A note about convected time derivatives for flows of complex fluids.

Stone, Howard A; Shelley, Michael J; Boyko, Evgeniy · Soft Matter · 2023

basic_science · Level V

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Abstract

We present a direct derivation of the typical time derivatives used in a continuum description of complex fluid flows, harnessing the principles of the kinematics of line elements. The evolution of the microstructural conformation tensor in a flow and the physical interpretation of different derivatives then follow naturally.