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.     

HYDRODYNAMICS OF LAMINAR LIQUID JETS. EXPERIMENTAL STUDY AND COMPARISON WITH TWO MODELS

Laminar jets of Newtonian liquids issuing from long vertical cylindrical nozzles and falling freely through stagnant air were studied experimentally for Reynolds numbers between 300 and 1000. Jet diameters were measured from still photographs, and radial distributions of axial velocity were obtained by laser Doppler anemometry. The effect of nozzle diameter, fluid viscosity and surface tension was investigated.

The experimental results were compared with numerical solutions of the Protean coordinate model developed by Duda and Vrentas. The boundary layer simplifications were confirmed to be valid only for the downstream region of the jet and for Reynolds numbers greater than 1000.

The experimental diameters were also compared with predictions from a form of the Bernoulli equation with a surface tension term. The asymptotic validity of the model was confirmed, provided that the dissipation term arising from fluid viscosity could be neglected.

Neither model correlated the jet formation region satisfactorily. For this region, an empirical correlation was developed which improves the diameter prediction and is complementary of either model.     

EVALUATION OF PENG ROBINSON EQUATION OF STATE IN CALCULATING THERMOPHYSICAL PROPERTIES OF COMBUSTION GASES

A set of simple equations of the thermodynamic and transport properties of the combustion gases of a gas turbine have been derived based upon the critically evaluated data and two equations of state: The virial equation of state and Peng-Robinson (PR) equation of state.

The properties which have been considered were, density, specific heat at constant pressure, enthalpy, entropy, viscosity and thermal conductivity.

The temperature range was (200-2600 K) theoretically while the pressure range was (0.3-1.2 MPa).

A computer program, to evaluate the departure of thermophysical properties using virial and PR equations of state, was used.

The Peng Robinson (PR) equation of state gave better estimated accuracy than the virial equation of state especially in evaluating the departure of thermodynamic properties.     

SOLVENT EFFECTS ON THE RHEOLOGY OF AQUEOUS POLYACRYLAMIDE SOLUTIONS†

The influence of solvent chemistry on steady shear viscosity and first normal stress difference for aqueous polyacrylamide solutions (Separan AP-273) was investigated in the Weissenberg rheogoniometer and capillary tube viscometer. It was found that these rheological properties are particularly sensitive to the chemistry of the solvent. For example, the zero shear rate viscosity of a 1000 wppm Separan solution with distilled water as the solvent was greater than that with Chicago tap water as the solvent by a factor of 25, while the first normal force difference varied by a factor of two. The addition of an acid or a base to the Chicago tap water-Separan solution also influenced the zero shear rate viscosity and first normal force difference. It was found that there is an optimum pH of approximately 10 which yields a maximum value of the zero shear rate viscosity for the Separan-tap water solution.

Limited data on the influence of solvent chemistry were obtained for 5000 wppm aqueous solutions of polyethylene oxide (WSR-301) and reveal the same quantitative trends found for the polyacrylamide solutions although the magnitude of the observed changes are smaller.     

VISCOMETRIC MEASUREMENT OF CHROMIUM(III)-POLYACRYLAMIDE GELS†

Gelled polymers are being used increasingly to modify the movement of injected fluids in secondary and enhaced oil recovery processes. A common gelation process involves the reduction of Cr(VI) to Cr(III) in the presence of polyacrylamide. The Cr(III) reacts or interacts with the polymer to form a gel network. Although correlations of gelation time with principal process variables have been obtained, viscometric data have not been reported during or after gelation. These data are needed for fluid flow calculations in surface equipment and estimation of flow behaviour in reservoir rocks.

A Weissenberg Rheogoniometer, with cone and plate geometry, was used to obtain viscometric data for the gelation of polyacrylamide and chromium (III). Solutions consisting of polyacrylamide polymer, sodium dichromate-dihydrate and sodium bisulfite were gelled under a steady shear field at constant temperature. The shear stress versus time profile for the galation process was interpreted to define a gelation time and to determine the apparent viscosity of the gelled fluid. The gelation time decreased as the applied shear rate increased up to about 14.25 sec^-1 and was affected by shear rate history. Viscometric properties of the gelled solutions were determined. Apparent viscosity of the gelled solutions decreased as the shear rate under which they were formed increased.

