Viscoelastic Polymer Solutions Research Articles

Phase Diagram of Pinch-off Behaviors During Drop-on-Demand Inkjetting of Alginate Solutions

Viscoelastic polymer solutions have been extensively utilized in inkjet printing for a variety of biomedical applications. The pinch-off of viscoelastic jets is a key step toward the generation of droplets in inkjet printing. This complex process is governed by the interplay of four stresses, including inertial stress, capillary stress, viscous stress, and elastic stress. Depending on polymer solution properties and process conditions, four types of pinch-off phenomenon were observed during inkjetting of viscoelastic alginate solutions. In this study, material properties of alginate solutions with different concentrations have been characterized, and three dimensionless numbers (Ohnesorge number Oh, Deborah number De, and Weber number We) have been proposed to analyze different pinch-off behaviors. The phase diagram in terms of these three dimensionless numbers has been constructed to classify the regimes for different pinch-off types during inkjetting of viscoelastic alginate solutions. It is found that (1) at low De and Oh, the capillary stress is mainly balanced by the inertial stress, resulting in front pinching. (2) At medium De and low Oh, with the increase of We, the pinch-off type may change from front pinching to hybrid pinching to exit pinching. (3) At low Oh and high De, the capillary stress is mainly balanced by the elastic stress, resulting in exit pinching. (4) At high Oh and De, the viscoelastic effect is dominant. With the increase of We, middle pinching turns to be exit pinching due to the increase in the initial ligament diameter near the forming droplet.

Nanoparticle dispersion in porous media in viscoelastic polymer solutions

Flow of viscoelastic fluids in porous media is ubiquitous in biological and industrial processes, and the choice of viscoelastic fluids is of foremost importance for their effect on macroscopic flow and transport properties. In this paper we study the macroscopic properties of flow and transport of viscoelastic fluids through a model porous media by means of Direct Numerical Simulation (DNS). We show that flow of a viscoelastic fluid modeled via a FENE-P constitutive model features three distinct regimes of flow resistance: a plateau at low Deborah numbers, and a shear-thinning phase followed by an abrupt flow thickening above a critical Deborah number, consistent with experimental observations. Congruous to this shear-thickening, we observe the onset of hydrodynamic instabilities resulting in fluctuations in pressure drop and flow resistance. These fluctuations intensify with increasing the fluid elasticity. Finally, we investigate Lagrangian attributes of viscoelastic flow and transport through porous media. We find that although the fluid elasticity broadens the Lagrangian velocity distributions, it does not alter the long-term particle dispersion in disordered porous media.

FEATURES OF POLYMER SOLUTION FLOW IN THE POROUS-FRACTURED RESERVOIR

This article presents the results of numerical flow simulation of simple and viscoelastic (polymer solution) fluids through a crack by using polymer solutions for enhanced oil recovery from the reservoir. The determined regularities of viscoelastic (polymer solution) liquid behavior with longitudinal velocity gradient and manifested in this case elastic deformations effects have a decisive meaning in the understanding of the mechanism "anomalously" high oil recovery ability from the reservoir by using water-polymer flooding of the porous-fractured reservoir. Understanding the nature of increased oil recovery with the use of polymer solutions will lead to the development of recommendations on the choice of regimes of water-polymer flooding of the porous-fractured reservoir.

Continuous erythrocyte removal and leukocyte separation from whole blood based on viscoelastic cell focusing and the margination phenomenon

The removal of erythrocytes from whole blood is an essential step during sample preparations intended for biomedical analyses and clinical diagnoses. To address the limitations of present methods, such as centrifugation and chemical lysis, we propose a novel microfluidic device for erythrocyte removal with high-efficiency and leukocyte separation from bulk flows of highly concentrated erythrocytes using a viscoelastic non-Newtonian fluid. The proposed device is designed based on the principle of viscoelasticity-induced particle migration toward the center of the microchannel. In addition, we based the functionality of our device on a bio-inspired phenomenon known as margination according to which erythrocytes migrate to the axial center of blood vessels. Fluorescent particles (10 μm) were added to blood suspensions of various concentrations (hematocrit) of erythrocytes in viscoelastic polymer solutions. Optimal hematocrit and flow rate conditions were determined for erythrocyte removal and for the separation of 10 μm particles. We also demonstrated the capability of our device to separate leukocytes with high efficiency (˜94%) and with a high-enrichment factor (10-fold).

