Factors affecting cake resistance in non-Newtonian filtration

A methodology for evaluation of surface effects including polymer adsorption-gel formation or slip within the pores of a filter cake has been developed and applied to constant pressure filtration of calcium carbonate in aqueous hydroxyethyl cellulose (Natrosol 250G, Hercules Powder Company) slurries. The fundamental framework of non-Newtonian filtration is generalized to include the Blake, Kozeny-Ergun and Kozeny-Carman cake models and the cake resistances γ_K and α_R, in conjunction with the correction terms J_RN and J_gen, within a unified framework. Relationships are developed between the latter quantities and the effect of the bed model on the evaluations of the filtration characteristics is delineated. Significant polymer adsorption-gel formation was found to take place in the constant pressure filtration of calcium carbonate in aqueous Natrosol 250G slurries. The resultant cake porosities were larger and the effective cake porosities lower than comparable porosities for cakes deposited from water slurries. The wide variation of J_RN with the characteristic index N is attributed to the small size of the slurry particles. Polymer adsorption is shown to extend, and slip on the particle surface to reduce the variation of J_RN with N.     

Surface phenomena in capillary flow of polymer solutions

Evaluations of apparent slip and polymer adsorption are reported for laminar capillary flow of dilute aqueous solutions of the three homologues WSR 301, Coagulant and FRA of Polyox. Measurements were carried out using glass tubes coated with a silane compound (dimethyldiethoxysilane) as well as for the untreated glass tubes. The results indicate that flow enhancement is dominant at the very low polymer concentrations and flow retardation is dominant at the higher concentrations comprising the polymer concentration range investigated. A transition from a positive to a negative effective velocity at the wall was observed with increasing polymer concentration. A new analysis was applied to separate the contributions of polymer adsorption and slip in the evaluation of the effective velocity at the wall. Effective hydrodynamic thicknesses of the adsorbed polymer layers are presented as a function of the polymer molar mass and concentration and the wall shear stress. The thickness of the adsorbed layer at zero shear was also evaluated from the capillary flow data.     

Characterization of polymer adsorption in tube flow of drag reducing fluids

Elucidation of the polymer adsorption and flow characteristics at the tube wall is essential for an understanding of turbulent drag reduction. The polymer adsorbed onto the tube wall, in the flow of dilute solutions of linear random coiling macromolecules, also produces a concentrated fluid layer at the surface of the adsorption zone, as a result of the flow of the solvent micromolecules in the porous network comprising the adsorption zone.Velocity profiles are developed and used to determine the radial variation in the adsorption zone of porosity, as well as fractional surface coverages and mean separation or interpenetration distances between macromolecules in the various adsorption layers. The polymer concentration build-up in the concentrated fluid layer is also evaluated. Predictions of the latter for aqueous Polyox WSR-301 solutions are in qualitative agreement with experimental measurements and suggest that turbulent drag reduction is related to the level of polymer build-up in the concentrated fluid layer.     

Tube flow of a particulate-filled thermosetting polymer

The conservation equations of momentum, energy, and mass are numerically solved for the flow of filled thermosets reacting In a tube. The flow is assumed to be laminar and adiabatic with a constant volumetric flow rate. The critical radii are parameters that define the processability limits. The lower one is the value of the radius where an undesirable advance in the reaction extent takes place at the wall or where viscous heating leads to degradation. The upper critical radius is the radius where wall velocity is low and gelation takes place. The effects of filler volumetric fraction, wall slip velocity, and different inlet conditions are taken into account. Increasing wall slip velocity or filler fraction and decreasing inlet temperature or tube length amplify the processability zone.     

THE IMPORTANCE OF SOLVENT COMPOSITION AND ADSORPTION EFFECTS ON THE FLOW PROPERTIES OF

Capillary rheometry data are presented for concentrated solutions of polybutadiene dissolved in mixed volatile solvent systems composed of benzene, butadiene, and butene 1. Unusual flow phenomena, associated with polymer adsorption at capillary tube walls, are observed for polybutadiene in a solvent composed of benzene and butene 1, but not observed at the same polymer concentration in a pure benzene solvent or for a mixed binary solvent where the butene 1 is replaced by butadiene. The unusual flow phenomena include a diameter dependency in the viscosity measurements when end effects are eliminated, and a diameter dependency in the end correction itself. Correction of the diameter dependent viscosity data is successfully made by postulating an effective negative slip velocity (polymer adsorption). The thickness of the polymer adsorbed layer relative to the tube diameter is of the same order as observations for other polymer solutions both in capillary and packed bed flows. It is argued that the flow phenomena observed in the polybutadiene-benzene-butene 1 solutions and not observed in the polybutadiene-benzene-butadiene solutions of identical composition is related to the solvent system itself—benzene and butadiene being a good mixed solvent for polybutadiene relative to benzene and butene 1 in the same ratio. The work was initiated and completed in response to material handling problems encountered in a commercial process for the manufacture of polybutadiene.     

