Drag reduction in dilute polymer solutions

The problem of drag reduction in a helically coiled tube is examined experimentally. The general problems involved in the correlation of drag reduction data are analyzed critically, and some important recommendations are made based on the findings of this work. A phenomenological approach is suggested for correlating the drag reduction data. An examination of the straight-tube data from the literature and the coiledtube data obtained in this work shows that for a variety of aqueous polymer solutions the data could be uniquely correlated by the following equation: where β = reduced friction factor and De′ = modified Deborah number.     

Diffusion of electrolytes in dilute polymer solutions

The diffusion of sodium chloride in dilute solutions of carboxymethylcellulose (CMC) was studied using the porous frit technique. It was found that at relatively low CMC concentrations the diffusivity of sodium chloride (D) is higher than that in water (D₀); with increasing CMC concentration, the diffusivity decreases gradually and reaches a value lower than that in water. The relation between the diffusivity (D) and CMC concentration (C_p) was represented by the equation D = a – bC_p. The effect of temperature on the diffusivity of sodium chloride in CMC solutions was found to obey the Arrhenius equation with an activation energy of 2230 cal/mol.     

Expansion-contraction behavior of dilute polymer solutions

Expansion-contraction behavior of capillary jets of dilute polymer solutions has been studied by using small diameter capillary tubes. The test liquids were water, glycerine solution and dilute solutions of polyethylene oxide and guar gum. It has been found that polyethylene oxide molecules degraded considerably at high shear rates; however the molecular degradation had little effect on the observed expansion-contraction behavior of capillary jets. On the other hand, the solvent viscosity had an appreciable effect on the issuing jets and on the final magnitude of the evaluated normal stresses     

Quasielastic scattering from dilute polymer solutions

The initial slope $\text{Ω(q)}$ of the time-dependent scattering function and the static structure factor S(q) of macromolecules in good solvents are calculated without using the Gaussian assumption. For S(q), the scaling relation S(q)～q^?1.7 is confirmed in the intermediate q range, whereas no q dependent cross-over behaviour can be observed. The calculation of $\text{Ω(q)}$ reveals a q³ dependence in this range and no evidence is seen for an exponent apart from 3. The time-dependent scattering function S(q,t) is treated within the framework of the Gaussian assumption. Hydrodynamic as well as excluded volume interactions are incorporated. It has been found that excluded volume effects decrease the decay of the scattering function in comparison with the Gaussian chain.     

Flow microcalorimetry on dilute polymer solutions

A flow microcalorimeter designed to measure the heat of mixing of dilute polymer solutions is described. The instrument is sensitive to steady state heating rates of ～10 μJ/sec. Measurements of heats of mixing of solutions of differing concentrations of n-hexane and cyclohexane are reported and are compared with recommended data of McGlashan and Stoeckli. Values of:

$\text{K}{}_1\text{=}\text{lim}\text{V}{}_2\text{→ 0}$

$\text{(}\text{H}\text{?}{}_1\text{?}\text{H}\text{?}{}^0{}_1\text{RTv}{}^2{}_2$ are obtained for four polymer—solvent systems: polyisobutylene—benzene, 0.22; polystyrene (PS)—cyclohexane, 0.33; PS—n-butyl acetate, ?0.06 all at 25°C; and PS—toluene, ?0.05 at 40°C. Various theoretical calculations of second virial coefficients A₂ made with use of the calorimetric data are compared with previously measured A₂ for the first two mixtures.     

Vortex flow of dilute polymer solutions

It has been observed that very d longchain polymers which are effective in turbulent drag reduction inhibit the formation of a vortex or air core as water drains from a tank. This paper considers the fluid mechanical velocity profile measurements have been performed. There appear to be at least two distinct mechanisms for the vortex inhibition—one involving the viscosity enhancement caused by polymer addition, and the other related to the viscoelastic properties of the polymer solutions. This second mechanism is shown to arise due to the generation of high normal stresses as the air core begins to form. The very close correlation between vortex inhibition and turbulent drag reduction suggests that normal stresses may also play an important role in this latter phenomenon.     

