Effect of wall slip on the viscoelastic particle ordering in a microfluidic channel

The formation of a line of equally spaced particles at the centerline of a microchannel, referred as “particle ordering,” is desired in several microfluidic applications. Recent experiments and simulations highlighted the capability of viscoelastic fluids to form a row of particles characterized by a preferential spacing. When dealing with non-Newtonian fluids in microfluidics, the adherence condition of the liquid at the channel wall may be violated and the liquid can slip over the surface, possibly affecting the ordering efficiency. In this work, we investigate the effect of wall slip on the ordering of particles suspended in a viscoelastic liquid by numerical simulations. The dynamics of a triplet of particles in an infinite cylindrical channel is first addressed by solving the fluid and particle governing equations. The relative velocities computed for the three-particle system are used to predict the dynamics of a train of particles flowing in a long microchannel. The distributions of the interparticle spacing evaluated at different slip coefficients, linear particle concentrations, and distances from the channel inlet show that wall slip slows down the self-assembly mechanism. For strong slipping surfaces, no significant change of the initial microstructure is observed at low particle concentrations, whereas strings of particles in contact form at higher concentrations. The detrimental effect of wall slip on viscoelastic ordering suggests care when designing microdevices, especially in case of hydrophobic surfaces that may enhance the slipping phenomenon.     

Impedance‐based viscoelastic flow cytometry

Elastic nature of the viscoelastic fluids induces lateral migration of particles into a single streamline and can be used by microfluidic based flow cytometry devices. In this study, we investigated focusing efficiency of polyethylene oxide based viscoelastic solutions at varying ionic concentration to demonstrate their use in impedimetric particle characterization systems. Rheological properties of the viscoelastic fluid and particle focusing performance are not affected by ionic concentration. We investigated the viscoelastic focusing dynamics using polystyrene (PS) beads and human red blood cells (RBCs) suspended in the viscoelastic fluid. Elasto‐inertial focusing of PS beads was achieved with the combination of inertial and viscoelastic effects. RBCs were aligned along the channel centerline in parachute shape which yielded consistent impedimetric signals. We compared our impedance‐based microfluidic flow cytometry results for RBCs and PS beads by analyzing particle transit time and peak amplitude at varying viscoelastic focusing conditions obtained at different flow rates. We showed that single orientation, single train focusing of nonspherical RBCs can be achieved with polyethylene oxide based viscoelastic solution that has been shown to be a good candidate as a carrier fluid for impedance cytometry.     

Continuous separation of microparticles in a microfluidic channel via the elasto-inertial effect of non-Newtonian fluid

Pure separation and sorting of microparticles from complex fluids are essential for biochemical analyses and clinical diagnostics. However, conventional techniques require highly complex and expensive labeling processes for high purity separation. In this study, we present a simple and label-free method for separating microparticles with high purity using the elasto-inertial characteristic of a non-Newtonian fluid in microchannel flow. At the inlet, particle-containing sample flow was pushed toward the side walls by introducing sheath fluid from the center inlet. Particles of 1 μm and 5 μm in diameter, which were suspended in viscoelastic fluid, were successfully separated in the outlet channels: larger particles were notably focused on the centerline of the channel at the outlet, while smaller particles continued flowing along the side walls with minimal lateral migration towards the centerline. The same technique was further applied to separate platelets from diluted whole blood. Through cytometric analysis, we obtained a purity of collected platelets of close to 99.9%. Conclusively, our microparticle separation technique using elasto-inertial forces in non-Newtonian fluid is an effective method for separating and collecting microparticles on the basis of size differences with high purity.     