ON THE SWELLING OF SUBMERGED JETS OF DILUTE AND SEMI-DILUTE POLYMER SOLUTIONS

Profound jet swelling is shown to exist when a dilute or semi-dilute solution of PEO (POLYOX WSR 301) is ejected from a capillary tube into a stagnant fluid. The jet swells up to ten times the diameter of the capillary tube depending on the shear rate in the tube and on the density difference between the ejected and the stagnant fluid. The diameter ratio (jet/tube) grows as the 1/3 power of the shear rate, regardless of the density difference, tube diameter and polymer concentration and provided the tube is long enough for the development of the flow profile. For SEPARAN AP 45 solutions, displaying a non-Newtonian behaviour in shear, it is shown that the 1/3 power law holds between the diameter ratio and the shear stress, instead of the shear rate. The analogy between the swelling behaviour of these dilute and semi-dilute polymer solutions and the one observed in concentrated solutions and melts is discussed. The possibility of utilizing the submerged jet technique to compute the polymer solution normal stresses is considered.     

ON THE SWELLING OF SUBMERGED JETS OF DILUTE AND SEMI-DILUTE POLYMER SOLUTIONS

Profound jet swelling is shown to exist when a dilute or semi-dilute solution of PEO (POLYOX WSR 301) is ejected from a capillary tube into a stagnant fluid. The jet swells up to ten times the diameter of the capillary tube depending on the shear rate in the tube and on the density difference between the ejected and the stagnant fluid. The diameter ratio (jet/tube) grows as the 1/3 power of the shear rate, regardless of the density difference, tube diameter and polymer concentration and provided the tube is long enough for the development of the flow profile. For SEPARAN AP 45 solutions, displaying a non-Newtonian behaviour in shear, it is shown that the 1/3 power law holds between the diameter ratio and the shear stress, instead of the shear rate. The analogy between the swelling behaviour of these dilute and semi-dilute polymer solutions and the one observed in concentrated solutions and melts is discussed. The possibility of utilizing the submerged jet technique to compute the polymer solution normal stresses is considered.     

EFFECT OF POLYMER MOLECULAR WEIGHT, SOLVENT AND CASTING SOLUTION COMPOSITION ON THE PORE SIZE AND THE PORE SIZE DISTRIBUTION OF POLYETHERSULFONE (VICTREX) MEMBRANE

The effect of the molecular weight of polyethersulfone (Victrex) polymers, the nature of the solvent and the polymer concentration on the effective hydrodynamic radius of polymer in the membrane casting solution was investigated. The membranes were prepared from the casting solutions studied above and ultrafiltration experiments were performed with polyethylene glycol solutes. The average pore sizes and the pore size distributions on the membrane surfaces were further calculated from the ultrafiltration performance data obtained above. Strong correlations were found between the effective hydrodynamic radius of the polymer in the casting solution and the average pore size on the membrane surface. The mechanism of the pore formation was proposed on the basis of the polymer size—pore size correlation.     

Wall slip of molten polymers

There is considerable experimental evidence that the classical no-slip boundary condition of fluid mechanics is not always a valid assumption for the flow of high molecular weight molten polymers. In fact, molten polymers slip macroscopically at solid surfaces when the wall shear stress exceeds a critical value. Moreover, for linear polymers there exists a second critical wall shear stress value at which a transition from a weak to a strong slip occurs. These two modes of slip (weak and strong) are due to flow-induced chain detachment/desorption at the polymer/wall interface and to chain disentanglement of the polymer chains in the bulk from a monolayer of polymer chains adsorbed at the interface. In this review, the two physical mechanisms of slip are discussed and validated on the basis of published experimental data. The slip velocity of molten polymers is a complex function and has been reported to depend on wall shear and normal stresses, temperature, and molecular characteristics of polymers (molecular weight and its distribution). Proposed slip models, static and dynamic, are also reviewed and their significance on the rheology and flow simulations of molten polymers is discussed.     