Fluid Viscoelasticity Drives Self-Assembly of Particle Trains in a Straight Microfluidic Channel

Hop on board: The authors present experimental evidence of particle trains in viscoelastic polymer solutions. It turns out that such lines of particles in viscoelastic liquids are easy to produce, prompting future applications in biomedical engineering and materials science---for example, in optimized flow cytometry, deterministic cell encapsulation and microfluidic fabrication of materials with enhanced localized properties. Also, the simple setup here can be coupled with other microfluidic techniques, to clarify the hydrodynamic interactions between particles.

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.

“Phase diagram” for viscoelastic Poiseuille flow over a wavy surface

We experimentally examine the Poiseuille flow of viscoelastic fluids over wavy surfaces. Five precision microfabricated flow channels are utilized, each of depth 2d = 400 μm, spanwise width w = 10d and with a sinusoidal undulation of amplitude A = d/20 on one of the spanwise walls. The undulation wavelength λ is varied between each of the channels, providing dimensionless channel depths α in the range 0.2π ≤ α = 2πd/λ ≤ 3.2π. Nine viscoelastic polymer solutions are formulated, spanning more than four orders in elasticity number El and are tested in the wavy channels over a wide range of Reynolds and Weissenberg numbers. Flow velocimetry is used to observe and measure the resulting flow patterns. Perturbations to the Poiseuille base flow caused by the wavy surfaces are quantified by the depth of their penetration P into the flow domain. Consistent with theoretical predictions made for wavy plane-Couette flow [J. Page and T. A. Zaki, “Viscoelastic shear flow over a wavy surface,” J. Fluid Mech. 801, 392–429 (2016)], we observe three distinct flow regimes (“shallow elastic,” “deep elastic” and “transcritical”) that can be assembled into a “phase diagram” spanned by two dimensionless parameters: α and the depth of the theoretically predicted critical layer Σ∼El. Our results provide the first experimental verification of this phase diagram and thus constitute strong evidence for the existence of the predicted critical layer. In the inertio-elastic transcritical regime, a surprising amplification of the perturbation occurs at the critical layer, strongly influencing P. These effects are of likely importance in widespread inertio-elastic flows in pipes and channels, such as in polymer turbulent drag reduction.

Numerical Simulations of Viscoelastic Fluid Flows Past a Transverse Slot Using Least-Squares Finite Element Methods

This paper presents a least-squares (LS) finite element method for linear Phan-Thien–Tanner (PTT) viscoelastic fluid flows. We consider stabilized weights in the LS method for the viscoelastic model and prove that the LS approximation converges to the linearized solutions of the linear PTT model; the convergence is at the optimal rate for the velocity in the $$H^{1}$$ -norm and at suboptimal rates for the stress and pressure in the $$L^{2}$$ -norm, respectively. For numerical experiments we first consider the flow through a planar channel to illustrate our theoretical results. The LS method is then applied to a flow through the slot channel with two depth ratios and the effects of physical parameters are discussed. Numerical solutions of the channel problem indicate that flow characteristics of the viscoelastic polymer solution are described by the results obtained using the method. Furthermore, we present the hole pressure for various Weissenberg numbers, and compare with that derived from the Higashitani–Pritchard (HP) theory.

