Viscoelastic Boger Fluids Research Articles

Collective effects in the sedimentation of particles in a viscoelastic fluid

The sedimentation of a suspension of rigid spherical particles in a polymeric fluid is studied with experiments and numerical simulations. It is shown that settling in a viscoelastic Boger fluid is time-dependent and inhomogeneous; both experiments and simulations exhibit the formation of particle-rich, fast-settling regions and particle-depleted regions with back flow (shown). When a cross shear flow is imposed, the mean particle settling rate is drastically reduced, suggesting that both fluid elasticity and the particle volume fraction of the suspension have important effects.

Rough geometries with viscoelastic Boger fluids: Predicting the apparent wall slip with a porous medium approach

Multiphase fluids and highly non-Newtonian fluids often show wall slip. The typical approach to reduce wall slip in experiments is to use roughened geometries, which are thin porous layers. However, the presence of the roughness introduces in itself an apparent wall slip due to the flow within the porous layer. To account for wall slip typically, measurements must be run at several gaps in a plate-plate device. With Newtonian fluids, the apparent wall slip can be conveniently accounted for in the measurements at a single gap since it can be accurately predicted using models describing the flow of Newtonian fluids through and over porous media. Here, we extend this approach to viscoelastic fluids by using Minale's model [Phys. Fluids 28, 023102 and 023103 (2016)] for the flow of second order fluids (SOFs) through and over a porous medium. In this work, we first validate the theoretical predictions and then propose an experimental protocol to measure a SOF with rough geometries by executing the experiments at a single chosen gap. Two Boger fluids are used as model SOFs, and three different rough geometries are considered: Two commercial crosshatched plates and a homemade pillared one. The apparent wall slip is shown to be reduced for the viscoelastic fluids, with respect to the Newtonian case, and agreement with the theoretical predictions is excellent.

Discretized modeling for centrifugal spinning of viscoelastic liquids

A theoretical investigation of the behavior of Newtonian and viscoelastic jets during centrifugal spinning (CS) is presented in this paper. We used a discretized model, which provides a numerical framework to solve complex continuum equations, to model the spinning behavior of the viscoelastic Boger fluid. The jet was modeled as a series of beads connected with massless springs. After defining the viscoelastic, surface tension and aerodynamic drag forces for each bead, we solve Newton's second law of motion to obtain the trajectory of the jet. We first compared the jet profile predictions of the Newtonian fluid from the bead-spring model with an asymptotic thin-fiber model and obtained consistent results. Finally, we performed a parameter study to understand the effects of various properties such as viscoelasticity, surface tension and process conditions on the behavior of the viscoelastic jet. We also compared the simulation results with the experimental observations of PIB/PB Boger fluids to validate the discretized model.

The jetting behavior of viscoelastic Boger fluids during centrifugal spinning

We present an experimental visualization study of centrifugal spinning, which is a novel method of producing nanofibers. The investigation was conducted using Newtonian and viscoelastic fluids to study the effect of viscoelasticity, driving force, and the flow rate on the initial thinning behavior, jet contour shapes, and radii. Boger fluids based on Newtonian polybutene and viscoelastic polyisobutylene were utilized as test fluids in the current study. Our results reveal that increasing the viscoelasticity leads to a faster initial thinning of the polymer jet. However, the effect is strongly coupled with the rotation speed, and due to a faster increase in extensional viscosity for highly viscoelastic fluids, the thinning slows down with the increase in the angular velocity. Initial thinning is shown to be faster for the lower flow rates. Viscoelasticity and centrifugal force have a significant influence on the jet contour radii. The maximum radius will decrease for more viscoelastic fluids, and with the increase in angular velocity due to the development of the elastic hoop stress. The comparison of experiments with the discretized element modeling with the FENE-P model confirms the model predictive potential for the thinning behavior. Finally, the centrifugal spinning experiments are compared to electrospinning in order to observe a qualitative similarity.

Electrospinning of Poly(vinyl alcohol)-Based Boger Fluids To Understand the Role of Elasticity on Morphology of Nanofibers

This study aims at investigating the effect of solution elasticity on fiber diameter of electrospun nanofibers using viscoelastic Boger fluids of poly(vinyl alcohol) having varying degrees of elasticity (expressed in terms of relaxation time (λ) and Deborah number (De)) and similar viscosity. On electrospinning, the solutions with higher elasticity formed fibers with larger diameter, thereby, experiencing lower extension (on the order of 104), compared to the solutions of lower elasticity, which underwent higher extensions (up to 106), resulting in finer fibers. The diameter of the spun nanofibers was found to have a strong dependence on λ of the solutions. Effect of elasticity was also evident when the fiber diameter increased slightly with the increase in flow rate for solutions with higher elasticity. However, the effect of distance was negligible on the fiber diameter. The results suggest that the elasticity of the solution has an important role in governing the final diameter of electrospun fibers.

