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A theory is presented which describes the dynamics of blade-coating of a viscoelstic fluid onto a moving sheet. The method begins with the usual “lubrication” approximation, and develops the solution as a perturbation about the Newtonian case. Viscoelasticity is described by an empirical constitutive equation which shows non-Newtonian viscosity and finite normal stress behavior consistent with typical observations of polymeric fluids. Theoretical results indicate a small increase in coating thickness due to departure from Newtonian behavior, and a significant decrease in the magnitude of the pressure developed under the blade. Consequently, the blade loading can be reduced significantly by viscoelastic effects. The results for the loading may be an artifact of the specific constitutive model, since it can be shown that some viscoelastic fluids, specifically an “elastic Newtonian” fluid, would exhibit increased loading relative to the inelastic Newtonian case.

Lodge's molecular network theories are quite successful in describing the linear viscoelastic behavior of polymer solutions and melts, but cannot account for the rate‐of‐strain dependence of various material functions. By allowing the junction‐creation rate and the probability of loss of junctions to depend on the second invariant of the rate‐of‐strain tensor, more realistic constitutive equations were obtained. Two rheological models are proposed by assuming two different mechanisms for the effect of the rate of strain on the kinetics of the network. The experimental data on three fluids (representative of eight viscoelastic fluids) are used to test the models in various flow situations. For steady simple shearing and small‐amplitude, sinusoidal simple shearing, both model A and model B are capable of fitting the four functions η, −(τ11−τ22), η′, and G′ rather well over many decades of shear rate or frequency. For suddenly changing flow experiments model A is inadequate. Model B however appears to be the...

The flow of a non-Newtonian fluid with an exponential rheological equation is investigated in the barrel of an extruder screw with consideration of the presence of circulating motion of the fluid in it.

The analytical solution to the equation of motion is given for the steady laminar flow of a uniformly conducting incompressible non-Newtonian fluid between two parallel planes. The fluid is under the influence of a constant pressure gradient and is subjected to a steady magnetic field perpendicular to the direction of motion. Two non-Newtonian models are considered: the Bingham plastic model and the power-law model. Flow rates and the velocity profiles for various values of the Hartmann number and the generalized Hartmann number are presented and compared with those corresponding to Newtonian fluids.

To study the effects of the high elongational viscosity on the free (“grid-generated”) turbulence of polymer solutions, a Burgers-type model equation is proposed and formed by replacing the Newtonian viscosity of the original Burgers equation with a non-Newtonian viscosity. By using the proposed model equation, numerical experiments were carried out to compute the energy decays, the changes in the energy spectra, and the variations of the mean square of the velocity gradient with time. Comparisons between the Newtonian and the non-Newtonian cases were based on the same Reynolds numbers and the same initial random velocity fields generated by a Gaussian process with two types of spectrum. Measurements on real grid turbulence are discussed in the light of these calculations. The computational results show, in general, the suppression of “shock waves” because of the non-Newtonian viscosity effect, but the turbulent decay rate at large Reynolds number is not always increased, which is surprising. It appears that the calculations support qualitatively the idea of vortex stretching inhibition in polymer turbulence due to high elongational viscosity.

Creeping flow past a sphere is solved for a limiting case of fluid behaviour: an abrupt change in viscosity.

Since the shear rate of a non-Newtonian fluid is of importance in fixing the rheological or viscometric behavior of such a material, the present study has been concerned with the development of a general relationship between impeller speed and the shear rate of the fluid. The resulting relationship was then used to interpret and correlate power-consumption data on three non-Newtonian fluids by use of a generalized form of the conventional power-number–Reynolds-number plot for Newtonians. Flat-bladed turbines from 2 to 8 in. in diameter were used exclusively. Tank diameters ranged from 6 to 22 in. and power inputs from 0.5 to 176 hp./1,000 gal. The study encompassed a 130-fold range of Reynolds numbers in the laminar and transition regions. The results to date indicate that power requirements for the rapid mixing of non-Newtonian fluids are much greater than for comparable Newtonian materials.

The periodic squeeze motion of a thin fluid film formed between two parallel planes is considered. The fluid is assumed to exhibit shear dependence and relaxation properties. Analysis shows that a time‐average super‐ or subambient pressure is generated which depends on the ratio of the periods of the compression and expansion strokes. Fluid consistency, shear rate exponent, plate geometry, and stroke affect the magnitude of the pressure values. The relaxation constant of the fluid enters only into the transient and the periodic parts of the squeeze film response. These effects are not obtained for Newtonian fluids or if the compression and expansion periods are equal.

This paper presents a study of flux, film thickness, and velocity profiles in the drainage and withdrawal processes of non-Newtonian fluids on flat plates. The flow equations for the drainage from a vertical plate are solved for a three-constant or Ellis model fluid. The solution is compared with that of the Newtonian fluid. The withdrawal case is solved for the power law fluid. The solution consists of matching of the equation of capillary statics in the liquid bath to the flow equation in the entrained film. Experimental data of coating of an endless belt with a film of a non-Newtonian fluid are presented and discussed in view of the theory developed.

The equations of motion and continuity are solved together with the slow-flow stress equations for an incompressible Rivlin-Ericksen fluid. The boundary conditions for slow flow past a sphere are satisfied by matching inner (Stokes) and outer (Oseen) Reynolds-number expansions of the stream function. The terms in the inner expansion are the solutions of non-linear partial differential equations which are solved approximately by expanding in terms of a non-Newtonian parameter λ. The drag force on the sphere is obtained from the solution.

1. Flow between two parallel plates. Assume that a layer of nonNewtonian fluid with the theological equation (0.2) is loated between two parallel plates y = h and y = h, and that the upper plate moves in the direction of the positive x axis with constant velocity V. The fluid adheres to the wails having the temperatures To and Tt (T O > T1). The system of equations of motion and heat conduction may be written in dimensionless form

Analysis of the laminar flow of a non‐Newtonian fluid between rotating parallel planes permits the viscosity to be calculated as a function of shear rate from data of torque vs angular velocity. Experimental results are presented which show that the non‐Newtonian viscosities thus obtained agree with capillary, Couette, and cone‐and‐plate instruments over a four‐decade shear rate range.

Equations are given for the velocity distribution and couple when a sphere is rotated in an inelastic, power law non-Newtonian fluid, and the application of the equations to measuring the fluid parameters at low shear rates is discussed.

The stability of a rotating layer of Maxwellian fluid heated from below is considered. It is found that the Coriolis force has a destabilizing effect on the fluid having a viscoelastic nature in contrast with its stabilizing effect on the Newtonian fluid.

A theoretical relation has been obtained for the mass flux to a rotating disk in a non‐Newtonian fluid which includes the convective transport in the radial direction. This result has then been used to obtain improved values for the diffusivities of oxygen in aqueous sodium chloride solutions which were rendered non‐Newtonian by addition of Polyox WSR 301.