Flow Of Dilute Polymer Solutions Research Articles

The nature of flows through porous media

The present paper points out that the pressure drop of a porous media flow is only due to a small extent to the shear force term usually employed to derive the Kozeny—Darcy law. For a more correct derivation, additional shear terms have to be taken into account since the fluid is also exposed to elongational forces when it passes through the porous media matrix. These are usually not taken into account in the conventional theoretical treatment of flow through porous media as is explained in the literature. This explains why the available theoretical derivations of the Kozeny—Darcy relationship, which are based on one part of the shear-caused pressure drop only, require an adjustment of the constant in the theoretically derived equation to be applicable to experimental results. Details of this derivation are given in this paper and existing derivations are extended to yield better agreement with experiments. To verify experimentally some of the results of the theoretical derivation provided, porous media flows of dilute polymer solutions are studied experimentally. It is shown that the addition of small amounts of high molecular weight polymers to a solvent with Newtonian flow properties causes drastic pressure drop increases if the flow rate exceeds an onset flow rate corresponding to a critical Deborah number of the porous matrix-polymer solution system. This can only be explained if the flow field in the porous medium is exposed to shear and elongational strain. The extent of this interaction is deduced from experimental findings.

Instabilities with reduced frictional drag in the rotating channel flow of dilute polymer solutions

A numerical investigation is conducted on secondary flows and roll-cell instabilities in the laminar channel flow of dilute polymer solutions subjected to a steady spanwise rotation. Finite difference calculations of the full nonlinear equations of motion for a Maxwell fluid and a Rivlin-Ericksen fluid of the second grade are presented which indicate that there is a double-vortex secondary flow at weak and rapid rotation rates with an instability in the form of longitudinal roll cells at intermediate rotation rates (regimes analogous to those for a Newtonian fluid). However, for a given physical pressure gradient and rotation rate, the introduction of a minute amount of a polymeric additive to a Newtonian fluid so that the Weissenberg number is of the order of 10−5 has a stabilizing effect on rotating channel flow and gives rise to secondary flows with a substantially reduced frictional drag. Comparisions with previously conducted experimental and analytical studies are made along with a brief discussion of potential applications to the field of polymeric drag reduction.

Experimental study on effect of elasticity on drag reduction and turbulent fluctuations in laminar‐turbulent transition region in pipe flow of dilute polymer solutions

AbstractBy utilizing the fact that physical properties exclusive of elasticity of dilute polyacrylamide solutions do not change with elapsed time after preparation, the effect of elasticity on drag reduction and turbulent fluctuations in pipe flow was investigated experimentally.The oscillations of axial velocity and velocity gradient and the drag reduction in the laminar‐turbulent transition region are affected significantly by the value of elasticity. The laminar‐turbulent transition region moves to a higher Reynolds number as the value of elasticity increases.

Flow of Dilute Polymer Solutions Through Curved Pipes : 2nd Report, Pressure Loss in 360°Bends

Experiments on flows of water and dilute aqueous solutions of polyethylene oxide are carried out in the Reynolds number range of 103 to 5× 104. Concentration of polymer solutions is varied from 1ppm to 100ppm. The ratios of curvature radius to pipe radius, R/a, are 18.7, 34.3 and 47.3. Measured pressure distributions along a bend axis are classified in three types by their patterns. Flow property of each pattern is clarified by using the method of flow visualization. Drag reduction in a bend flow is smaller than that in a straight pipe flow. Pressure loss coefficients are correlated with the Reynolds number, the ratio of radius R/a and the Weissenberg number. The empirical formulas presented for the bend loss coefficient are useful from an engineering viewpoint.

UPPER BOUND ON THE STRESS-INDUCED MIGRATION EFFECT IN LAMINAR FALLING FILM FLOWS OF DILUTE POLYMER SOLUTIONS

The role of stress-induced migration in falling film flows of dilute polymer solutions is analysed for the limiting case of fully developed concentration field (FDCF). This theoretically derived asymptote is anticipated to serve as an upper bound on the migration effect and our predictions are shown to be consistent with available experimental observations. However, considerable difference between the FDCF asymptote and the experimental data suggests lack of fully developed conditions in most experiments and hence implies the possibility of flow length dependence, a factor hitherto not considered. Finally, a simple approach based on a two-phase model is developed in order to estimate the order of magnitude of film thickness variation that develops along the film length as migration progresses.

