Flow Of Polymer Solutions Research Articles

The Oldroyd-B fluid in elastic instabilities, turbulence and particle suspensions

The Oldroyd-B fluid has become the starting point for almost all complex flow calculations and analysis involving the behavior of dilute polymer solutions. The reasons for this are clear: based on the kinetic theory of high molecular weight “phantom” chains near equilibrium, the resulting model, in its simplest form, produces a single mode description of the solution constitutive equation in terms of a single symmetric dyad order parameter. The physical connection to the individual chains is therefore unambiguous through the end-to-end configuration tensor. The flow of the fluid resulting from the mathematical solution of the constitutive equation coupled to Cauchy’s equation of motion and continuity has been examined for decades and its strengths and weaknesses in predicting the features of non-linear viscometric and non-viscometric polymer solution flows are well known. Moreover, “simple” extensions (e.g. the FENE-P model) can ameliorate the most serious of these shortcomings. For example, the multi-mode Oldroyd-B model can provide quantitative predictions of the linear viscoelasticity of a wide range of polymer solutions. Remarkably, even with all its shortcomings, the Oldroyd-B fluid has been invaluable in predicting at least qualitatively, features as complex as purely elastic instabilities, turbulent drag modification, and even the effective rheology of particles suspended in polymer solutions. While remaining mindful of the model’s shortcomings, any student of these diverse fields may find the Oldroyd-B fluid an important starting point.

Effect of elastic instability on mobilization of capillary entrapments

The flow of viscoelastic polymer solutions and their use as displacing agents in porous media are important for industrial applications, such as enhanced oil recovery and soil remediation. The complexity of flow and high elasticity of conventionally used viscoelastic polymer solutions can lead to purely elastic instability in porous media. In this study, we investigate the impact of this instability on displacing capillary entrapments at low Reynolds numbers using a microfluidic approach. Our unique design consists of a single-capillary entrapment connected to two symmetric serpentine channels. This design excludes the effect of viscous forces and enables a direct focus on displacement processes driven solely by elastic forces. After the onset of purely elastic instability, an unstable base flow is observed in the serpentine channels. We discuss that the pressure fluctuations caused by this unstable flow create an instantaneous non-equilibrium state between the two ends of the capillary entrapment. This provides the driving pressure to overcome the capillary threshold pressure and eventually displace the entrapped oil. In our geometry, we observe that the displacement coincides with the emergence of a fully developed elastic turbulent state.

Experimental study on the flow and heat transfer behavior of polymer solutions in the closed liquid ring vacuum pump system

The closed liquid ring vacuum pump system, which mainly includes the liquid ring vacuum pump and the heat exchanger, is widely used for gas pumping in various industries. In this paper, the energy saving effect in the liquid ring vacuum pump and the flow and heat transfer behavior in the shell-and-tube heat exchanger are investigated for aqueous solutions of rigid xanthan gum (XG) and flexible Polyacrylamide (PAM), and the effects of the concentration, Reynolds number, polymer conformation and flow geometry on the flow behavior of polymer solutions are studied. Results show that, despite the significant differences in molecular conformation and rheological properties between XG and PAM, the similar energy saving rate, about 1.5 ∼ 17.5%, is obtained in the liquid ring vacuum pump. However, in the shell-and-tube heat exchanger, XG solutions exhibit the more obvious pressure drop enhancement and heat transfer reduction than that of PAM solutions for the same concentration. Furthermore, due to the polymer shear degradation, the shaft power in the liquid ring vacuum pump decreases first and then stabilizes, conversely, the flow resistance decreases and the flow rate increases in the heat exchanger. The great difference in the flow condition between the intense rotating gas–liquid two-phase flow field and the gentle liquid pipe flow causes the different flow behavior for XG and PAM solutions.

Flows of Linear Polymer Solutions and Other Suspensions of Rod-like Particles: Anisotropic Micropolar-Fluid Theory Approach.