DIFFUSION IN NON-IONIC AND IONIC POLYMER SOLUTIONS: EFFECTS OF SHEAR RATE AND POLYMER CONCENTRATION

Diffusion coefficients for ferricyanide ions in aqueous polymer solutions have been calculated from laminar flow mass transfer data obtained in a concentric annulus apparatus by the electrochemical voltammetric method. The electrolyte solutions containing one to five percent polyvinyl alcohol or polyacrylic acid were pumped through the annulus. Flow was longitudinal, and the shear rate ranged from 7 to 800 s-1 The diffusion coefficient for ferricyanide in the polymer solutions depended on polymer concentration in a different way for the non-ionic (polyvinyl alcohol) solutions compared to the polyelectrolyte (polyacrylic acid) solutions. Over the range of concentrations studied, the diffusion coefficient as a function of polymer concentration for polyacrylic acid solutions reached a minimum, increased to a maximum, and then decreased slightly.The polyvinyl alcohol data showed minimum and maximum but no decrease, and the minimum occurred at a higher polymer concentration. For each type of solution, the diffusion coefficient decreased from five to twenty percent as the shear rate was increased from 100 to 800 s-1.The diffusion data can be related to polymer molecule uncoiling and stretching in the flowing solution and to solvation of the molecules present.     

DIFFUSION IN NON-IONIC AND IONIC POLYMER SOLUTIONS: EFFECTS OF SHEAR RATE AND POLYMER CONCENTRATION

Diffusion coefficients for ferricyanide ions in aqueous polymer solutions have been calculated from laminar flow mass transfer data obtained in a concentric annulus apparatus by the electrochemical voltammetric method. The electrolyte solutions containing one to five percent polyvinyl alcohol or polyacrylic acid were pumped through the annulus. Flow was longitudinal, and the shear rate ranged from 7 to 800 s-1 The diffusion coefficient for ferricyanide in the polymer solutions depended on polymer concentration in a different way for the non-ionic (polyvinyl alcohol) solutions compared to the polyelectrolyte (polyacrylic acid) solutions. Over the range of concentrations studied, the diffusion coefficient as a function of polymer concentration for polyacrylic acid solutions reached a minimum, increased to a maximum, and then decreased slightly.The polyvinyl alcohol data showed minimum and maximum but no decrease, and the minimum occurred at a higher polymer concentration. For each type of solution, the diffusion coefficient decreased from five to twenty percent as the shear rate was increased from 100 to 800 s-1.The diffusion data can be related to polymer molecule uncoiling and stretching in the flowing solution and to solvation of the molecules present.     

RHEOLOGICAL AND MIST IGNITION PROPERTIES OF DILUTE POLYMER SOLUTIONS

A spinning disc atomizer has been used to characterize the mist flammability of Jet A and diesel fuels that contain high molecular weight polymers. The critical disc velocity required to produce significant flame propagation was shown to depend on polymer concentration, molecular weight, solvent viscosity, and polymer degradation.

The viscoelastic properties of these same polymer solutions have been characterized by a maximum Darcy viscosity measured from flow in packed tubes. For the polymers discussed in this paper, the maximum Darcy viscosity was independent of the bead size or tube length; however, it was strongly affected by the same variables that affected mist flammability; i.e., polymer concentration, molecular weight, solvent viscosity, and polymer degradation.

The critical ignition velocity of dilute polymer solutions is shown to depend on the Darcy viscosity in a similar manner as observed for viscous oils. At low viscosities, the ignition velocity is only slightly affected, but the dependence grows stronger as the viscosity (both shear and Darcy) increases. A close correspondence was also shown to exist between the ignition velocity of a polymer solution with a high Darcy viscosity and the ignition velocity of a Newtonian oil with approximately the same high shear viscosity.

Numerous similarities are described between flow-induced birefringence of dilute polymer solutions with opposed capillary jets and viscoelastic resistance of dilute polymer solutions in packed tubes. These similarities suggest that the maximum Darcy viscosity is associated with a condition of almost complete extension and alignment of the polymer molecules.     

