Anomalous flow at the inlet of pitot tubes in dilute polymer solutions part I

Summary Experimental results about pressure defect of Pitot tubes placed into a laminar jet of dilute polymer solutions are presented.A fast response measuring system of pressure and visualization techniques made evident that the anomalous Pitot tube response is associated with an anomalous flow pattern, in the vicinity of the inlet of the tube and inside it.The flow of effective macromolecular solutions penetrates into the Pitot tubes to a deeper extent than newtonian fluids do; entering the probe, the stremlines break up into vortices, while the pressure signal strongly fluctuates around its mean value. When the recovery of pressure becomes full, these effects disappear.

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Sommario Vengono presentati alcuni risultati sperimentali sul mancato recupero di pressione di tubi di Pitot immersi in getti di soluzioni acquose diluite di macromolecole.L'uso di un sistema rapido di misura della pressione di arresto ed il ricorso a tecniche di visualizzazione hanno reso evidente che il mancato recupero è associato ad un carattere anomalo del flusso all'ingresso del tubo e nel suo interno.Il flusso di quelle soluzioni macromolecolari che risultano efficaci agli effetti del fenomeno in studio, penetra all'interno del tubo di Pitot più profondamente di quanto non facciano i fluidi newtoniani: entrando nel tubo le linee di corrente si rompono in vortici ed il segnale di pressione fluttua energicamente attorno al suo valore medio.Entrambi questi aspetti svaniscono quando il recupero di pressione torna al suo valore teorico di arresto.

     

Anomalous flow at the inlet of pitot tubes in dilute polymer solutions part II

Summary Some correlations are presented of experimental data, which mainly concern the transition from normal to anomalous flow at the inlet of Pitot tubes in dilute polymer solutions.Such transition is associated with the onset of pressure defect, and reveals some aspects of statistical regularity; when the polymer solution is fresh, it happens at a given value of the ratio of flow velocity to Pitot tube diameter v/d, and it seems not dependent or only slightly dependent on the diameter value alone. But the aging of the solution enhances the importance of the diameter value, and the transition value of v/d increases in a different way for different diameters, more quickly in the case of the bigger ones.This behaviour together with the observation that the viscosity does not affect significantly the phenomenon, brings the authors to confirm that such solutions cannot be considered as a viscoelastic continuum, but as a fluid with a structure due to large associations of water molecules and macromolecules, whose linear dimension is significant with respect to the probe diameter.

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Sommario Vengono presentate alcune correlazioni fra i dati sperimentali che riguardano essenzialmente la transizione da flusso normale a flusso anomalo in prossimità ed all'interno della bocca dei tubi di Pitot immersi in soluzioni diluite di polimeri.La transizione è associata alla genesi del recupero incompleto di pressione e presenta caratteri di regolarità in senso statistico; con soluzioni fresche si ha transizione mediamente attorno ad un dato valore del rapporto v/d tra la velocità del flusso ed il diametro del Pitot, in modo indipendente o scarsamente dipendente dal valore del solo diametro.Ma, invecchiando la soluzione, anche il valore del diametro in sè rivela influenza, poiché il valore relativo alla transizione del rapporto v/d cresce più rapidamente per i diametri più grandi. Questo comportamento, assieme alla constatazione che la viscosità non ha influenza rilevante sul fenomeno, conduce a confermare che queste soluzioni non possono essere ritenute un continuo visco-elastico, ma piuttosto un fluido strutturato da larghe associazioni di molecole di acqua e macromolecole, con una dimensione lineare non insignificante in confronto al diametro del Pitot.

     

The rheology of suspensions of porous zeolite particles in polymer solutions

We present data and predictive models for the shear rheology of suspended zeolite particles in polymer solutions. It was found experimentally that suspensions of zeolite particles in polymer solutions have relative viscosities that dramatically exceed the Krieger–Dougherty predictions for hard sphere suspensions. Our investigations show that the major origin of this discrepancy is due to the selective absorption of solvent molecules from the suspending polymer solution into zeolite pores. The effect raises both the polymer concentration in the suspending medium and the particle volume fraction in the suspension. Consequently, both the viscosity of the polymer solution and the particle contribution to the suspension viscosity are increased. We propose a predictive model for the viscosity of porous zeolite suspensions by incorporating a solvent absorption parameter, α, into the Krieger–Dougherty model. We experimentally determined the solvent absorption parameter by comparing viscosity data for suspensions of porous and nonporous MFI zeolite particles. Our results are in good agreement with the theoretical pore volume of MFI particles.     