Turbulent mixing of concentrated viscoelastic polymer solution: Influence of submerged sparge shape and orientation

Aqueous solutions (∼0.01–0.2%) of long chain polymers are used during gravity thickening to aggregate particle suspensions. These polymers are often dosed into turbulent flow through submerged pipes (sparges) to maximise their distribution. At high concentrations, these viscoelastic solutions mix poorly with surrounding flows unless highly diluted. If varying the bluff body sparge shape can enhance mixing, such dilution may be avoided.Turbulent mixing of concentrated (0.2%) polymer solutions sparged into turbulent flows within a transparent channel was captured using high-speed imaging to understand the complex mixing phenomena. Square and round sparges were investigated at 0 or 180° to the channel flow. At 0°, vortex shedding from square sparge edges enhanced mixing, but the 180° orientation produced better overall mixing. Image analysis gave the first quantification of flow past bluff bodies issuing viscoelastic fluid jets at industrial flow regimes, from which more appropriate turbulence model closures for fluid dynamics modelling of the process may be derived.

Sphere sedimentation in wormlike micelles: Effect of micellar relaxation spectrum and gradients in micellar extensions

We report experiments on the flow of wormlike micellar solutions based on cetylpyridinium chloride/sodium salicylate past a falling sphere via a combination of particle tracking velocimetry, particle image velocimetry, rheology, and flow induced birefringence (FIB). Recent studies have shown that beyond a critical extensional Deborah number, a falling sphere in wormlike micelles never reaches a constant terminal velocity; instead, it settles with an unsteady velocity. This behavior is linked to the wormlike micellar chain scission in the wake of the sphere. Similar instabilities in viscoelastic polymer solutions, where polymer chain scission is highly unlikely, are thought to be the results of a single-mode relaxation spectrum of the polymer chains or the asymmetry in the polymer chain extensions on the flanks of the falling sphere. In this paper, we examine the effect of micellar relaxation spectrum and gradients in micellar extensions on sphere instability in wormlike micelles over a wide range of flow parameters (10−2 < DeE < 40.7 and 10−6 < Re < 10). In wormlike micelles with a single-mode relaxation spectrum, the sphere instability occurs for DeE ≥ 2.6. However, for similar conditions (2.5 ≤ DeE ≤ 40.7 and 10−2 < Re < 10), spheres never exhibit unsteady motion in the wormlike micelles with a broad spectrum of relaxation times. This indicates the importance of the micellar relaxation spectrum on dynamics of sphere sedimentation in wormlike micelles. We show that a criterion based on the ratio of dissipated energy to the stored elastic energy of micelles can successfully describe the effect of micellar relaxation spectrum on sphere sedimentation dynamics. In addition, for conditions that give rise to sphere instability, FIB indicates that micellar extensions on sphere sideways are perfectly symmetric.

Wall slip of complex fluids: Interfacial friction versus slip length

Using a dynamic Surface Force Apparatus, we demonstrate that the notion of slip length used to describe the boundary flow of simple liquids, is not appropriate for viscoelastic liquids. Rather, the appropriate description lies in the original Navier's partial slip boundary condition, formulated in terms of an interfacial friction coefficient. We establish an exact analytical expression to extract the interfacial friction coefficient from oscillatory drainage forces between a sphere and a plane, suitable for dynamic SFA or Atomic Force Microscopy non-contact measurements. We use this model to investigate the boundary friction of viscoelastic polymer solutions over 5 decades of film thicknesses and one decade in frequency. The proper use of the original Navier's condition describes accurately the complex hydrodynamic force up to scales of tens of micrometers, with a simple "Newtonian-like" friction coefficient, not frequency dependent, and reflecting closely the dynamics of an interfacial depletion layer at the solution/solid interface.