Electrospun nanofibers from a porous hollow tube

Single electrospinning jets are known to have low production rates. A 0.1 m² nonwoven mat containing 1 g of 100 nm fibers may take several days to create from a single jet. Inexpensive methods of higher production rates are needed for laboratory research applications. In this paper we present experimental results of many simultaneous electrospinning jets from the surface of tube having a porous wall. The pores in the wall are small and resist the flow of the polymer. Holes drilled half way into the wall of the tube provide points of reduced flow resistance. A polymer solution of 15 wt% polyvinylpyrrolidone (PVP) in ethanol is pushed by low air pressure of 1-2 kPa through the tube wall at the drilled holes. On the outer surface of the tube polymer drops form at the locations of the drilled holes. The solution is charged from 40 to 60 kV to electrospin the polymer. Multiple polymer jets launch from the tube surface and form fibers. A 13 cm long tube with 20 holes can produce 0.3-0.5 g/h of nanofiber. Production rates can easily be scaled by increasing the tube length and the number of holes.     

A mechanism for extrusion instabilities in polymer melts

A mechanism for explaining some of the instabilities observed during the extrusion of polymer melts is further explored. This is based on the combination of non-monotonic slip and elasticity, which permits the existence of periodic solutions in viscometric flows. The time-dependent, incompressible, one-dimensional plane Poiseuille flow of an Oldroyd-B fluid with slip along the wall is studied using a non-monotonic slip equation relating the shear stress to the velocity at the wall. The stability of the steady-state solutions to one-dimensional perturbations at fixed volumetric flow rateis analyzed by means of a linear stability analysis and finite element calculations. Self-sustained periodic oscillations of the pressure gradient are obtained when an unstable steady-state is perturbed, in direct analogy with experimental observations.     

Experimental study and modeling of wall slip of polymethylmethacrylate considering different die surfaces

Wall slip of polymethylmethacrylate (PMMA) was studied on different flow channel surfaces using a rheological slit die and a high pressure capillary rheometer. As die surfaces polished steel, ground steel, and Si doped Diamond like carbon (DLC) were used. A new wall slip model is presented in this paper which assumes a lubricating film between the polymer melt and the die surface. The slip velocity has a power law dependency on wall shear stress. In the double logarithmic plot the wall slip curves are linear and can be parallel shifted to higher values with increasing temperature. The predicted dependencies of the wall slip velocity could be confirmed with experiments conducted with PMMA on polished steel. Furthermore, the die surface influences the flow behavior of PMMA. No wall slip was found on ground steel and on DLC. No complete film could be established by the lubricant on the ground steel die wall. The DLC‐coating exhibits a similar surface roughness and surface energy to polished steel, but the chemical composition is different. It is a metastable form of amorphous carbon containing sp² and sp³ bonds. As a consequence slip additives have a low ability to bond to this material. POLYM. ENG. SCI., 58:1391–1398, 2018. © 2017 Society of Plastics Engineers     

THE FLOW OF MICROEMULSIONS THROUGH PACKED BEDS AND CAPILLARY TUBES

The flow behavior of water-in-oil microemulsions through beds packed with glass spheres was studied experimentally. The microemulsions used in this study exhibited a shear thinning viscosity described by a simple power law model. The flow of the microemulsions was accompanied by significant apparent slip effects, quantified by an effective slip velocity. The effective slip velocity increased with increasing surfactant concentration, but it differed in magnitude for the packed bed and the capillary tube flows.

In the absence of apparent slip effects, the capillary-power law (CPL) model predicted the superficial velocities in the packed beds with an average error of less than 6%. This provides a direct verification of the applicability of the capillary-power law model to inelastic shear thinning fluids in the absence of “anomalous” wall effects.     

A numerical simulation of the cavity filling process with PVC in injection molding

Filling cold mold cavities with hot polymer melts at high pressures is of great practical interest. The transport approach to this process of solving the general equations of change with suitable equations of state to describe the flowing material has been largely ignored. No analytic solution is possible, and the non-steady state flow adds a dimension which makes digital computation discouraging because of the core storage and execution time requirements. The mold filled in this simulation is a disk which hot polymer melt enters through a tubular entrance located at the center of the top plate. The tube is 2.54 cm. long and has a radius of 0.24 cm. The plate separation and outer radius of the disk cavity may be varied. A constant pressure applied at the entrance of the tube causes the flow. The cavity walls are kept at various low temperatures. The reported results are for rigid polyvinyl chloride (PVC). The general transport equations, i.e. continuity, momentum, and energy, for a constant density power law fluid are used to solve the flow problem. Convergence to the differential solutions is guaranteed but since a lower limit was imposed on the time increment by the core storage limit of the computer facilities (27K) and long execution times, all results are semiquantitative for the problem as stated. Using the results obtained it is possible to predict “fill times”. The formation of a frozen polymer skin as the cavity fills may be followed via the velocity profiles. The temperature profiles which reflect cooling and the amount of viscous heat generated provide the basis for studying resin thermal degradation effects. Finally, because so much of the total pressure drop is disispated in the entrance tube, and so much viscous heat is generated there, this study indicates that the design of the gate and runner system is perhaps the most important facet of success in mold filling.     