Lateral migration and focusing of colloidal particles and DNA molecules under viscoelastic flow

Much difficulty has been encountered in manipulating small-scale materials, such as submicron colloidal particles and macromolecules (e.g., DNA and proteins), in microfluidic devices since diffusion processes due to thermal (Brownian) motion become more pronounced with decreasing particle size. Here, we present a novel approach for the continuous focusing of such small-scale materials. First, we successfully focused fluorescent submicron polystyrene (PS) beads along equilibrium positions in microchannels through the addition of a small amount water-soluble polymer [500 ppm poly(ethylene oxide) (PEO)]. Lateral migration velocity significantly depends upon the viscoelastic effect (Weissenberg number: Wi) and the aspect ratio of particle size to channel height (a/h). Interestingly, focusing using viscoelastic flows was also observed for flexible DNA molecules (λ-DNA and T4-DNA), which have radii of gyration (R(g)) of approximately 0.69 μm and 1.5 μm, respectively. This small-scale material manipulation using medium viscoelasticity will contribute to the design of nanoparticle separation and genomic mapping devices.     

黏弹性聚合物溶液在突扩孔道内的流动特性

采用上随体Maxwell本构方程,描述油藏条件下以第一法向应力差为主要特征的聚合物溶液的流变性.利用有限体积法对黏弹性聚合物溶液在突扩孔道内的流动特征进行数值模拟.绘制了流函数和速度的等值线图.研究了黏弹性的变化对微观波及效率的影响.数值模拟结果表明,聚合物溶液的黏弹性是影响波及效率的主要因素.凹角处的流动区域随着弹性的增加在不断增大,因此滞留区域不断减小,微观波及效率不断增大.具有黏弹特性的聚合物溶液相比于纯黏性的牛顿流体更利于提高驱油效率.这一结论有助于驱油工业上聚合物溶液的设计和优选.     

Sheathless elasto-inertial particle focusing and continuous separation in a straight rectangular microchannel

Particle focusing in planar geometries is essentially required in order to develop cost-effective lab-on-a-chips, such as cell counting and point-of-care (POC) devices. In this study, a novel method for sheathless particle focusing, called "Elasto-Inertial Particle Focusing", was demonstrated in a straight microchannel. The particles were notably aligned along the centerline of the straight channel under a pressure-driven flow without any additional external force or apparatus after the addition of an elasticity enhancer: PEO (poly(ethylene oxide)) (～O(100) ppm). As theoretically predicted (elasticity number: El≈O(100)), multiple equilibrium positions (centerline and corners) were observed for the viscoelastic flow without inertia, whereas three-dimensional particle focusing only occurred when neither the elasticity nor the inertia was negligible. Therefore, the three-dimensional particle focusing mechanism was attributed to the synergetic combination of the elasticity and the inertia (elasticity number: El≈O(1-10)). Furthermore, from the size dependence of the elastic force upon particles, we demonstrated that a mixture of 5.9 and 2.4 μm particles was separated at the exit of the channel in viscoelastic flows. We expect that this method can contribute to develop the miniaturized flow cytometry and microdevices for cell and particle manipulation.     

Single line particle focusing induced by viscoelasticity of the suspending liquid: theory, experiments and simulations to design a micropipe flow-focuser

We perform 3D numerical simulations, heuristic modeling and microfluidic experiments to demonstrate, for the first time, the presence of a bistability scenario for transversal migration of particles suspended in a viscoelastic liquid flowing in a pipe. Our results show that particle migration, either at the centerline or at the wall, can be controlled by the rheological properties of the suspending liquid and by the relative dimensions of the particle and tube. Proper selection of these parameters can promote strict aligning of particles on a line, i.e., 3-D focusing. Simple design rules are given to rationally control particle focusing under flow in micropipes.     

Lateral and cross-lateral focusing of spherical particles in a square microchannel

The inertial migration of particles in micro-scale flows has received much attention due to its promising applications, such as the membrane-free passive separation of particles or cells. The particles suspended in rectangular channels are known to be focused near the center of each channel face as the channel Reynolds number (R(C)) increases due to the lift force balance and the hydrodynamic interactions of the particles with the wall. In this study, the three-dimensional positions of neutrally buoyant spherical particles inside a square microchannel are measured using the digital holographic microscopy technique, and a transition from the lateral tubular pinch to the cross-lateral focusing with increasing R(C) is reported. The particles are found to migrate first in the lateral direction and then cross-laterally toward the four equilibrium positions. A general criterion that can be used to secure the fully developed state of particle focusing in Lab-on-a-Chip applications is also derived. This criterion could be helpful for the accurate estimation of the design parameters of inertial microfluidic devices, such as R(C), channel length and width, and particle diameter.     