Simultaneous and continuous measurement of shear elasticity and viscosity of liquids at multiple discrete frequencies

This paper presents the extension of the classical torsional resonance viscometer towards the characterization of linear viscoelastic fluids. By simultaneously tracking multiple resonance frequencies, shear viscosity and elasticity can be monitored at multiple discrete frequencies at the same time. The proposed method is applied to the well-established sensor design of a simple rod-like structure, hence enabling a robust and versatile measurement system that can be used in different applications, such as in-line measurement or hand-held devices. In order to simultaneously control different resonance frequencies, multiple independent phase-locked loops are used, of which each subsystem is responsible for one natural vibration. An analytical description of the relationship between measurement parameters and physical fluid parameters is presented that is valid both for Newtonian and linear viscoelastic fluids. Consequently, calibration of the sensor is possible using Newtonian fluids only. To demonstrate the sensor, viscoelastic polymer and surfactant solutions are investigated at five frequencies between 2 kHz and 20 kHz. Additionally, the test fluids are characterized by means of a classical rotational rheometer (low frequency range) and diffusing-wave spectroscopy (high frequency range). The comparison of all methods shows very good agreement and validates the application of the sensor as resonant rheometer for viscoelastic fluids.

Steady viscoelastic flow around high-aspect-ratio, low-blockage-ratio microfluidic cylinders

We employ a state-of-the-art microfabrication technique (selective laser-induced etching, SLE) to produce microfluidic cylinder geometries that explore new geometrical regimes. Using SLE, two microchannels are fabricated in monolithic fused silica substrate with height H=2 mm and width W=0.4 mm (aspect ratio α=H/W=5) containing cylinders of radius r=0.02 mm (blockage ratio β=2r/W=0.1), centered at the channel mid-width, W/2. An ‘sc’ channel contains a single cylinder, while a ‘dc’ channel contains two axially-aligned cylinders separated by a distance L=1 mm (L=50r). Compared with cylinder geometries fabricated by soft lithography (which typically have α ≪ 1 and β ≳ 0.5), these rigid glass devices provide a quasi-two-dimensional flow along the direction of the cylinder axis and also more clearly reveal the effects of the strong extensional wake regions located at the leading and trailing stagnation points. Using flow velocimetry and quantitative birefringence measurement techniques, we study the behaviour of a well-characterized viscoelastic polymer solution in flow around the cylinders. The small cylinder radii result in low inertia and very high elasticity numbers El ≈ 2400. For the sc device, we report strong flow modification effects around the cylinder as the flow rate is incremented. This is associated with the deformation of polymer molecules primarily in the upstream wake region, leading to the onset of a purely elastic flow asymmetry upstream of the cylinder. Stretched polymer molecules are advected around the cylinder and relax downstream of the cylinder, resulting in an extremely long elastic wake extending for > 300r downstream. In the dc channel, at lower flow rates, similar flow modification effects are observed to develop around, and downstream of, both cylinders. However, at higher flow rates the wake of the first cylinder extends > 50r downstream, and begins to interact with the second cylinder. The second cylinder becomes encapsulated by the wake of the first and is effectively obviated from the flow field. The results will be of relevance to understanding practical applications of viscoelastic fluids, for example in particle suspension and porous media flows, and also for benchmarking against numerical simulations using viscoelastic constitutive models.

Microliter viscometry using a bright-field microscope: η-DDM.

The rheological properties of a medium can be inferred from the Brownian motion of colloidal tracer particles using the microrheology procedure. The tracer motion can be characterized by the mean-squared displacement (MSD). It can be calculated from the intermediate scattering function determined by Differential Dynamic Microscopy (DDM). Here we show that DDM together with the empirical Cox-Merz rule is particularly suited to measure the steady-shear viscosity, i.e. the viscosity towards zero frequency, due to its ability to provide reliable information on long time and length scales and hence small frequencies. This method, η-DDM, is tested and illustrated using three different systems: Newtonian fluids (glycerol-water mixtures), colloidal suspensions (protein samples) and a viscoelastic polymer solution (aqueous poly(ethylene oxide) solution). These tests show that common lab equipment, namely a bright-field optical microscope, can be used as a convenient and reliable microliter viscometer. Because η-DDM requires much smaller sample volumes than classical rheometry, only a few microliters, it is particularly useful for biological and soft matter systems.