Post gelation studies indicated that gels exhibited a residual stress at zero shear rate and behaved as Bingham plastics under steady shear. Gels formed at low shear rates were more viscous than gels formed at high shear rates. However, the structure of these gels was susceptible to shear degradation.     

FLOW PROPERTIES OF LLOYDMINSTER AND COLD LAKE CRUDES

Data are presented on the viscosities of Cold Lake Crude and Lloydminster crude, over a temperature range of 278-323 K, up to a shear rate of 662 s^-1

The effect of diluents on the flow properties has been measured and discussed. An Arrhenius-type relation between viscosity and temperature was verified and problems associated with the use of a Contraves Rheomat 30 viscometer were discussed, with respect to measurements of time-dependent material functions such as stress growth, stress relaxation and hysteresis behaviour.     

DRAG AND MASS TRANSFER IN SLOW NON-NEWTONIAN FLOWS OVER AN ENSEMBLE OF NEWTONIAN SPHERICAL DROPS OR BUBBLES

An approximate solution for the slow motion of an ensemble of spherical drops through a power law fluid is obtained using Happel's free-surface cell model. It is shown that the drag coefficient decreases with decrease of the flow index and that this reduction is more significant at low voidage and large viscosity ratio parameter. The effect of the pseudoplastic anomaly on the mass transfer rate is more pronounced at low voidage for large values of viscosity ratio parameter, unlike the case of a single spherical drop

The present analysis covers the whole range of values of viscosity ratio parameter from infinity (an assemblage of solid spheres) to zero (a swarm of bubbles) and reduces to the solutions for those cases already known

The results for the motion of an ensemble of spherical drops also provide the basis for proposing a tentative expression for the expansion of liquid-liquid fluidized bed at low Reynolds number.     

VISCOSITY OF BIOMATERIALS

Viscosity data for honey, corn oil, mayonnaise, yogourt, blood and banana puree have been analyzed using two Theological models: the Herschel-Bulkley model and a proposed model. The proposed model contains three parameters: a yield stress, a parameter having the units of time and a parameter having the units of viscosity.

The model parameters were obtained by non-linear regression and the proposed model was shown to compare favorably with the Herschel-Bulkley equation.

An Arrhenius-type of correlation could be verified between the viscosity of banana puree and the inverse of the temperature. Also, the time parameter (t₁) of the proposed model could be correlated with the temperature and the parameter η₁.

It is asserted that the proposed model should replace advantageously the commonly used Casson expression.     

CONCENTRATED VISCOUS CRUDE OIL-IN-WATER EMULSIONS FOR PIPELINE TRANSPORT

The need to utilize viscous crude oils will increase in the next decade. One means to facilitate pumping of heavy crudes in pipelines is to transport them as concentrated oil-in-water emulsions. Stable emulsions could be prepared by alkali treatment with four of seven viscous crudes studied. Surfactants are formed by reaction of natural acids in the crude with alkali. At crude volume fractions of 60%, emulsion apparent viscosity was lowered as much as 10,000 times.

Viscosities of crude emulsions formed by alkali treatment varied with the nature of the crude and with the ratio of base added to the TAN of the crude. Emulsion viscosities and particle diameters reach extrema close to the equivalence point.

The addition of tall oil enhanced the emulsification ability of some of the crudes with alkali treatment, but one crude required non-ionic surfactant to form an emulsion.     

Freeze-Drying of Pharmaceutical Proteins in Vials: Modeling of Freezing and Sublimation Steps

The commercial finite element code FEMLAB was used to perform two-dimensional axisymmetric simulations of the temperature profiles and the moving front velocities of standard BSA (bovine serum albumin)-based formulations used to stabilize pharmaceutical proteins during the freeze-drying process. The simulations were validated with both experimental and numerical approaches.

In an initial step, the heat transfer phenomena taking place during the cooling of liquid solutions was studied in commercial size glass vials without freezing or sublimation.

Then, this model was extended and validated for the freezing process of aqueous BSA-based solutions encountered in the industrial freeze-drying processes with the same vials in order to confirm the identified values of the different thermal conductances between the product and the shelf and between the product and the surroundings.

Finally, the conductances between the product and the shelf and between the vial and the surroundings thus determined were used in a dynamic sublimation model with two zones and a moving sublimation front similar to the ones previously proposed in the literature.

The simulations showed a satisfactory agreement between experimental and simulated data.