Simulations of a sphere sedimenting in a viscoelastic fluid with cross shear flow

The settling rate of heavy spheres in a shear flow of viscoelastic fluid is studied by numerical simulation. Experimental data [Tonmukayakul et al., US Patent Application US20110219856 (2011); van den Brule and Gheissary, J. Non-Newton. Fluid Mech. 49 (1993) 123–132] have shown that both shear thinning and the elasticity of the suspending polymeric solutions affect the settling rate of the solids. In the present work, simulations of viscoelastic flow past a single, torque-free sphere with a cross shear flow are used to study the effect of the elasticity of the carrying fluid on the sphere’s settling rate. The FENE-P constitutive model is used to represent a viscoelastic Boger fluid, with parameters obtained by fitting rheological data. A twofold increase in drag, i.e. a decrease in settling rate, is obtained with increase in the cross shear Weissenberg number, Wi⩽15, even though the shear viscosity of the solution decreases over this same range. At small Weissenberg number, Wi<2, the simulations remain in quantitative agreement with the experiments. At higher Weissenberg number, the numerical results remain in qualitative agreement with settling experiments although the magnitude of the simulated decrease in settling rate is smaller than that observed in experiments. The detailed physical mechanism for the increase in the drag experienced by the sphere in the simulations is presented and we show that τ11 component of the viscous stress (with 1, the sedimentation direction) is the primary cause of the increase in sphere drag.

Competition Between Viscoelasticity and Surfactant Dynamics in Flow Focusing Microfluidics

AbstractThe goal of this work is to quantify the impact of viscoelasticity on a tipstreaming phenomenon observed in flow focusing microfluidic devices. Tipstreaming, or thread formation, is a phenomenon caused by surfactant transport to, from, and along, deforming interfaces that leads to long filaments in microfluidic devices. Viscoelasticity also leads to stable filaments, so possible synergies are investigated here. The ability to generate extremely long and thin filaments that will break up via interfacial instabilities will lead to the formation of droplets much smaller than the device lengthscales. Viscoelastic Boger fluids are used as the dispersed phase liquid in a flow focusing device and surfactant is added to the continuous phase liquid. We find a region of operating space in which viscoelasticity appears to couple with surfactant transport to form long threads. The phenomenon is described qualitatively and is related to fluid relaxation times. magnified image

Influence of confinement on the steady state behavior of single droplets in shear flow for immiscible blends with one viscoelastic component

By using a counter rotating plate-plate device, single droplets in shear flow have been microscopically studied at confinement ratios ranging from 0.1 to 0.75. The droplet-to-matrix viscosity ratio was fixed at 0.45 and 1.5. Results are presented for systems with a viscoelastic Boger fluid matrix or a viscoelastic Boger fluid droplet, at a Deborah number of 1. Although the separate effects of confinement and component viscoelasticity on droplet dynamics in shear flow are widely studied, we present the first systematic experimental results on confined droplet deformation and orientation in systems with viscoelastic components. Above a confinement ratio of 0.3, wall effects cause an increase in droplet deformation and orientation, similar to fully Newtonian systems. To describe the experimental data, the Shapira–Haber theory [Shapira, M., and S. Haber, Int. J. Multiph. Flow 16, 305–321 (1990)] for confined slightly deformed droplets in Newtonian-Newtonian systems is combined with phenomenological bulk models for systems containing viscoelastic components [Maffettone, P. L., and F. Greco, J. Rheol 48, 83–100 (2004); M. Minale, J. Non-Newtonian Fluid Mech. 123, 151–160 (2004)]. The experimental results are also compared to a recent model for confined droplet dynamics in fully Newtonian systems [M. Minale, Rheol. Acta 47, 667–675 (2008)]. For different values of the viscosity ratio, component viscoelasticity and Ca-number, good agreement was generally obtained between experimental results and predictions of one or more models. However, none of the models can accurately describe all experimental data for the whole range of parameter values.