We formulate equations governing flows of suspensions of rod-like particles. Such suspensions include linear polymer solutions, FD-virus, and worm-like micelles. To take into account the particles that form and their rotation, we treat the suspension as a Cosserat continuum and apply the theory of micropolar fluids. Anisotropy of suspensions is determined through the inclusion of the microinertia tensor in the rheological constitutive equations. We check that the model is consistent with the basic principles of thermodynamics. In addition to anisotropy, the theory also captures gradient banding instability, coexistence of isotropic and nematic phases, sustained temporal oscillations of macroscopic viscosity, shear thinning and hysteresis. For the flow between two planes, we also establish that the total flow rate depends not only on the pressure gradient, but on the history of its variation as well.

Viscoelastic fluid flow in microporous media

This paper describes an experimental investigation of the flow of flexible polymer solutions through a distinctive micro-porous structure (typical pore sizes of 500 microns) with the primary focus on the interaction of the viscoelasticity of the working fluid with the micro-porous structure. In particular, we relate the bulk flow properties to measurable rheological parameters, demonstrating that a key parameter in estimating the pressure drop through the porous media (for a variety of polymer types, concentrations, solvents, molecular weights, and states of degradation) is the extensional relaxation time (or, more correctly, a characteristic time for extensional stress growth). A Weissenberg number (Wi) is calculated as a product of this extensional relaxation time and the nominal shear rate in the flow. Results, suitably normalised with Newtonian pressure-drop data, show a critical Wi of roughly 0.01 where all working fluids in two different pore structures reveal the onset of elastic dominance over viscous forces as the flowrate increases. Such a low critical value of Wi is due to the estimate of a nominal shear rate based on pore size, which severely underestimates the maximum shear rates within the complex pore structure. Significant deviation from the universal behaviour is observed for high concentrations of the polyacrylamide, which is thought to be a result of shear-thinning for these systems. Systematic degradation of the polyethylene oxide solutions caused an exponential decay in elasticity, which is reflected in the pressure-drop measurements. These imply that, although the flow through porous media is known to be a complex combination of both shear and extensional flow, the extensional effects are of primary importance in this context (or that transient stretching in the media is well represented by this relaxation time) of viscoelasticity. The findings highlight the significance of the transient extensional flow through the neck regions between the pores of the media, which are regions of contraction/expansion.

Pseudo-Laminarization of Mixed Microbubble Water and Complex Fluids in Capillary Flows

Symmetry in fluid flow is determined by external factors such as magnetic or electric fields. Owing to the electrical properties of fluids, liquids containing fine bubble or ionic surfactant molecules differ from the normal fluid flow. Therefore, the pressure drop and frictional coefficient in a pipe are measured and estimated for water alone, for mixed microbubble water (MB), and for complex fluids (anionic surfactant solution and polymer solution) in capillary flow with constant flow rate. For water alone, good agreement is obtained between the experimental and theoretical values for laminar Hagen–Poiseuille flow and the Blasius expression in turbulent flow. For the MB, pseudo-laminarization is suggested up to a Reynolds number of 4.2×103. Both the anionic surfactant solution and the polymer solution exhibit the same tendency as that of the MB. In explaining these behaviors, elasticity and electrical interaction are discussed, and electrical interaction on the capillary wall is strongly suggested to be a contributing factor. Additionally, surface tension is investigated and supports the discussion.

Molecular dynamics of shear banding flow in associative polymers solutions: effect of sticker groups location

Non-equilibrium molecular dynamics are used in a coarse-grained scale to simulate the simple shear flow of telechelic and non-telechelic associative polymer solutions. The work includes the study of inception of flow and stress relaxation in transient flows and the constitutive curve at steady state. The instabilities (plateau stress, stress maxima) and the formation of bands with different velocity gradient and concentration depend on the location of the hydrophobic sites (sticker sites, SS) in the chain. Results allow to shed light on the origin of banded flow within the transient state, related to depletion of bridges between aggregates. This situation induces instabilities in the velocity profiles and concentration inhomogeneities along the velocity gradient during the stress overshoot. As the steady state is reached, instabilities disappear for systems where the SS are in the middle of the chain. The conformation relaxation occurs during a time scale larger than that of the stress, but this is not sufficient condition for the presence of banded flow in telechelic polymer solutions, as it holds in polymer melts. The difference in concentration among the bands suggests the existence of a shear-gradient concentration coupling mechanism under banded flow conditions, such as spatial non-homogeneities in the network density, induces chain diffusivity in the gradient direction and increasing normal stresses, especially in telechelic chains. The role of normal stresses on the flow-concentration coupling instability is analyzed in detail.

