Generalized Newtonian Fluid Research Articles

BEM-NN computation of generalised Newtonian flows

This paper presents a boundary-element-only method (BEM) for the calculation of generalised Newtonian fluid (GNF) flows. The volume integral arising from non-linear effects is approximated via a particular solution technique. Multilayer perceptron networks (MLPN) and radial basis function networks (RBFN) are used for global approximation of field variables and hence volume discretisation is not required. The iterative numerical formulation is achieved by viewing the material as being composed of a Newtonian base (artificially assigned with a constant, but maybe different from subdomain to subdomain, viscosity) and the remaining component, which is accordingly defined from the original constitutive equation. This decoupling of the non-linear effects allows a Picard-type iterative procedure to be employed by treating the non-linear term as a known forcing function. However, convergence is sensitive to the estimate of this forcing function and an adaptive subregioning of the domain is adopted to control the accuracy of the estimate of this non-linear term. The criterion for subregioning is that the velocity gradient should not vary significantly in each subdomain. This strategy enables convergence of the present method (BEM-NN) at power-law index as low as 0.2 for the difficult power law fluid. The use of MLPNs (instead of single layer perceptrons) and RBFNs is another contributing factor to the improved convergence performance. The overall scheme is very suitable for coarse-grain parallelisation as each subdomain can be independently analysed within an iteration. Furthermore, within each subdomain process, there are other parallelisable computations. The present method is verified with circular Couette and planar Poiseuille flows of the power-law, Carreau–Yasuda and Cross fluids.

Laminar, unidirectional flow of a thixotropic fluid in a circular pipe

In this paper we study the unidirectional, axisymmetric flow of a bentonite mud in a circular pipe. Bentonite mud is an inelastic, thixotropic, generalised-Newtonian fluid. We use a rheological model that characterises this behaviour in terms of a single parameter Λ which is a measure of the amount of structure in the fluid. The behaviour of Λ is determined by a single rate equation which models the tendency of fluid structure to increase whilst being limited by the imposed shear rate. We find that, for certain parameter ranges, the model is not structurally stable, but that this problem can be eliminated by including diffusion of fluid structure. A graph of the equilibrium shear stress for a given shear rate (the rheogram) is not monotonic, yet no mechanical instability occurs in pipe flow. We contrast this with recent work on the pipe flow of a Johnson-Segalman-Oldroyd fluid which displays spurting and oscillatory behaviour. The difference lies in the relative magnitude of normal stress effects in the two fluids. There appear to be no grounds for discarding the constitutive model studied here simply because of the non-monotonicity of the equilibrium rheogram.

Error estimates for a mixed finite element method for a non-Newtonian flow

We consider in this paper two models of generalized Newtonian fluids (GNF), the Carreau viscosity expression and the power law. The calculation of flows following these laws is considered in a mixed formulation and approximated by a conforming triangular finite-element method of Taylor Hood type using P 2 continuous approximation of the velocity and P 1 continuous approximation of the pressure. The purpose of the paper is to describe the dependence of the numerical efficiency of the method with respect to the chosen law and in particular to the exponent in the power law. For a Carreau model with a strictly positive second plateau this efficiency is the same as for a Newtonian fluid. For a power law with exponent n − 1 the efficiency decreases from the Newtonian case, n = 1, to the limit case, n = 0.

Material Functions for Generalized Newtonian Fluids

The concept of the generalized Newtonian fluid (GNF) provides a useful basis for the formulation of constitutive equations for real materials. The purpose of this paper is to review the rational foundations of the generalized Newtonian fluid, and to discuss the problems involved in its practical application to real materials. Of special interest are the types of material constants which must appear and the dimensionless groups which govern the solutions of boundary value problems. It is demonstrated that, if the material function of a GNF contains one material constant with units of viscosity, it must also contain at least one material constant with units of time (or reciprocal time). The role of this characteristic time for both purely-viscous and elastic fluids is discussed.

Experimental tests of generalised newtonian models containing a zero‐shear viscosity and a characteristic time

AbstractThis paper is a summary of six experiments which have contributed to our understanding of the utility of generalized Newtonian fluid (GNF) models, and particularly those which have a “zero‐shear viscosity” and some kind of a “characteristic time”. The accumulated evidence seems to support the use of such models for a wide range of technical applications: steady state flow in complex systems, steady state heat transfer, and slow unsteady‐state flow.