The results of this study demonstrated that the freeze-drying process of pharmaceutical proteins in glass vials for standard industrial operating conditions was mainly controlled by the heat transfer from the shelf and the surroundings to the product sublimation front.     

AN ANALYSIS OF CELLULAR FLOW OBSERVED ON THE INTERFACE OF A PARTIALLY FORMED DROPLET†

In [16], during an experiment designed to model the internal circulation of a forming droplet, secondary surface flows were observed on the droplet interface.

After summarizing the experimental results of [16], we present one possible mechanism, based on the surface surfactant mass transport equation of Levich and the surface stress-strain boundary conditions at a free surface, that provides a good qualitative explanation of the origins and the nature of the secondary motion observed in [16]. The critical hypotheses in this mechanism are that the normal component of ihe vorticity at the free surface is determined primarily by the components of the velocity field tangential to the level lines of the surface surfactant density, near the maxima and minima of that density function and that the normal component of the fluid stress does not vanish at such points.

The consequent analysis of the mass transport equation in the interface shows that the resulting surface motion may be viewed as arising from a resonance phenomenon analogous to the forced vibrations of a spring at resonance.

The effects of adsorbtion-desorbtion and surface dilational viscosity may be incorporated in this mechanism. A method for the experimental measurement of surface dilational viscosities is proposed.     

Peel Adhesion of Solid Films-The Surface and Bulk Effects

The peel strength of rubber and paint films has been measured over a range of peeling velocities using a dead weight method. At low peel rates the peel force is fairly constant but rises rapidly at higher peeling speeds.

Experiments show that the peel strength is a function both of the energy of interfacial bonds which must be broken as peeling proceeds and of bulk energy losses in a viscoelastic peeling material.

The interfacial effect has two components: an equilibrium surface force which accounts for the peel strength at low velocities, and a viscous peeling force which depends on the peeling rate. This viscous interfacial force explains the increase in peel strength of purely elastic films at higher peeling velocities.

The energy loss in the bulk of the peeling film introduces two additional effects: a magnification of the peel strength in steady peeling over a certain velocity range, and a slowing down or stopping of peeling as transient relaxation occurs shortly after the application of the peel force.     

EVALUATION OF POLYMER ADSORPTION-GEL FORMATION AND SLIP IN POLYMER SOLUTION FLOWS

A superposition model for evaluation of the effects of polymer adsorption-gel formation and slip of polymer solutions exhibiting both phenomena has been applied to the capillary flow of aqueous solutions of two molecular weight grades of hydroxyethyl cellulose (Natrosol 250, types G and HR, supplied by Hercules Powder Company). The flow behaviour of the solutions investigated was non-Newtonian. Evaluations are presented of the effective thicknesses of polymer adsorption-gel formation and pure solvent layers, as a function of the wall shear stress, tube radius and polymer concentration, corresponding to the determinations of the effective velocity at the wall.

The results of the analysis indicate the surface characteristics undergo a dramatic change from polymer adsorption-gel formation at the tube surface to the phenomenon characterized by slip in a narrow tube radius interval which has important implications in enhanced oil recovery by polymer solution floods. It also provides an explanation for the contrasting behaviours observed in the flow of aqueous Natrosol solutions through packed beds (Sadowski, 1963) and filter cakes (Kozicki et al., 1972).     

MASS TRANSFER THROUGH PERMEABLE WALLS: A NEW INTEGRAL EQUATION APPROACH FOR CYLINDRICAL TUBES WITH LAMINAR FLOW

Mass transfer through cylindrical semipermeable walls is analyzed. The solution is obtained in terms of integral equations. Despite the existence of a non-homogeneous boundary condition on the semipermeable wall, the solution thus obtained is particularly advantageous since the associated eigenvalue problem is independent of the Sherwood number. This parameter takes into account the main conductances at the tube wall.

The approach is applied to the case of mass transfer from the interior of a capillary tube with semipermeable walls to an external fluid. The flow in the tube is laminar, and the external flow is assumed turbulent.

The mathematical methodology employed provides a framework to develop numerical schemes of fast and sure convergence.     