Apparent elongational viscosity of dilute polymer solutions

Apparent elongational viscosity studies were made on dilute solutions of high molecular weight polymers using a fiber spinning apparatus designed for low shear viscosity liquids with substantial elongational effects. The experimental method involved the flow of solutions of polyacrylamide and poly(ethylene oxide) from a tube into an evacuated vessel. Experimental results showed that the apparent elongational viscosity obtained from the jet shape increased linearly with the stretch rate.     

Adsorption measurements in dilute solutions of a drag-reducing polymer

Experimental evidence supporting an adsorptional mechanism for the reduction of friction drag in the turbulent pipe flow of dilute solutions of a polyoxyethylene in water has been obtained in the form of adsorption measurements, measurements indicating increased additive concentrations at the pipe wall, and additive axial dispersion measurements. An analytical method used to determine very low concentrations of polyoxyethylene in water (2–100 ppm) is reported.     

Turbulent heat and mass transfer in dilute polymer solutions

A new model based on Levich's three-zone model is developed to discuss the turbulent heat and mass transfer in drag-reducing solutions. The proposed model, which has no adjustable parameters and is represented in an explicit form, provides satisfactory predictions of the maximum heat and mass transfer reduction in smooth and rough pipes. The mass transfer to a disk rotating in drag-reducing solutions is also discussed using the proposed model.     

Turbulent flow behaviour of dilute polymer solutions in an annulus

An experimental study has been carried out to investigate the turbulent flow behaviour of dilute polymer solutions in an annulus. The polymers used are two grades of Separan, AP30 and MG500, both are known to exhibit drag reduction characteristics in turbulent pipe flow. Similar drag reduction phenomena have been observed in annulus flow. At a given Reynolds number, the friction factor decreases with increase in polymer concentration and appears to reach a minimum (or maximum drag reduction) at certain optimum concentration. An estimate of the critical wall shear stress, which marks the onset of drag reduction, is consistent with pipe flow results, suggesting that the critical value is independent of flow geometry and size. A lower drag reduction, achieved in an annulus in comparison with circular pipes, is attributed mainly to a diameter effect.     

Huggins' constant and unperturbed parameter of dilute polymer solutions

A novel method developed to evaluate the unperturbed parameter K_θ from the viscometric data of dilute polymer solutions can be considerably simplified by making the reasonable assumption that the Huggins' constant under theta conditions, k_Hθ, is equal to ½ for a number-average degree of polymerization of over about 2000. Two linear equations are derived pertaining to the present analysis, one to deal with the experimental data, and the other specially to estimate the intrinsic viscosity [η]θ which corresponds to κ_Hθ. All calculations were done by the linear least-squares method. The K_θ was computed by the Mark–Houwink–Sakurada equation. It is shown that reliable results on K_θ can be obtained for polystyrene and poly(vinyl acetate).     

Thermomechanics of dilute polymer solutions: multiple bead-spring model

Using the Rouse—Zimm model of the marcomolecule, the stress constitutive equation of dilute polymer solutions is derived in the form of a functional of temperature and deformation histories.The non-equilibrium thermodynamics of the system is also considered by relating excess free-energy, entropy and dissipation first to the distribution function and then to the histories of temperature and deformation. Similarly to the case of the stress, the excess internal energy functional can be derived without explicit knowledge of the distribution function.     

Internal viscosity-normal mode description of ultrasonic absorption in dilute polymer solutions

A normal mode model of ultrasonic absorption in dilute polymer solutions is constructed by including internal viscosity and stiffness terms in the polymer equations of motion. The normal mode Smoluchowski equation is solved and the relaxing specific heat calculated by averaging over two different energy absorption terms: a bending force term of the type used by Harris and Hearst and an energy term resulting from a change in the end to end distance of the polymer. The results are then compared with some recent ultrasonic absorption measurements of Cochran, Dunbar, North and Pethrick on dilute polystyrene-toluene solutions. We find that both specific heat terms provide an explanation of the shape, position and molecular weight independence of the single relaxation for large molecular weights, but are unable to describe the molecular weight dependence observed by Cochran et al. when the molecular weight goes below 10 000. There is also some difficulty in obtaining exact numerical agreement between the calculated and observed absorption amplitudes.     

