# Help with friction factors for non-Newtonian fluids

I've been researching about friction factors for non-Newtonian fluids and I've found quite inconsistent results. The power-law model correlations I've tested do not agree (within some interval) as to the values they provide and some correlations can differ as much as 7x from another. Since most correlations I've tried are rather simple formulations I think I can rule bad coding out.

Simply put, I need a "engineering solution" that should be good for most non-newtonian fluids; a correlation that the good engineering practice might regard as "standard", for general use.

So far I tried the correlations of Dodge & Metzner (1959), Kemblowski (1973), Thomas (1960), Tomita (1959) and Szilas (1981). As the base source of information I mention the articles of Dodge & Metzner (https://doi.org/10.1002/aic.690050214) and Garcia and Steffe (Journal of Food Process Engineering 9 (1987) 93-12).

Thanks.

• I don't think you can generalize non-Newtonian fluids, you have to model each different type differently. Dec 16, 2021 at 17:48
• I worked a little with a shear thinning fluid (a hair coloring product). Empirically made graphs of flow vs p, for various tube ID's. A newtonian fluid would be straight lines thru graph origin, with various slopes corresponding to ID. This fluid had "hockey stick" shapes, with asymptotes of high P region all roughly converging on a common point on the horizontal axis. This was good enough for system design, and we set up the system's operation point to avoid the transition region (where graph lines curved), which made it predictable. Dec 16, 2021 at 18:20
• So thixotropic or rheopectic? Dec 16, 2021 at 18:59
• @TigerGuy, I start to think exactly like that. Dec 16, 2021 at 19:12
• @SolarMike: thixotropic I would say, as the field of application is the oil industry (crude oil, diesel, a few cleansing gels perhaps) and AFAIK those fluids exhibit a thixotropic behaviour. Dec 16, 2021 at 19:15

When the friction coefficient $$\zeta$$ of a fluid is not classical it is often just a generalization as a memory kernel $$\zeta\left(t\right)$$ that still satisfies the steady-state, creeping-flow result of the NS fluid in the Fourier domain. For example, around a sphere of radius $$a$$, $$\zeta^*\left(\omega\right)=6\pi\eta^*\left(\omega\right) a$$, where $$f^*\left(\omega\right)=\mathcal{F}_{t\to\omega}\left\{f\left(t\right)\right\}$$ and $$\eta^*\left(\omega\right)$$ is just the complex viscosity of the complex fluid. See J. Non-Newt. Fluid Mech. 200:3-8 (2013). You can measure $$\eta^*\left(\omega\right)$$ on a rheometer.