RHEOLOGICAL CHARACTERIZATION OF NON-NEWTONIAN FLUIDS WITH A NOVEL VISCOMETER

A hydrostatic head viscometer and its novel viscosity equation were developed to determine flow characteristics of Newtonian and non-Newtonian fluids. The objective of this research is to test capabilities of the hydrostatic head viscometer and its novel non-Newtonian viscosity equation by characterizing rheological behaviors of well-known polyethylene oxide aqueous solutions as non-Newtonian fluids with 60 wt.% sucrose aqueous solution as a reference/calibration fluid. Non-Newtonian characteristics of 0.3-0.7 wt.% polyethylene oxide aqueous solutions were extensively investigated with the hydrostatic head viscometer and its non-Newtonian viscosity equation over a 294-306 K temperature range, a 0.14-40 Reynolds number range, and a 55-784 s^-1 shear rate range at atmospheric pressure. Dynamic viscosity values of 60 wt.% sucrose aqueous solution were determined with the calibrated hydrostatic head viscometer and its Newtonian viscosity equation over a 3-5 Reynolds number range at 299.15 K and atmospheric pressure and compared with the literature dynamic viscosity value.     

THE EFFECT OF CONVECTION ON AXISYMMETRIC PARABOLIC DENDRITES

Moving boundary solutions of the Navier Stokes and energy equations are obtained for shape-preserving isothermal paraboloids of revolution by using the Oseen viscous flow approximation. The theoretical results are in good agreement with the precise data of Glicksman et al. on succinonitrilc.

The intensity of thermal convection as indicated by the Grashof number is shown to increase approximately as the inverse of the square of the super-cooling which may have important implications in microgravity experiments.     

RHEOLOGICAL CHARACTERIZATION OF NON-NEWTONIAN FLUIDS WITH A NOVEL VISCOMETER

A hydrostatic head viscometer and its novel viscosity equation were developed to determine flow characteristics of Newtonian and non-Newtonian fluids. The objective of this research is to test capabilities of the hydrostatic head viscometer and its novel non-Newtonian viscosity equation by characterizing rheological behaviors of well-known polyethylene oxide aqueous solutions as non-Newtonian fluids with 60 wt.% sucrose aqueous solution as a reference/calibration fluid. Non-Newtonian characteristics of 0.3–0.7 wt.% polyethylene oxide aqueous solutions were extensively investigated with the hydrostatic head viscometer and its non-Newtonian viscosity equation over a 294–306 K temperature range, a 0.14–40 Reynolds number range, and a 55–784 s^?1 shear rate range at atmospheric pressure. Dynamic viscosity values of 60 wt.% sucrose aqueous solution were determined with the calibrated hydrostatic head viscometer and its Newtonian viscosity equation over a 3–5 Reynolds number range at 299.15 K and atmospheric pressure and compared with the literature dynamic viscosity value.     

Adhesion of Plasticized Polyvinyl Butyral) to Glass

A study of safety glass provides a good example of the interplay among the many physical properties involved in “adhesion”, and the relationship between adhesion and performance. This work demonstrates the value of applying known fundamentals to practical problems.

An idealized model of a windshield fracture event is described in terms of interactions among mechanical responses of the interlayer, the fracture characteristics of the glass and the high speed, low angle peel behavior.

Data on the surface energies of glass, polyvinyl butyral) and water show that at thermodynamic equilibrium a stable system comprising glass, water and polyvinyl butyral) phases, an aqueous phase must lie between the glass and PVB.

The potassium salts are shown to be effective because they are deliquescent and give solutions at equilibrium with the water in the PVB at water contents of ∼0.40% or higher. The greater the amount of salt at the interface and the higher the water content of the sheeting during lamination, the thicker the interfacial layer and delamination occurs more readily. This relationship is quantified using a modified form of the Stefan equation.

Data on diffusion of water and salt are shown to be consistent with the amount of salt at the interface required for the observed performance (∼ 3 mg KAc/m²).

Data on electrical resistivity of the interface correlate with peel force and provide convincing support for the hypothesis.     

A GENERALIZED BUBBLE RISE VELOCITY CORRELATION

A generalized bubble rise velocity correlation is developed to cover the range of conditions:

liquid-phase density = 45.1 to 74.7 lb/ft³,

liquid-phase viscosity = 0.233 to 59 cP., and

interfacial tension = 15 to 72 dynes/cm

The gas-phase is air and the bubble size ranged from 1.2 to 15 mm. The developed correlation is based upon new dimensionless groups which contain the parameters affecting bubble rise velocity as well as their interaction, The correlation is independent of flow regimes and applicable for Reynolds numbers from 0.1 to 10⁴. It is in good agreement with work appearing in the literature.