EFFECT OF SUCCESSIVE CONTRACTIONS AND EXPANSIONS ON THE APPARENT VISCOSITY OF DILUTE POLYMER SOLUTIONS

In this paper, we examine the flow of dilute polymer solutions through a succession of contraction-expansion. A strong increase of the apparent viscosity, i.e., a thickening behavior is observed beyond a critical flow rate. The influence of geometrical parameters (number of contraction-expansion, length-to-radius ratio of the constricted sections) and physico-chemical parameters (visocsity and salinity of the solvent, nature of the polymer), on the onset and the magnitude of this thickening behavior has been displayed. The results are interpreted in terms of an increase of the elongational viscosity of the solution, associated with a stretching of the deformable macromolecules.

The flow of dilute polymer solution in a narrow channel. II. Plane Poiseuille flow

As an extension of the previous paper, we derive a similar theory for the plane Poiseuille flow of a dilute polymer solution. The strict enforcement of reflective boundary conditions allows an approximate solution to the Fokker–Planck–Kolmogorov equation to be obtained which is found to be consistent with solutions obtained by Galerkin methods and Monte Carlo simulation. The approximate theory also allows us to derive analytical expressions for the slip velocity and the effective viscosity which are again consistent with the plane Couette flow results derived in the previous paper. The theory is also extended to the nonlinear Warner spring model via Monte Carlo simulation.

The flow of dilute polymer solution in a narrow channel. I. The slip effect in simple shear flow

Existing experimental data have suggested that the flow of a dilute polymer solution near a wall exhibits a slip effect. In the case of a plane shear flow, the suspension of macromolecules contributes a nonuniform stress field profile across the channel which causes the velocity field to deviate from its otherwise linear profile. The apparent slip velocity can be calculated from such deviation. In this paper, we consider the flow problem of a suspension of bead-spring molecules in the presence of solid reflective boundary. Analytical and simulation solutions to the problem are obtained which do not require any small shear rate assumption. The added stresses contributed by the molecules are used to derive the slip velocity and the effective viscosity. Extension to nonlinear Warner spring model is also attempted by the simulation and the results give rise to some qualitative features which cannot be accounted for by the linear model.

Flow of Dilute Polymer Solutions through Curved Pipes : 1st Report, Frictional Loss in the Fully Developed Flow Region

Experiments of the flow of dilute aqueous solutions of polyethylene oxide through curved pipes with circular cross-section are carried out over the Reynolds number range of 500 to 1×104. Concentration of the polymer solution is varied from 0.5ppm to 100ppm. The ratio of the curvature radius to the pipe radius, R/a, of curved pipes is set at 16.3, 28.8 and 46.0. These fluid are found to cause frictional drag reduction under the turbulent flow condition in a curved pipe as well as in a straight pipe. Experimental values of a frictional loss are correlated with the Weissenberg number, the Reynolds number and the radius ratio R/a. The empirical formulas for the frictional loss estimation are proposed separately for both the laminar and the turbulent flow regime. It is also shown that the transition to turbulent flow depends on the Weissenberg number as well as the Reynolds number.

Flow of dilute polymer solutions through curved pipes. 2nd report. Pressure loss in 360.DEG. bends.

Experiments on flows of water and dilute aqueous solution of polyethylene oxide are carried out over the Reynolds number range of 103 to 5×104. Concentration of polymer solutions is varried from 1 ppm to 100 ppm. The ratios of curvature radius to pipe radius R/a are 18.7, 34.3 and 47.3. Measured pressure distributions along a bend axis are classified in three types by their patterns. Flow property of each pattern is clarified by using the method of flow visualization. Drag reduction in bend flow is smaller than that in straight pipe flow. Pressure loss coefficients are correlated with the Reynolds number, the ratio of radius R/a, and the Wissenberg number. The empirical formulas presented for the bend loss coefficient are useful from an enginnering viewpoint.