Data fitting in photon correlation spectroscopy studies of dilute polymer solutions

Two methods of processing data from photon correlation studies of polydisperse polymer samples in dilute theta solution have been compared using computer generated correlation functions. Force-fitting a single exponential to the data gives a value for the diffusion coefficient D only slightly less than D_z, the z-average value returned by the cumulants method. Both methods are shown to give the same concentration dependence for D.     

Flow and dynamic behavior of dilute polymer solutions in hydrodynamic chromatography

Recently, hydrodynamic chromatography (HDC) has become an important probe for determining the molecular size or molecular shape in the sub-micron range. Although a lot of studies on HDC were performed, the clear understanding on the transport behavior of polymer solutions in porous media has not been achieved yet. In this study, the flow and dynamic behavior of polymer molecules in a packed HDC column is fully analyzed by extending the molecular kinetic approach of dilute polymer solution in aconfined geometry to elucidate the effects of relativeparticle sizes as well as theflow strength on theretention factor (R _f ). R _f equation of each simple polymer model was developed- and the numerical simulation was worked out to illustrate the R _f for rigid rod(RR) polymers. Theoretical predictions were in remarkable agreement with our experimental results of xanthan gum and other published data despite of several approximations. Significant size effects were observed, and for RR model the R _f decreased with increasing the flow strength within a particular range. This feature emphasized a transition behavior from weak to strong flow due to theorientalional effect of xanthan molecules. It should be noted that our major concern is restricted solely to the hydrodynamic force.     

Differences in behavior between dilute and concentrated polymer solutions in elongational flow

In this paper, the different behavior of dilute and concentrated solutions (or melts) during an elongational flow is discussed. Some experimental results obtained with a concentrated polyacrylamide solution in water are presented together with a brief review of previous results relative to dilute solutions and melts. An interpretation of the data is attempted on the basis of well known concepts of macromolecular physics together with assumptions concerning the destruction and reformation of entanglements during the flow of the polymer.     

Mass transfer from cylinders rotating in Newtonian fluids and dilute polymer solutions

A new theoretical expression for tubulent mass transfer from a rotating cylinder has been proposed using Levich's three-zone model. The predictions of this model, which has no adjustable parameters, were compared with available experimental data and with other correlations for Newtonian fluids and the agreement was found very satisfactory. Equally good agreement was found between the predictions of our model and the available data for mass transfer from a rotating cylinder under the conditions of maximum drag reduction.     

Dynamic light scattering from dilute and semi-dilute water soluble flexible polymer solutions

Summary Low angle quasi-elastic light scattering has been used to measure translational diffusion coefficients of sodium salts of partly hydrolyzed polyacrylamide samples in the presence of added NaCl.Experiments have been performed both in the dilute concentration range and above the critical concentration for overlapping of polymeric chains.The results reported in the semi-dilute domain are in agreement with the scaling laws predicting the concentration dependence of diffusion coefficients of flexible coils in good solvent condition.     

Some limitations on the detection of high elongational stress effects in dilute polymer solutions

The elongational flow behavior of dilute polymer solutions is of great current interest because it has been suggested that elongational viscosity effects may be involved in a number of phenomena such as turbulent drag reduction and flow cavitation suppression. Unfortunately, recent experiments, in trying to investigate elongational effects, have produced widely varying results. In this paper, an attempt is made to analyze one of the factors that contribute to this diversity. By using a generalized convected Maxwell model, it is shown that in a transient elongational flow, both stretching rate and flow time must reach the proper values before high stress levels can be observed. This is true for both accelerating flows such as through a cone or wedge and decelerating flows such as in a free jet. Since most previous experiments have not considered flow time, consistent results cannot be expected. Consequently, the proper control of all flow conditions is an essential requirement when trying to observe high stress levels. The results presented here provide valuable guidelines in this regard.