulating by induced-charge electrokinetic flow in a microchannel with a pair of conducting triangle hurdles

The induced-charge electrokinetic flow (ICEKF) in a rectangular micorchannel with a pair of conducting triangle hurdles embedded in the middle is investigated in this paper. A correction method is suggested to numerically estimate the induced zeta potential on the conducting surface. Two-dimensional pressure-linked Navier-–Stokes equation is used to model the flow field in the channel. The numerical results show flow circulations generated from the induced non-uniform zeta potential distribution along the conducting hurdle surfaces. It is demonstrated numerically that the local flow circulations provide effective means to enhance the flow mixing between different solutions; by adjusting the electric field applied through the microchannel with a non-symmetric triangle hurdle pair, an electrokinetic flow regulating effect can be obtained and this effect depends on the dimensions of the conducting converging–diverging section. The mixing and flow regulating using ICEKF described in this paper can be used in various microfluidics and lab-on-a-chip (LOC) applications.     

Rheometry of non-Newtonian electrokinetic flow in a microchannel T-junction

Two-dimensional finite element simulations of electrokinetic flow in a microchannel T-junction of a fluid with a Carreau-type nonlinear viscosity are presented. The motion of the electrical double layer at the channel walls is approximated by velocity wall slip boundary conditions. The fluid experiences a range of shear rates as it turns the corner, and the flow field is shown to be sensitive to the non-Newtonian characteristics of the Carreau model. A one-to-one mapping between the Carreau parameters and the end wall pressure is demonstrated through statistical analysis of the pressure profile for a broad range of physical and operating parameters. Such a mapping allows the determination of the Carreau parameters of an unknown fluid if the end wall pressure profile is known; thus a highly efficient viscometric device may be constructed. A graphical technique to show that the inverse problem is well posed is shown, and a method for solving the inverse problem is presented. The challenges that must be overcome before a practical device can be constructed are discussed.