Magnitude and direction of thermal diffusion of colloidal particles measured by thermal field-flow fractionation

In this paper we provide experimental evidence showing that various types of submicrometer-sized particles (latexes, inorganic, and metallic), suspended in either aqueous or nonaqueous carrier liquids to which a temperature gradient dT/dx is applied, experience a force in the direction opposite to that of dT/dx. This behavior is similar to that of small particles such as soot, aerosols, and small bubbles suspended in stagnant gases across which temperature gradients are applied, a phenomenon known as "thermophoresis in gases." We report the use of a thermal field-flow fractionation (ThFFF) apparatus in two different configurations to establish the direction of particle motion subject to a temperature gradient. The first approach employed the conventional horizontal ThFFF channel orientation. In this case, small electrical potentials were applied across the narrow channel thickness either to augment or to act in opposition to the applied thermal gradient, depending on whether the accumulation wall was maintained at a positive or negative potential relative to the depletion wall. Thus, by observing the changes in the retention behavior of surface-charged latices or silica particles with changes in potential difference across the channel thickness, we were able to ascertain the direction of migration of the particles in the thermal gradient. The second approach involved the use of a ThFFF column oriented vertically in an implementation of a technique known as thermogravitational FFF. In this approach, the convective flow along the channel length (due to density gradients associated with the temperature gradient) couples with the thermal diffusion effect across the channel thickness to result in a combined particle retention mechanism. A retarded upward migration rate is indicative of accumulation of particles at the cold wall, while enhanced upward migration would indicate a hot-wall accumulation. From the results of our investigations, we conclude that submicrometer-sized particles suspended in either aqueous or nonaqueous carrier liquids and subjected to a temperature gradient migrate from the hot wall toward the cold wall of a ThFFF channel.     

Secondary-flow-aided single-train elastic-inertial focusing in low elasticity viscoelastic fluids

Elastic-inertial focusing has attracted increasing interest in recent years due to the three-dimensional (3D) single-train focusing ability it offers. However, multi-train focusing, instead of single-train focusing, was observed in viscoelastic fluids with low elasticity as a result of the competition between inertia effect and viscoelasticity effect. To address this issue, we employed the secondary flow to facilitate single-train elastic-inertial focusing in low elasticity viscoelastic fluids. A three-section contraction-expansion channel was designed to induce the secondary flow to pinch the multiplex focusing trains into a single one exactly at the channel centerline. After demonstrating the focusing process and mechanism in our device, we systematically explored and discussed the effects of particle diameter, operational flow rate, polymer concentration, and channel dimension on particle focusing performances. Our device enables single-train focusing of particles in viscoelastic fluids with low elasticity, and offers advantages of planar single-layer structure, and sheathless, external-field free operation.     

Simulation of Viscoelastic Fluid Flows in Expansion Geometry Using Finite Volume Approach简

The simulation results on viscoelastic fluid flows in sudden expansion geometry with different expansion ratios are presented. Oldroyd-B, linear Phan-Thien-Tanner （L-PTT） and Finitely Extensible Nonlinear Elastic （FENE-P） based constitutive equations were applied in two-dimensional Cartesian coordinates. The governing equations in transient and fully developed regions were solved using open source software called OpenFOAM. The flow patterns, including velocity profiles, shear stresses and first normal stress differences in some horizontal and vertical sections are illustrated. In addition, effects of the fluid type, flow dynamics and expansion ratio on the flow and vortex patterns in transient and fully developed regions are presented and discussed. The presented results show that existences of vortices cause the inverse velocity and negative stresses in expansion regions of the channel which increase with increment of expansion ratio and Weissenberg number （We）. Furthermore, some dead spaces can be observed at channel expansion regions close to the wall which are also increased. The results also show that at low We numbers all fluids show close behavior while at high We numbers the FENE-P fluid behavior shows high divergence from that of the two other fluids.     

