Mathematical models for non-Newtonian fluid flow and transport in pipes and slits.

What is it about?

We derived analytical relationships for velocity and transport of species in pipes and slits during the flow of generalized Newtonian fluids. These can be used, for example, in industries that flow polymers through pipes, to model blood in the body, or when investigating hydraulic fracturing processes underground. The transport relationships are important for determining where species carried in the fluids will go and how long it will take them to go there. Examples include drug delivery in blood, or contaminants in the environment. The analytical relationships were validated with high fidelity computer simulations.

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Photo by Chun Kit Soo on Unsplash

Photo by Chun Kit Soo on Unsplash

Why is it important?

Generalized Newtonian fluids appear everywhere, but are challenging to model. The analytical relationships for transport derived here were applied to Cross and Carreau model fluids, but were derived generally so that they can be applied to other fluid classes. Using pore-network or bundle of capillary tube models, the relations derived here can be used to model transport of very complex fluids flowing in porous media when there hasn't been an effective way to do so before.