"From the Edge to the Center": Viscoelastic Migration of Particles and Cells in a Strongly Shear-Thinning Liquid Flowing in a Microchannel.

Controlling the fate of particles and cells in microfluidic devices is critical in many biomedical applications, such as particle and cell alignment and separation. Recently, viscoelastic polymer solutions have been successfully used to promote transversal migration of particles and cells toward fixed positions in straight microchannels. When inertia is negligible, numerical simulations have shown that strongly shear-thinning polymer solutions (fluids with a shear viscosity that decreases with increasing flow rates) promote transversal migration of particles and cells toward the corners or toward the centerline in a straight microchannel with a square cross section, as a function of particle size, cell deformability, and channel height. However, no experimental evidence of such shifting in the positions for particles or cells suspended in strongly shear-thinning liquids has been presented so far. In this work, we demonstrate that particle positions over the channel cross section can be shifted "from the edge to the center" in a strongly shear-thinning liquid. We investigate the viscoelasticity-induced migration of both rigid particles and living cells (Jurkat cells and NIH 3T3 fibroblasts) in an aqueous 0.8 wt % hyaluronic acid solution. The combined effect of fluid elasticity, shear-thinning, geometric confinement, and cell deformability on the distribution of the particle/cell positions over the channel cross section is presented and discussed. In the same shear-thinning liquid, separation of 10 and 20 μm particles is also achieved in a straight microchannel with an abrupt expansion. Our results envisage further applications in viscoelasticity-based microfluidics, such as deformability-based cell separation and viscoelastic spacing of particles/cells.

Comparison of jets from Newtonian and non-Newtonian fluids induced by blister-actuated laser-induced forward transfer (BA-LIFT)

Blister-actuated laser-induced forward transfer (BA-LIFT) is a high-resolution printing technique, where small droplets are ejected from a thin liquid layer onto a receiver substrate. Experiments with a high-speed camera imaging setup demonstrate novel regimes during the jet formation for the transfer of viscoelastic shear-thinning polymer solutions compared to Newtonian fluids. The ratio of the ink film thickness $$H_{\text {f}}$$ to the blister height $$H_{\text {b}}$$ is used as a dimensionless number $$H_{\text {f}}/H_{\text {b}}$$ to classify different jet behaviors. We show that different $$H_{\text {f}}/H_{\text {b}}$$ thresholds can be defined depending on the elasticity of the ink layer for the induced jets to result in breakup.

Torque in Taylor–Couette flow of viscoelastic polymer solutions

When a polymer solution is sheared between concentric cylinders, with the inner rotating and the outer fixed, the torque on the inner cylinder is modified compared to a Newtonian fluid of the same viscosity revealing the different flow patterns that emerge above the linear stability threshold for circular Couette flow. Here, mixtures of relatively short and long linear polymers in dilute and semi-dilute concentrations were considered. Their shear viscosity and extensional relaxation time are quantified. The stability of the flow is monitored through torque measurements and flow visualisations for a constant rate of acceleration and deceleration of the inner cylinder in a wide range of polymer concentrations. The torque exhibits an hysteretic behaviour, typical of subcritical transition. For large concentrations, six different numbers of steady solitary pairs of vortices, called diwhirls, were observed depending on the deceleration rate and their torque contribution is reported.

Rheology and heat transport properties of a hydroxyethyl cellulose-based MRI tissue phantom

A saline solution of hydroxyethyl cellulose has been recommended for use as a tissue phantom in testing the behavior of medical devices in MRI scanners. It has been stated in the standards governing these tests that the viscosity of the fluid used should be large enough that bulk transport or convection currents are not supported. In this study we evaluated a hydroxyethyl cellulose phantom based on an ASTM standard to determine the degree to which it supports convective, as compared to conductive, heat transport. We study the rheological properties of this fluid, and find that it behaves as a typical viscoelastic polymer solution. As a result, it flows in response to local heating, such as would occur due to eddy-current heating of a metallic device in an MR scanner. We use laboratory experiments and numerical simulations to determine the convective and conductive contributions to the heat transport in a simple model of this system. Our results indicate that convective heat transport is of the same order of magnitude as conductive transport under conditions typical of MRI device tests. This indicates that heating tests conducted with this fluid are not completely conservative in terms of estimating local temperature changes for medical devices in vivo. It also indicates that convective processes should be included along with conduction in computer simulations of device heating in order to allow accurate comparison with experimental measurements.