Viscoelastic particle focusing in human biofluids

Saliva and blood plasma are non-Newtonian viscoelastic fluids that play essential roles in the transport of particulate matters (e.g., food and blood cells). However, whether the viscoelasticity of such biofluids alters the dynamics of suspended particles is still unknown. In this study, we report that under pressure-driven microflows of both human saliva and blood plasma, spherical particles laterally migrate and form a focused stream along the channel centerline by their viscoelastic properties. We observed that the particle focusing varied among samples on the basis of sampling times/donors, thereby demonstrating that the viscoelasticity of the human biofluids can be affected by their compositions. We showed that the particle focusing, observed in bovine submaxillary mucin solutions, intensified with the increase in mucin concentration. We expect that the findings from this study will contribute to the understanding of the physiological roles of viscoelasticity of human biofluids.     

Concentration‐controlled particle focusing in spiral elasto‐inertial microfluidic devices

Herein, we proposed a strategy for controlling the particle focusing position in Dean‐coupled elasto‐inertial flows via adjusting the polymer concentration of viscoelastic fluids. The physics behind the control strategy was then explored and discussed. At high polymer concentrations, the flowing particles could be single‐line focused exactly at the channel centerline under the dominated elastic force. The center‐line focusing in our spiral channel may employed as a potential pretreatment scheme for microflow cytometry detection. With further decreasing polymer concentrations, the particles would shift into the outer channel region under the comparable competition between inertial lift force, elastic force and Dean drag force. Finally, the observed position‐shifting was successfully employed for particle concentration at a throughput much higher than most existing elasto‐inertial microfluidics.     

Investigation of viscoelastic focusing of particles and cells in a zigzag microchannel

Microfluidic particle focusing has been a vital prerequisite step in sample preparation for downstream particle separation, counting, detection, or analysis, and has attracted broad applications in biomedical and chemical areas. Besides all the active and passive focusing methods in Newtonian fluids, particle focusing in viscoelastic fluids has been attracting increasing interest because of its advantages induced by intrinsic fluid property. However, to achieve a well-defined focusing position, there is a need to extend channel lengths when focusing micrometer-sized or sub-microsized particles, which would result in the size increase of the microfluidic devices. This work investigated the sheathless viscoelastic focusing of particles and cells in a zigzag microfluidic channel. Benefit from the zigzag structure of the channel, the channel length and the footprint of the device can be reduced without sacrificing the focusing performance. In this work, the viscoelastic focusing, including the focusing of 10 μm polystyrene particles, 5 μm polystyrene particles, 5 μm magnetic particles, white blood cells (WBCs), red blood cells (RBCs), and cancer cells, were all demonstrated. Moreover, magnetophoretic separation of magnetic and nonmagnetic particles after viscoelastic pre-focusing was shown. This focusing technique has the potential to be used in a range of biomedical applications.     

Inertial separation in a contraction-expansion array microchannel

We report a contraction-expansion array (CEA) microchannel that allows inertial size separation by a force balance between inertial lift and Dean drag forces in fluid regimes in which inertial fluid effects become significant. An abrupt change of the cross-sectional area of the channel curves fluid streams and produces a similar effect compared to Dean flows in a curved microchannel of constant cross-section, thereby inducing Dean drag forces acting on particles. In addition, the particles are influenced by inertial lift forces throughout the contraction regions. These two forces act in opposite directions each other throughout the CEA microchannel, and their force balancing determines whether the particles cross the channel, following Dean flows. Here we describe the physics and design of the CEA microfluidic device, and demonstrate complete separation of microparticles (polystyrene beads of 4 and 10 μm in diameter) and efficient exchange of the carrier medium while retaining 10 μm beads.     