Experiments on elongational flow of dilute polymer solutions: Part II: velocity field for the flow through small apertures

Following Part I which reported on the jet reaction and the excess pressure drop, this paper describes the results of flow velocities measured upstream of small apertures for dilute polymer solutions. The results suggest the existence of the two flow regimes reorted by Boger and Cable: the vortex growth regime and the divergent flow regime. The former corresponds to the regime of zero jet reaction and the latter to the regime of positive jet reaction. The axial velocity development for PEO solutions along the center line upstream of the aperture is found to yield an extremely high velocity rise at the onset of the vortex region and to give a nearly constant elongational rate within the vortex region. The constant elongational rate takes values such that the product with the relaxation time is about 0.5. Separan solutions do not provide so high a velocity rise at the onset of the vortex region but show an exponential rate of elongation in the vortex region. It is shown, by using the upper convected Maxwell model, that the steep velocity rise at the onset of the vortex region is given in the simplified flow model and the constant elongational rate within the vortex region holds the elongational stress nearly constant.

Quantitative description of rheological properties of dilute polymer solutions

The Rouse-Zimm model has been generalized to describe the rheology of dilute polymer solutions at moderate shear rates by allowing for a reduced-shear-rate dependent slippage of the carrier solvent in the neighbourhood of the polymer coil with respect to the macroscopic continuum. A comparison of the theoretical predictions with published viscosity data for monodisperse polymer systems shows good agreement. Thus it appears to be sufficient to measure the intrinsic viscosity in order to estimate all the material functions of interest for the steady and dynamic shear flow of dilute polymer solutions.

Viscoelastic flow of dilute polymer solutions in regularly packed beds

Viscoelastic flow of dilute polymer solutions in regularly packed beds

Laminar and turbulent flows of dilute polymer solutions: A physical model

Laminar and turbulent flows of dilute polymer solutions: A physical model

Simplified theory of the near-wall turbulent layer of Newtonian and drag-reducing fluids

We propose a simplified theory of a viscous layer in near-wall turbulent flow that determines the mean-velocity profile and integral characteristics of velocity fluctuations. The theory is based on the concepts resulting from the experimental data implying a relatively simple almost-ordered structure of fluctuations in close proximity to the wall. On the basis of data on the greatest contribution to transfer processes made by the part of the spectrum associated with the main size of the observed structures, the turbulent fluctuations are simulated by a three-dimensional running wave whose parameters are found from the problem solution. Mathematically the problem reduces to the solution of linearized Navier-Stokes equations. The no-slip condition is satisfied on the wall, whereas on the outer boundary of a viscous layer the conditions of smooth conjunction with the asymptotic shape of velocity and fluctuation-energy profiles resulting from the dimensional analysis are satisfied. The formulation of the problem is completed by the requirement of maximum curvature of the mean-velocity profile on the outer boundary applied from stability considerations.The solution of the problem does not require any quantitative empirical data, although the conditions of conjunction were formulated according to the well-known concepts obtained experimentally. As a result, the near-wall law for the averaged velocity has been calculated theoretically and is in good agreement with experiment, and the characteristic scales for fluctuations have also been determined. The developed theory is applied to turbulent-flow calculations in Maxwell and Oldroyd media. The elastic properties of fluids are shown to lead to near-wall region reconstruction and its associated drag reduction, as is the case in turbulent flows of dilute polymer solutions. This theory accounts for several features typical of the Toms effect, such as the threshold character of the effect and the decrease in the normal fluctuating velocity. The analysis of the near-wall Oldroyd fluid flow permits us to elucidate several new aspects of the drag-reduction effect. It has been established that the Toms effect does not always result in thickening of the viscous sublayer; on the contrary, the most intense drag reduction takes place without thickening in the viscous sublayer.