Rheological behavior of silica suspensions flocculated by bridging

The viscosity and stress relaxation behavior of silica suspensions in polyacrylamide (PAAm) solutions have been studied as a function of particle concentration, particle diameter, and molecular weight of PAAm by the use of a coaxial cylinder type rheometer. The effects of polymer adsorption on the flocculation of particles and the rheological behavior are discussed in terms of bridging. The suspensions of 10-nm silica are remarkably pseudoplastic because the particles are easily flocculated by bridging. The ability of PAAm to flocculate silica particles is very extensive at a molecular weight of 5.5 × 10⁶. For suspensions of 20-nm silica in a solution of PAAm with M_W = 5.5 × 10⁶ − 1 × 10⁷, the apparent viscosity irreversibly increases with shearing time at shear rates beyond a certain value. This may be due to the flocculation by the shear-induced bridging. The suspensions of 40-nm silica show similar flow behavior to the medium irrespective of molecular weight of PAAm. The bridging flocculation is not expected for large particles as one polymer molecule cannot bridge through many particles.     

Effect of polymers on pitot-tube readings

The pressures registered by a Pitot tube in uniform flows of aqueous polyacrylamide solutions have been measured. The tube readings are found to depend on the dimensions of the tube tip, the flow velocity, and the concentration and temperature of the solution. Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 5, pp. 115–118, 1968     

Peessure intensification on the front of a shock wave propagating in a heterogeneous system

An increase in pressure in the wave front as compared to the pulse initiating the wave has been observed experimentally in a study of shock-wave propagation in aqueous suspensions of bentonite [1]. In suspensions in which the solid phase is in the form of colloidal size particles =10^–7–10^–8 m of the mineral montmorillonite with mass content c=6%, with multishock loading an intensification of this effect from experiment to experiment was observed [2]. In order to study the principles involved in this anomalous intensification of pressure on the shock wave front, as well as to clarify the effect of the nature of the material in the dispersed phase, experiments were performed with particles of another broad class of clay-like minerals — kaolinite.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 86–92, September–October, 1986.     

Characteristics of HPAM dilute polymer solutions in three elongational flow situations

Previous work has shown that anomalous pressure behaviour occurs when dilute polymer solutions are subjected to elongational flows such as those existing upstream of a capillary tube entrance, of an orifice and of the stagnation point of a Pilot tube probe. Tests have been conducted with aqueous solutions of HPAM at various concentrations using the above three flow geometries. It is shown that pressure anomalies occured when critical values of the ratio between a velocity and length scale, representative of the strain rate, are exceeded. They are proportional to the power of the strain rate with an exponent larger than one. Based on previous and present results, it appears that the polymer solutions' behaviour may be characterized by three parameters: an anomalous stress magnitude, a relaxation time (inverse of the critical strain rate) and the exponent of the power law. The first two parameters depend on the polymer type, concentration and molecular weight, while the third depends only on the polymer type. The anomalous pressure is also affected by the conformation of the molecules as shown by results obtained with HPAM solutions containing varied amounts of NaCl.     

Wall effects for motion of spheres in power-law fluids

The steady motion of spheres representing particles inside tubes filled with different fluids has been investigated using both a finite-element and a finite-volume method. The rheology of the fluids has been modelled by the power-law able to describe the shear-thinning (pseudoplastic) behaviour of a series of polymer solutions. New results have been obtained for a series of tube/sphere diameter ratios in order to investigate the wall effects on the drag exerted by the fluid on the sphere. The results agree well with previous simulations for an unbounded medium (infinite diameter ratio). Experimental investigations have also been carried out and simulated, and the results compare favourably with the experiments. The present simulations revealed the convergence of the drag coefficient to a constant value independent of tube-to-sphere diameter ratio when the power-law index approaches zero.     

Effect of poly(ethylene oxide) on the rheological behavior of silica suspensions

The steady-shear viscosity, dynamic viscoelasticity, and sedimentation behavior were measured for silica suspensions dispersed in aqueous solutions of poly(ethylene oxide) (PEO). For suspensions prepared with polymer solutions in which the transient network is developed by entanglements, the viscosity at a given shear rate decreases, shows a minimum, and then increases with increasing particle concentration. Because the suspensions are sterically stabilized under the conditions where the particle surfaces are fully covered with by a thick layer of adsorbed polymer, the viscosity decrease can be attributed to the reduction of network density in solution. But under the low coverage conditions, the particles are flocculated by bridging and this leads to a viscosity increase with shear-thinning profiles. The polymer chains with high molecular weights form flexible bridges between particles. The stress-dependent curve of storage modulus measured by a stress amplitude sweep shows an increase prior to a drastic drop due to structural breakdown. The increase in elastic responses may arise from the restoring forces of extended bridges with high deformability. The effect of PEO on the rheological behavior of silica suspensions can be explained by a combination of concentration reduction of polymer in solution and flocculation by bridging.     

