On a variational principle for the Upper Convected Maxwell model

ten Bosch, B.I.M.

doi:10.1016/j.jnnfm.2022.104948

On a variational principle for the Upper Convected Maxwell model

Title

On a variational principle for the Upper Convected Maxwell model

Author

ten Bosch, B.I.M. (TU Delft Fluid Mechanics)

Date

2023

Abstract

A variational principle for the Upper Convected Maxwell model is presented. The stationary value of the appropriate functional is the drag on an immersed object. From the principle, a formula is derived for the derivative of the drag with respect to the Deborah number for an arbitrarily shaped particle in a circular duct under creeping flow conditions. The formalism is compared with the conventional reciprocal theorem. Whereas the reciprocal theorem gives the drag as a volume integral involving the Stokesian stress tensor, the variational principle involves the stress from the adjoint equation. For low Deborah numbers both approaches provide the correction to the Stokes drag as a volume integral involving only the Stokesian rate-of-strain tensor, in line with second-order fluid theory.

Subject

Drag
Reciprocal theorem
Upper Convected Maxwell model
Variational principle

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DOI

https://doi.org/10.1016/j.jnnfm.2022.104948

ISSN

0377-0257

Source

Journal of Non-Newtonian Fluid Mechanics, 311

Part of collection

Institutional Repository