Optimal Boundary Control of the Boussinesq Approximation for Polymeric Fluids

We consider an optimal control problem for non-isothermal steady flows of low-concentrated aqueous polymer solutions in a bounded 3D domain. In this problem, the state functions are the flow velocity and the temperature, while the control function is the heat flux through a given part of the boundary of the flow domain. We obtain sufficient conditions for the existence of weak solutions that minimize a cost functional under a given bounded set of admissible controls. It is shown that the marginal function of the considered control system is lower semi-continuous and the optimal states operator generates a continuous branch in a suitable function space.

The centre-mode instability of viscoelastic plane Poiseuille flow

Abstract

Investigating the Transition between Polymer Melts and Solutions in Nonlinear Elongational Flow

The Doi–Edwards tube model, coupled with relaxation mechanisms, such as reptation, contour length fluctuation, and constraint release, allows us to quantitatively predict the linear viscoelastic properties of entangled polymers. However, for nonlinear elongational flows, large discrepancies between theoretical predictions based on the tube model and experimental results still persist today. This is in particular obvious for the experimentally observed strong qualitative differences in extensional flow of entangled polystyrene (PS) melts and solutions despite having the same number of entanglements and exhibiting the same linear viscoelastic behavior. The cause of this non-universality is often attributed either to a monomeric friction reduction or to an interchain pressure effect. In this work, we investigate the changes in extensional flow behavior going from polymer solutions to the melt state. For this purpose, we measure with a filament stretching rheometer the nonlinear extensional responses of differently long PS chains, both in the melt state and diluted in short-chain matrices of the same polymer at varying concentrations. These concentrations have been chosen sufficiently high, such that the chains stay entangled. This allows us to discuss the influence of concentration and molar mass on the steady-state elongational viscosity to highlight scaling relations. The purpose of the present work is to conduct well-defined experiments to further investigate how the steady extensional viscosity of polymer solutions and blends varies with the concentration and with the molecular weight of the chains.

Drag reduction of aqueous suspensions of fine solid matter in pipe flows

AbstractIt is well known that drag reduction properties of polymer solutions in pipe flows are classified into two categories, based on the relationship between the friction factor and the Reynolds number. The degree of drag reduction either increases with an increase in the Reynolds number or is independent of the Reynolds number. In the latter case, the drag reduction behavior is referred to as type B behavior. In this study, the pressure losses of aqueous suspensions of biofibers and graphene oxide flat particles in pipe flows were measured to clarify the effect of the shape of suspended fine solid matter on the friction factor. The experimental results demonstrated that the behavior of the friction factor corresponded with the type B behavior of drag reduction. The mean velocity profile in the range of the turbulent flow was also estimated from the friction factor data.

Polymer effects on viscoelastic fluid flows in a planar constriction microchannel

A comprehensive understanding of the flow of viscoelastic polymer solutions in a contraction and/or an expansion geometry concerns numerous applications. The effects of polymer type, molecular weight, and concentration are investigated through controlled experiments with polyethylene oxide (PEO), polyvinylpyrrolidone (PVP) and hyaluronic acid (HA) solutions in a planar constriction microchannel in a wide range of Reynolds (Re) and Weissenberg (Wi) numbers. The polymer structure renders drastic differences amongst the contraction flows of 3000 ppm PEO, PVP, and HA solutions despite having similar molecular weights. The expansion flow vortices of these solutions remain analogous to those in the inertial flow of water. Increasing the molecular weight or concentration of PEO polymer promotes the elastic instabilities in both the contraction and expansion flows. It, however, suppresses (and even blocks) the inertial vortices in the expansion flow and makes them start from the salient corners, in contrast to the lips of the expansion walls in water. Interestingly, a sudden decrease in the size of inertial vortices is observed in the expansion flow of 500 ppm, 1 megadalton PEO solution when the elastic disturbances start appearing in the contraction flow. The observed flow regimes and vortex development in the polymer solutions are summarized in the same dimensionless Re−Wi and Re−χL parameter spaces, where χL is the normalized vortex length. The elasticity number, El=Wi/Re, is found to determine and distinguish the contraction and expansion flows.