Ink transfer of non-Newtonian fluids from an idealized gravure cell: The effect of shear and extensional deformation

In the presented study, we have investigated the effect of a complex flow field consisting of a combination of both shear and extensional deformation on the liquid transfer from an idealized gravure cell. The study was conducted for two classes of non-Newtonian fluid; a shear and extensional thickening nanoparticle dispersion and a extensional thickening viscoelastic polymer solution with a constant shear viscosity. The shear thickening fluid was a dispersion of fumed silica nanoparticles in polypropylene glycol and the viscoelastic fluid was a solution of polyethylene oxide (PEO) in water. The idealized gravure printing experiments were conducted using a combination of linear servo motor used to impose an extensional flow and a rotational servo motor to impose a shear flow during pickout. The fluid pickout from the gravure cell was studied as a function of the magnitude of the extensional and shear deformation rates. The fluid filament interface profile evolution during the pickout process was examined using a high speed camera. For the shear thickening fluid, the pickout resulting from a pure extensional flow field was found to be enhanced compared to Newtonian fluids at moderate velocities, resulting from the extensional thickening of the fluid. However, at large stretching velocities the pickout was found to decay dramatically due to extensional thinning of the fluid at large extension rates. The pickout behavior of the shear thickening fluid resulting from a pure shear field was found to exhibit a qualitatively similar trend to that of the extensional pickout although the pickout fraction was significantly smaller. Superposition of shear and extensional flow was found to initially improve pickout by driving the overall deformation rate higher and introducing an asymmetry in the gravure cell dewetting. At large rates, shear negatively affected pickout by causing an early onset of extensional thinning. In viscoelastic fluids, thickening of the extensional viscosity was found to enhance both the pure shear-induced pickout as well as the pure extensional-induced fluid pickout, with the shear-induced pickout relatively smaller compared to the extensional-induced pickout. For superimposed shear and extensional deformation, an enhancement in the fluid pickout was observed at certain velocity regimes, likely associated with the asymmetric dewetting from the gravure cavity wall assisted by the superimposed flows.

Efficient heat transfer enhancement by elastic turbulence with polymer solution in a curved microchannel

Heat and mass transfer in microscale flows are limited due to extremely low Reynolds number (Re). In a curved microchannel, however, complex flow behaviors, such as elastic instability and elastic turbulence, can be induced via viscoelastic fluid at vanishingly low-Re conditions, which is of great potential to enhance the heat transfer performance. The influence of elastic instabilities and turbulence on heat dissipation of exothermic components is experimentally investigated in this study. The heat transfer performance of both viscoelastic (polymer solutions) and Newtonian (sucrose solutions) fluid flows in a curved microchannel with a square cross section is experimentally characterized. Titanium–platinum (Ti–Pt) thin films embedded at the bottom wall of the polydimethylsiloxane (PDMS) microchannel serve as both microheater and temperature sensor. For viscoelastic fluids, the spectrum of outlet temperature fluctuation in broad frequency (f) region fits the power law of f −1.1. Heat transfer enhancement due to the elastic turbulence in a curved microchannel is thereby identified by the drastic growth of the Nusselt number (Nu, the ratio of convective to conductive heat transfer normal to the boundary) with the increase in the Weissenberg number (Wi, the ratio of elastic stress to viscous stress). The mechanism of heat transfer enhanced by the convection effect of elastic turbulence is also elucidated.