Flow of dilute polymer solutions through converging channels

Extensional motion of non-Newtonian fluids was studied by pushing dilute solutions of polyethylene oxide through miniature converging channels. The channels were conical or smoothly converging in shape, and each had an exit diameter around 0.13 mm to make Reynolds number effects comparable. Channels were also made by cementing small beads together, which created passages similar to those in packed beds. Pressure drop and flow rate were measured in each channel and the flow field was observed. Flow patterns and data for the solutions were the same as for water when the maximum rate of extension was below about 10 3 s −2. Above this, the pressure drop for a solution exceeded that of water, and when solution values reached twice the water values, the flow pattern changed abruptly from a simple converging motion to one dominated by a large unsteady vortex ring surrounding the channel opening on the upstream side. This secondary motion persisted at high flow rates, had a variety of forms, and at times produced tiny filaments of polymer, most likely by strain-induced crystallization. Non-Newtonian effects were found to increase with concentration and to decrease with temperature and ago; in each case, much of the effect could be traced to that parameter's influence on the onset of non-Newtonian behaviour. In bead channels with successive convergent sections, onset strain rates were much lower, around 10 2 s −1, indicating that strain history has a strong effect on onset. Disparate onset strain rates for the various single channels, from 300 s −1 to 6000 s –1, were accounting for by considering total extension of the polymer molecules in each flow. In fact, analyses suggest that molecules were stretched about six times their coil size in the converging flows. The large non-Newtonian effect when secondary motion is present is thought to result from high molecular extension or possibly from a contraction of the central flow.

A Study of Extensional Flow of Dilute Polymer Solutions : 2nd Report, Measurements of the Flow Velocities and the Extensional Stresses at Die Entries

希薄高分子溶液の伸張流を実験的に取扱った.すなわち,PEOおよびSeparanの100,200ppm水溶液を用い,オリフィスから溶液が流出する際の装置の受ける反力を測定し,また,細管へ溶液が流入する際の流速をレーザー流速計を用いて測定した.両者の実験結果から,運動量の法則により,伸張流における応力を求めた.この結果は,希薄分子溶液のトムズ効果や構成方程式の検討に基本的に有用と思われる.

Flows of dilute hydrolyzed polyacrylamide solutions in porous media under various solvent conditions

AbstractExperimental results on pressure losses of flows of dilute polymer solutions through porous media are summarized. The polymer products employed in this study consisted of partially hydrolyzed polyacrylamides (HPAM) with different degrees of hydrolysis. The effect of the hydrolysis on the pressure drop is investigated in a porous media test section designed to minimize polymer degradation. The investigations were carried out for various solvent conditions, and it is shown that the maximum increase in pressure drop is mainly dependent on the molecular weight of the polymers. The onset of the polymer action is measured for various fluid and solvent properties. Particular attention is given to measurements near θ‐conditions. The results stress the importance of the solvent properties on the actions of the polymers and on the resultant pressure drop for porous media flows. The addition of salt ions to solutions of partially hydrolyzed polyacrylamides yields onset behavior previously observed for nonionic polymers. The differences measured between various solvent properties can be explained by the actual hydrodynamic molecule dimensions for a given molecular weight and polymer concentration. To quantify the influences of the solvent properties on the polymers, measurements were carried out in aqueous solutions for various pH values and therefore at various degrees of dissociation. The importance of separating polymer effects caused by their linear dimension in the solution from those that are introduced by and increase in solvent viscosity is shown. Measurements were performed to quantify the effects of solvent viscosity on the polymer action and to separate these effects from those due to changes in molecule dimensions. The implications of the present results are stressed in connection with applications of polymer solutions in tertiary oil recovery, and the positive features of the molecule actions on flow in such applications are described.

Elongational flow of dilute drag reducing fluids in a falling jet

An elongational flow of dilute polymer solution in a falling jet was studied. Measurements were made of the stress and velocity distribution along the falling jet by means of a photographic technique. The results show that the relaxation time in dilute drag reducing fluids is much longer than those predicted in a simple shear flow, and suggest the possibility of using a very high value of the relaxation time in a wall turbulence model. Also, the increase in Trouton ratios determined for a simple elongational flow is possibly as high as 27 000.

Molecular models and the Taylor stability of dilute polymer solutions

The stability of the Couette flow of dilute polymer solutions is investigated within a model where the molecule is characterized by a Zimm relaxation time together with a deformability coefficient α lying between zero (underformable molecules) and one (perfectly deformable). It is found that the influence of elasticity on the stability is maximun when the Deborah number of the flow is around one, but it is only when α is less than 0.5 that the critical Taylor number is mostly larger than the constant Newtonian value of the narrow-gap limit.