Modeling Monophasic Flow of Polymer Solutions in Porous Media: Assessing Relative Impact of Intrinsic Fluid Properties and Pore Microstructure

Polymer solutions are often described as viscoelastic fluids, whose rheological behavior dynamically evolves according to the flow shear rate due to successive contractions and relaxations of inner deformable components. Contrary to shear-thickening and shear-thinning fluids, viscoelastic fluids can undergo an increase in the normal stress-differences even in simple geometries, leading to counterintuitive flow patterns. In this paper, we investigate numerically the monophasic flow of viscoelastic fluids through microfluidic devices. The objective is to qualitatively assess how modification of the rheological properties and the geometry of porous media representative element affect the flow regime at microscale. Deviations from equivalent Newtonian model are analyzed to quantify the contribution of elasticity in the flow. It is demonstrated that depending on the geometry, flow of polymer solution can display anisotropic features and flow resistance at relatively low viscoelastic numbers, which is coherent with previous microscopic experimental and numerical studies. Ensued applications of the formulated microscale model are discussed.

Free Boundary Problem in a Polymer Solution Model

An initial boundary value problem with a free boundary for a third-order integro-differential equation for the unsteady flow of an aqueous polymer solution in a strip is studied. Questions concerning the solvability of the problem and the qualitative behavior of the solution in dependence on the initial data are investigated: time-local resolvability is established under natural conditions on the input data and conditions of global solvability are found for the problem of strip narrowing. Conditions for the bowing-up of the solution in finite time in the model problem of strip expansion are presented. The problem of small perturbations of the flow of a strip of viscous fluid with respect to a parameter proportional to the relaxation viscosity is also consider.

Constriction length dependent instabilities in the microfluidic entry flow of polymer solutions.

Transport phenomena of fluids and particles through contraction and/or expansion geometries have relevance in many applications. Polymer solutions are often the transporter in these processes, giving rise to flow complexities. The separation distance between a contraction and a following expansion in microfluidic entry flow can affect the interplay between the shear and extension force dominated flow regimes, but the process is still little understood. We investigate the rheological responses of such constriction length dependent instabilities with three different polymer solutions and water in planar contraction-expansion microchannels differing only in the constriction length. The viscoelastic polyethylene oxide (PEO) solution is found to exhibit strong constriction length-dependent instabilities in both the contraction and expansion flows. Such a dependence is, however, completely absent from the flow of shear-thinning xanthan gum (XG) solution and Newtonian water. Interestingly, it is only present in the expansion flow of the both shear thinning and viscoelastic polyacrylamide (PAA) solution.

Near-surface rheology and hydrodynamic boundary condition of semi-dilute polymer solutions.

Understanding confined flows of complex fluids requires simultaneous access to the mechanical behaviour of the liquid and the boundary condition at the interfaces. Here, we use evanescent wave microscopy to investigate near-surface flows of semi-dilute, unentangled polyacrylamide solutions. By using both neutral and anionic polymers, we show that monomer charge plays a key role in confined polymer dynamics. For solutions in contact with glass, the neutral polymers display chain-sized adsorbed layers, while a shear-rate-dependent apparent slip length is observed for anionic polymer solutions. The slip lengths measured at all concentrations collapse onto a master curve when scaled using a simple two-layer depletion model with non-Newtonian viscosity. A transition from an apparent slip boundary condition to a chain-sized adsorption layer is moreover highlighted by screening the charge with additional salt in the anionic polymer solutions. We anticipate that our study will be a starting point for more complex studies relating the polymer dynamics at interfaces to their chemical and physical composition.

CFD simulation of HPAM EOR solutions mechanical degradation by restrictions in turbulent flow

Polymer flooding is a widely used enhanced oil recovery (EOR) technology. The purpose of the polymer is to increase water viscosity to improve reservoir sweep efficiency. However, mechanical elements of the polymer injection facilities may impact the viscosity of the polymer negatively, decreasing it drastically. Mechanical degradation of the polymer occurs in case of flow restrictions with abrupt diameter changes in valves and control systems. Such flow restrictions may induce mechanical stresses along the polymer chain, which can result in its rupture. In this research, physical experiments and numerical simulations using CFD (Computational Fluid Dynamics) were used to propose a model for estimating the mechanical degradation for the flow of polymer solutions. This technique involves the calculation of velocity gradients, pressure drawdown, and polymer degradation of the fluid through geometry restriction. The simulations were validated through polymer injection experiments. The results show that with the greater volumetric flow and lower effective diameters, there is more mechanical degradation due to polymer shearing; nonetheless, this depends on the rheology properties inherent in each polymer in an aqueous solution.
 This method is suitable to estimate the mechanical degradation of the polymer solution in flooding facilities and accessories. Further, the results obtained could enhance the use of the polymer, calculating its actual mechanical degradation, minimizing it, or using it to support the development of new accessories.

