Abstract
A fully-developed flow of a non-Newtonian pseudoplastic fluid through a circular pipe has been studied using a four-parameter model, as an example, for the shear-rate dependent apparent viscosity. The model used in this investigation is a modification of the two-parameter Ostwald-de Waele power law [1], which correctly represents the lower and upper regions of Newtonian behavior characteristic of pseudoplastic polymer melts and solutions. Since there has only one set complete experimental data available for the shear-rate dependent viscosity, we use them to show that a perfect match can be achieved between the modified power-law viscosity model and the experimental data. Such a perfect match is required for an accurate prediction of the flow behavior in internal flow problems.
Highlights
A non-dimensional parameter governing the flow has been identified, which is the ratio of the length scale, introduced by the empirical correlation of the variable viscosity and the radius of the pipe
It is our opinion that this kind of length scales must exist for all problems whose formulation would be incomplete without empirical correlations to model the physics of problems, but have rarely been discussed
When the value of the non-dimensional parameter is small, the fluid behaves like a Newtonian fluid with a viscosity equal to the zero-shear-rate viscosity, as the shear-rate magnitude is not large enough to induce non-Newtonian behavior
Summary
A non-dimensional parameter governing the flow has been identified, which is the ratio of the length scale, introduced by the empirical correlation of the variable viscosity and the radius of the pipe. The studies of external boundary-layer flows of non-Newtonian fluids [9] [10] [11] [12] [13] [14] [15] [16] established that self-similar solutions of the boundary-layer equations do not exist, as the power law introduces a characteristic length scale in the problem formulation. In this investigation, the modified power-law proposed by [9] has been used to study fully-developed flow in a circular pipe, which is a typical example of internal flow. The results have been compared with those predicted using the power-law model
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