Visualizations of Boger fluid flows in a 4:1 square–square contraction

AbstractVisualizations of the 3‐D flow in a 4:1 square–square sudden contraction for two viscoelastic Boger fluids and two Newtonian fluids were carried out at low Reynolds numbers. In these creeping flow conditions, the vortex length remained unchanged for Newtonian fluids, whereas a nonmonotonic variation with flow rate was observed for the Boger fluids. Initially, the corner vortex slightly increased with flow rate to a local peak at a Deborah number of De2 ≈ 6, before decreasing significantly to a minimum at De2 ≈ 15 (De2 is based on downstream characteristics). Finally, for Deborah numbers &gt; 20 there was intense vortex enhancement until a periodic flow was established at higher flow rates (De2 ≈ 45–52). The strong elastic vortex enhancement was preceded by the appearance of diverging streamlines on the approach flow and, for the Boger fluid with higher polymer concentration, vortex enhancement took place through a lip vortex mechanism. AIChE J, 2005

Flow structures and stability in Newtonian and non-Newtonian Taylor-Couette flow

In the present paper the pattern formation and stability of Newtonian and non-Newtonian fluid in a wide-gap Taylor-Couette system (ri/r0 = 0.5) is investigated. Flow visualization and measurement of two-dimensional flow fields with Particle Image Velocimetry are performed in silicone oil as reference fluid and in a viscoelastic Boger fluid. Here we present first results regarding the influence of the boundaries on the fluid flow at moderate aspect ratios. The transition sequence in the Boger fluid is similiar to a Newtonian fluid at lower rotation rates of the inner cylinder. Due to the studied range of aspect ratios the fluid flow behaviour is strongly influenced by the boundaries. In the Boger fluid the wavy vortex flow is inhibited for aspect ratio Γ < 4.48.The observed wavy vortex flow in the Boger fluid is damped in comparison with Newtonian fluid.

An experimental study of drop deformation and breakup in extensional flow at high capillary number

An experimental study is reported of the flow-induced stretching of drops in a four-roll mill at low Reynolds number, but for capillary numbers that are large compared to the critical capillary number for onset of stretching. We mainly consider Newtonian drops in a Newtonian suspending fluid, but also present a brief study of Newtonian drops in a viscoelastic (Boger fluid) suspending fluid. The stability of the drops following cessation of flow is determined, in either case, by the ratio of their extended length to the undeformed radius. If this ratio is large enough, the drops will break into two or more parts via the capillary flow process known as end-pinching. However, for Newtonian drops in a Newtonian suspending fluid, it is shown that the critical degree of stretch for breakup increases sharply with increase of the capillary number that characterizes the stretching process. Furthermore, it is shown, in this case, that the critical stretch ratio is not unique, but that there can be a discrete range of stretch ratios above the first (or smallest) critical value where the drop is again stable before it encounters a second larger “critical” stretch ratio. This “restabilization” is associated with the transition from two to three drops in the breakup process. Newtonian drops in the viscoelastic Boger fluid are found to be slightly more stable than the same drops in a Newtonian fluid when stretched at strain rates just exceeding the critical value. By this we mean that the critical elongation ratio necessary for the drops to break upon cessation of flow is increased by about 20%. When stretched at a higher strain rate, approximately 2.15 times the critical value, large drops in the viscoelastic fluid (above 100 microns in radius for this particular suspending fluid) are destabilized relative to their counterpart in a Newtonian suspending fluid, while smaller drops are strongly stabilized.

The effect of sphere–wall interactions on particle motion in a viscoelastic suspension of FENE dumbbells

A new method for simulating the motion of particles in viscoelastic Boger fluids is extended to problems with bounded geometries. Viscoelasticity is incorporated into the Stokesian dynamics method by modeling a viscoelastic fluid as a suspension of finite-extension nonlinear-elastic (FENE) dumbbells. Wall–particle and wall–bead interactions are included by using the image system method of Blake; particle–particle and particle–bead interactions are also modified by the presence of the wall. The method of incorporating sphere–wall interactions is verified by doing calculations for several problems involving particle–wall interactions in Newtonian fluids. The method is then used to study particle–wall interactions in viscoelastic dumbbell suspensions by examining several problems of interest: the sedimentation of a spherical particle near vertical and tilted walls; the sedimentation of a nonspherical particle between two flat plates; and the migration of a neutrally buoyant sphere in plane Poiseuille flow. We find that a single sphere falling near a wall moves toward the wall and exhibits anomalous rotation. When the wall is tilted by an amount less than a few degrees, the sphere still moves toward the wall, but tilting the wall greater than an angle of approximately 1.5° results in the sphere falling away from the wall. A nonspherical particle settling in a channel exhibits an oscillatory motion, but ultimately becomes centered in the channel with its long axis parallel to gravity. Finally, it is shown that a neutrally buoyant sphere in plane Poiseuille flow migrates to the channel center in wide channels, but migrates to the walls when the sphere is sufficiently large relative to the channel width.

Stability of viscoelastic flow around periodic arrays of cylinders

Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (Wec), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above Wec which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above Wec a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplifieds spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.