Numerical simulation of non-isothermal viscoelastic flows at high Weissenberg numbers using a finite volume method on general unstructured meshes

In this numerical study, an original approach to simulate non-isothermal viscoelastic fluid flows at high Weissenberg numbers is presented. Stable computations over a wide range of Weissenberg numbers are assured by using the root conformation approach in a finite volume framework on general unstructured meshes. The numerical stabilization framework is extended to consider thermo-rheological properties in Oldroyd-B type viscoelastic fluids. The temperature dependence of the viscoelastic fluid is modeled with the time-temperature superposition principle. Both Arrhenius and WLF shift factors can be chosen, depending on the flow characteristics. The internal energy balance takes into account both energy and entropy elasticity. Partitioning is achieved by a constant split factor. An analytical solution of the balance equations in planar channel flow is derived to verify the results of the main field variables and to estimate the numerical error. The more complex entry flow of a polyisobutylene-based polymer solution in an axisymmetric 4:1 contraction is studied and compared to experimental data from the literature. We demonstrate the stability of the method in the experimentally relevant range of high Weissenberg numbers. The results at different imposed wall temperatures, as well as Weissenberg numbers, are found to be in good agreement with experimental data. Furthermore, the division between energy and entropy elasticity is investigated in detail with regard to the experimental setup.

Vortex merging and splitting: A route to elastoinertial turbulence in Taylor-Couette flow

Experimental evidence is reported of a new merge-split transition (MST) to elastoinertial turbulence (EIT) in Taylor-Couette flows of viscoelastic polymer solutions, caused by merging and splitting of base Taylor vortices when crossed by elastic axial waves. Vortex merging and splitting are random in nature and increase in frequency with Reynolds number. When superimposed on a RSW flow state, they cause abrupt changes in the axial spatial wavelength, leading to the transition from a RSW to the EIT state. MST is thus identified as an inertial feature solely triggered by elasticity and independent of any shear-thinning behavior.

Convection Heat Transfer and Pressure Drop for Dilute Polymer Solutions Flow Inside Multi- Channels Flat Tube (Dept.M)

Convection heat transfer and pressure drop is investigated experimentally, for the flow of dilute polymer solutions (polyacrylamide) inside multi-channels flat tube and compared with water. An experimental apparatus equipped with the required measuring devices is designed and constructed to assess the effects of the operating parameters on convection heat transfer and pressure drop. The flat Aluminum multi-channels extruded tube composed of 22 parallel rectangular mini-channels (3.6 mm x 3.85 mm) with hydraulic diameter of 3.72 mm. Different polymer concentrations are considered; 10, 20, 50 and 100 ppm. This work covers a range of Reynolds number from 300 to 1200 and heat flux from 15 to 41kW/m2. The experimental measurements for flow rate, temperature, pressure, and pressure drop are taken to perform the required analysis. Therefore, the average value of convection heat transfer coefficient and friction factor for different operating parameters are computed. The obtained experimental results show that, the laminar-turbulent transition occurs in the range of Re=1100-2000. Pressure drop and in turn friction factor takes higher values for laminar flow of polymer solutions compared with water. Friction factor decreases with increasing Reynolds number for both polymer solutions and water flow inside the flat tube. Surface temperature of flat tube decreases with increasing Reynolds number for both polymer solutions and water. Accordingly, convection heat transfer coefficient and in tum Nusselt number are increased. When using polymer solutions, the surface temperature of flat tube increases compared with water. Therefore, Nusselt number is decreased. The reduction value in Nu increases with increasing concentration of polymer solution. The average value for this reduction in Nu was about 15%. An empirical correlation for Nusselt number is obtained in the range of the studied operating parameters. Comparison between the obtained experimental results with the previous data is done and gives the same trend.