Evolution of shock waves in polydisperse gas suspensions with a nonuniform particle concentration distribution

The results of a numerical investigation of the laws of shock wave propagation in polydisperse (two-fraction) gas suspensions with a non-uniform initial particle concentration distribution are presented. Examples of shock wave propagation in extended layers of a gas suspension with linearly increasing, linearly decreasing and sinusoidal laws of variation of the particle concentration are considered. It is shown that when shock waves pass through layers of a gas suspension with increasing and decreasing laws of variation of the particle concentration, respectively, amplification and attenuation of the waves are observed; when shock waves travel through gas suspensions with a periodic law of variation of the particle concentration the pressure distribution behind the wave fronts is nonmonotonic. The solutions corresponding to polydisperse and monodisperse gas suspensions with an effective particle size are examined. The nonequilibrium and thermodynamic-equilibrium solutions are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 183–190, September–October, 1991.     

Electrical double layer and rheological properties of yttria-stabilized zirconia suspensions in solutions of high molecular weight polyacrylic acid polymers

This work deals with the effect of the adsorption of two high molecular weight polyacrylic acid polymers (Carbopol) on the interfacial properties, and the rheology of aqueous zirconia suspensions. Since the Carbopol-covered particles can be thought of as soft colloids, Ohshimas theory was used to gain information on the surface potential and the charge density of the polymer layer (Ohshima H (1995) Electrophoretic mobility of soft particles. Colloids Surf A Physicochem Eng Aspects 103:249–255). The effect of the pH of the solution on the double layer characteristics is related to the different conformations of the adsorbed molecules provoked by the dissociation of the acrylic groups present in polymer molecules. The electrokinetic properties of the suspensions are studied for different pH and Carbopol concentrations in solution in order to investigate the possible stabilization of the suspensions by electrostatic repulsion between the particles. The rheological behavior of the suspensions was investigated in steady-state and dynamic conditions, and the corresponding yield stress and storage modulus were obtained in absence and presence of polymer in solution. The competition between bridging flocculation provoked by polymer adsorption and electrosteric stabilization determines the rheological properties of the suspensions. In the pH range investigated, bridging flocculation predominates at the neutral pH because of the graft of the uncoiled polymer to more than one particle, while at the extreme pH values (pH 3, pH 9) steric or electrosteric stabilization seems to be the predominant mechanism that explains the rheological results. These facts were confirmed by estimating the zirconia particle (or aggregate) diameter in the liquid medium by means of light scattering measurements.     

Structure of detonation waves in gas suspensions of fuel containing the oxidant

The structure of detonation waves in air suspensions of unitary fuels (fuels containing an oxidant such as gunpowder and high explosives) is investigated. In such systems, complete combustion of the particles is possible at a high mass concentration of the fuel. As a result, the structure of detonation differs from that in gas-drop [1–3] and gas [4, 5] mixtures. The shock adiabats characteristic for air suspensions [6, 7] are used to investigate the field of integral curves which describe the structure of detonation waves in disperse media. Calculated distributions of the parameters which characterize the gas and particles in the detonation front are given. The influence of the rate of combustion of the particles and the intensity of interphase friction on the structure of the detonation is investigated. Results of the calculation of the structure of relaxation shock waves in gas suspensions of the solid fuel of rockets are given in [8]. Unsteady problems of convective combustion and the transition of combustion of air suspensions into detonation are analyzed in [9, 10].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 47–53, September–October, 1981.     

Rheological equations of state of weakly concentrated suspensions of rigid ellipsoidal particles

Rheological equations of state of dilute suspensions of rigid ellipsoidal particles (ellipsoids of revolution) are derived [1–4] from the vantage point of the structural-continuum approach, with attention given both to rotational Brownian motion of particles and to their inertia and the outer force fields. Interaction between particles is ignored in those treatments given the low concentration of the suspended particles. In this paper, the earlier findings [1–4] are generalized to higher concentrations. The effect of hydrodynamical interaction between particles on the rheological behavior of the suspension is treated in the light of the Simha approach [5].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 141–145, January–February, 1973.     

Studies on transport phenomena in polymer solutions and suspensions flowing through tubes of tortuous wall geometry

Attempts have been made to analyse the momentum and heat transfer characteristics in tortuous flow of non-Newtonian fluids such as suspensions and polymer solutions through tubes of diverging–converging geometry. The results of the study indicate that the transfer coefficients are significantly higher in such systems as compared to the conventional couette flow (through uniform cylindrical tubes). Moreover, the simultaneous increase in pressure drop due to the tortuous wall geometry has been observed to be relatively insignificant. Fluids with different rheological characteristics such as Bingham plastic fluids, pseudoplastic fluids, Ellis model fluids and fluids obeying Reiner–Philippoff rheology have been studied. The specific advantages of these geometries in providing enhanced performance efficiency have been effectively highlighted.     

