On a variational principle for the Upper Convected Maxwell model

Research output: Contribution to journalArticleScientificpeer-review

37 Downloads (Pure)

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.

Original languageEnglish
Article number104948
Number of pages7
JournalJournal of Non-Newtonian Fluid Mechanics
Volume311
DOIs
Publication statusPublished - 2023

Keywords

  • Drag
  • Reciprocal theorem
  • Upper Convected Maxwell model
  • Variational principle

Fingerprint

Dive into the research topics of 'On a variational principle for the Upper Convected Maxwell model'. Together they form a unique fingerprint.

Cite this