A numerical study on viscoelastic droplet migration on a solid substrate due to wettability gradient

This study investigates the viscoelastic effects on droplet migration induced by a wettability gradient on a rigid substrate by a numerical simulation based on OpenFOAM with the volume‐of‐fluid method. The droplets are set with different rheological properties to investigate the effect of the elastic parameters. The Oldroyd‐B model was employed. Quantitative differences in the migration and deformation between Newtonian and viscoelastic droplets were investigated by changing the degree of elasticity. The droplet migration shows conspicuously higher mobility for high elasticity, especially during the accelerating period. Moreover, the displacement and velocity increased with the decrease of a viscoelasticity parameter, and the velocity enhancement was regulated by the elastic instability shown at a high Weissenberg number. In addition, the velocity of the droplet changes more significantly over the range of contact angles of 130° to 60° compared to other wettability‐gradient surfaces.     

Dissipative particle dynamics simulation of depletion layer and polymer migration in micro- and nanochannels for dilute polymer solutions

The flows of dilute polymer solutions in micro- and nanoscale channels are of both fundamental and practical importance in variety of applications in which the channel gap is of the same order as the size of the suspended particles or macromolecules. In such systems depletion layers are observed near solid-fluid interfaces, even in equilibrium, and the imposition of flow results in further cross-stream migration of the particles. In this work we employ dissipative particle dynamics to study depletion and migration in dilute polymer solutions in channels several times larger than the radius of gyration (Rg) of bead-spring chains. We compare depletion layers for different chain models and levels of chain representation, solvent quality, and relative wall-solvent-polymer interactions. By suitable scaling the simulated depletion layers compare well with the asymptotic lattice theory solution of depletion near a repulsive wall. In Poiseuille flow, polymer migration across the streamlines increases with the Peclet and the Reynolds number until the center-of-mass distribution develops two symmetric off-center peaks which identify the preferred chain positions across the channel. These appear to be governed by the balance of wall-chain repulsive interactions and an off-center driving force of the type known as the Segre-Silberberg effect.     

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.     

Efficient microfluidic enrichment of nano-/submicroparticle in viscoelastic fluid

The enrichment and focusing of the nano-/submicroparticle (e.g., 150–1000 nm microvesicle shed from the plasma membrane) in the viscoelastic fluid has great potentials in the biomedical and clinical applications such as the disease diagnosis and the prognostic test for liquid biopsy. However, due to the small size and the resulting weak hydrodynamic force, the efficient manipulation of the nano-/submicroparticle by the passive viscoelastic microfluidic technology remains a major challenge. For instance, a typically long channel length is often required to achieve the focusing or the separation of the nano-/submicroparticle, which makes it difficult to be integrated in small chip area. In this work, a microchannel with gradually contracted cross-section and high aspect ratio (the ratio of the height to the average width of channel) is utilized to enhance the hydrodynamic force and change the force direction, eventually leading to the efficient enrichment of nano-/submicroparticles (500 and 860 nm) in a short channel length (2 cm). The influence of the flow rate, the particle size, the solid concentration, and the channel geometry on the enrichment of the nano-/submicroparticles are investigated. With simple structure, small footprint, easy operation, and good performance, the present device would be a promising platform for various lab-chip microvesicle-related biomedical research and disease diagnosis.     

Predictive/fitting capabilities of differential constitutive models for polymer melts—reduction of nonlinear parameters in the eXtended Pom-Pom model

A phenomenological modification of the eXtended Pom-Pom (XPP) model is proposed with the aim to reduce the number of free nonlinear parameters. The modified XPP model includes three parameters per mode in total (two linear viscoelastic parameters—linear relaxation time λ and shear modulus G, and one nonlinear parameter). The original XPP model contains five parameters (two linear viscoelastic parameters and three nonlinear ones, one nonlinear parameter participates in the second normal stress difference prediction). The predictive/fitting capabilities of the modified model are compared with the Giesekus, eXtended Pom-Pom, and modified Leonov models using various low-density PE materials in steady and transient shear and uniaxial elongational flows. It has been found that the modified model is capable of predicting/fitting the rheological properties, with the exception of the second normal stress difference, for studied LDPE materials with sufficient accuracy, including strain hardening in uniaxial elongational flow.