Construction of a method for calculating a plane boundary layer in weak solutions of polymers with laminar,transitional, and turbulent flow zones

The investigation of the effect of small polymer additives on the characteristics of the flow of a viscous liquid is, at the present time, one of the most promising approaches to the lowering of the friction resistance. One interesting question in this connection is the study of the effect of small polymer additives on the characteristics of the transitional region of flow in a boundary layer, as well as on the value of the friction resistance with the presence of laminar, transitional, and turbulent sections in the boundary layer. The article sets forth a possible method for calculation of a plane boundary layer and the friction resistance for the case of the motion of a body in weak polymer solutions with a constant concentration, taking account of the change in the flow conditions in the layer and based on the use of integral relationships. Questions connected with the development of a boundary at a body, with the feeding of a polymer in it, as well as with the effect of degradation or destruction of the polymer in the solution, are not discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–48, May–June, 1977.     

Experimental investigation of a turbulent jet carrying heavy particles of a disperse phase

The results are given of an experimental investigation of an immersed jet carrying heavy spherical particles in the case of uniform velocity fields of the particles and the gas and uniform concentration of the particles at the nozzle exit. The laser-optical method was used to measure the velocity fields of the gas and the particles and the concentration of the latter in the flow-rate concentration range of the additive from 0 to 1.5 and particle diameters from 35 to 67 m. It was found that the flow in the jet is essentially nonequilibrium, the disequilibrium and intensity of the mixing in the jet depending on the concentration of the additive and the diameter of the particles. The investigation of the initial section revealed a somewhat anomalous behavior of the jet at a comparatively small (₀=0.5) flow-rate concentration of the additive, and this indicates a need to take into account the prehistory of the flow in the construction of a method for calculating the initial section of a two-phase jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 26–31, September–October, 1981.     

Dynamic equilibrium shape of a film of viscous or viscoelastic liquid

A theoretical and experimental investigation has been made into the dynamic equilibrium shape of an axisymmetric film of liquid formed when a jet encounters an obstacle. It is shown that the stresses due to elastic deformation of the liquid have a significant influence on films of polymer solutions. The elastic moduli of solutions of polyoxyethylene and polyacrylamide are estimated from experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 9–18, March–April, 1980.     

A model of the steady-state motion of suspensions

The authors examine the steady-state one-dimensional motions of suspensions whose particles have a density equal to that of the corresponding dispersion medium. As a whole, the mechanical behavior of such suspensions is described by equations of motion that coincide in form with the Navier-Stokes equations for a certain incompressible fluid whose viscosity is a known function of the particle concentration in the suspensions. To close these equations, the authors postulate a principle of minimum energy dissipation for steady-state motion, which plays the paxt of an equation of state for the suspension. This new equation permits the determination of the spatial distribution in the concentration of solids. Exact solutions are presented for certain variational problems associated with the Poiseuille flow of a fluid of this kind in circular tubes and Couette flows between concentric cylinders and parallel planes. It is shown that in most cases separation of the suspension takes place.     

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.

The main purpose of this study was to examine the viscous and elastic properties and capillary flow of fiber suspensions in Newtonian fluids as well as in polymer solutions. The fillers used were glass, carbon, nylon and vinylon fibers. Glycerin was used as a Newtonian suspending medium and HEC and Separan solutions as viscoelastic suspending media. The viscosity and the first normal-stress difference were measured using a coaxial cylindrical rotating viscometer and a parallel-plate rheogoniometer respectively. The influence of the concentration, aspect ratio, diameter and flexibility of the fibers on the viscous and elastic properties of the fiber suspensions was investigated. Empirical equations were obtained for the relative viscosity and first normal-stress difference for the fiber suspensions in glycerin. The capillary flow of these suspensions is discussed in part II.     

Experimental investigation into the influence of polymer additives in water on the relative permeabilities of porous media

A method has been developed for investigating the relative permeabilities of porous media for oil and for aqueous solutions of polymers; experimental equipment has been developed for determining the phase permeabilities by a stationary method. Investigations were made of the influence of polyacrylamide additives on the change in the relative permeabilities for the simultaneous flow of water and a nonpolar hydrocarbon liquid. It was established that addition of the polymer can lead to a simultaneous reduction in the relative permeability for the wetting liquid and an increase for the nonwetting liquid. The phase permeabilities were obtained for oil and water moving behind a fringe of polymer substance. It was established that the phase permeability for the water phase is a function of the saturation and the amount of sorbate. A cycle of experimental investigations was made into the influence of the rate of pumping and the concentration of the dissolved polymer on the change in the relative permeabilities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 163–167, July–August, 1980.