Rheological characterisation of hydroxyapatite filled polyethylene composites. Part 2 – Isothermal compressibility and wall slip

Abstract

Rheological characterisation of hydroxyapatite–high density polyethylene (HA–HDPE) composites has been performed in terms of isothermal compressibility and wall slip. Addition of HA to the polymer melt decreases the compressibility of the melt. The unfilled HDPE was found to exhibit wall slip at shear stresses as low as 0·10 MPa. The flow curves of the composites showed three distinct regions: a gradient at low shear rates; a plateau region; and a gradient at higher shear rate. An increase in rheometer pressure seems to suppress the slip in composites. The 40 vol.-% HA–HDPE composite exhibited two critical shear stresses, one corresponding to wall slip, which occurs in the lower shear rate region of the flow curve, and the other corresponding to a plateau, which is identified with the stick–slip behaviour of unfilled HDPE reported in the literature. The plateau shear stress increased with filler volume fraction and this effect is attributed to the decreased compressibility of the melt. A good correlation with a negative correlation coefficient was found to exist between compressibility and shear stress in the plateau region. The slip observed in unfilled HDPE and at low shear rates in the 40 vol.-% HA–HDPE systems has been explained in terms of a low molecular weight polymer layer formed at the melt/wall interface. The large interfacial slip observed in the plateau region is attributed to complete disentanglement of adsorbed chains from free chains at the melt/wall interface at and beyond the plateau region.     

Use of molecular dynamics to investigate polymer melt-metal wall interactions

The classical boundary condition of fluid dynamics, i.e. the no-slip condition is violated during the flow of various complex fluids including polymer melts and polymeric suspensions. It is recognized that the dynamics of the behavior of the macromolecules at the wall, their adsorption, and disentanglement from each other and from the wall all play significant roles during shearing and flow. During wall slip it is not clear whether the macromolecules detach from the wall (adhesive failure of the slip condition) or whether the macromolecules remain tethered to the wall but disentangle from the neighboring macromolecules (cohesive failure). In this study, we seek to shed light to the basic mechanisms of the wall slip of polymers by focusing on the dynamics of the polymer behavior at the wall for three polymers, two of which exhibit significant strong wall slip, high density polyethylene (HDPE) and poly(dimethylsiloxane) (PDMS), and one which does not exhibit wall slip under typical extrusion conditions, i.e. a block copolymer BAMO/AMMO, (crystalline blocks of poly(3,3-bis(azidomethyl)-oxetane), BAMO, and amorphous blocks of poly(3-azidomethyl)-3-methyl-oxetane, AMMO). The cohesive energy densities of the three polymers were found to be in the same range, with the cohesive energy density of BAMO/AMMO being slightly higher than those of the other two. The molecular dynamics based cohesive energy density values compared well with calculations based on the determination of the group molar attraction constants. On the other hand, the energy of adhesion value exhibited by the copolymer BAMO/AMMO/iron oxide is significantly higher than the energy of adhesion values for the iron oxide/PDMS and iron oxide/HDPE systems. Considering that over the same broad range of shear stresses the block copolymer BAMO/AMMO does not exhibit wall slip and the other two polymers HDPE and PDMS do, these findings suggest that at least for these three polymers wall slip is more likely to occur on the basis of an adhesive failure mechanism.     

The turbulent diffusion of drag-reducing polymer solutions from a point source in flow through a pipe

Solutions containing salt(NaCI) were injected into water flow through a fine tube at the centre of a pipe. Tests were made to ensure that the flow was turbulent and well developed at the injection point; and that neither the injection process nor the injector caused any appreciable flow disturbance. Radial concentration profiles were measured at various downstream distances by withdrawing samples from the flow and measuring their electrical conductivity. A comparison was made between water, and aqueous solutions of polyethyleneoxide and polyacrylamide. Results for the eddy diffusivity in water agreed with those from previous investigations. Turbulent diffusivities were found to be greatly reduced in the polymer solutions (even after allowance had been made for the reduced wall shear stress) compared to the values for water alone. There were detailed differences in the effects of the two different kinds of polymer and these were attributed to their different viscoelasdc properties in the concentration ranges studied.