TY - JOUR
T1 - On a variational principle for the Upper Convected Maxwell model
AU - ten Bosch, B. I.M.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - Drag
KW - Reciprocal theorem
KW - Upper Convected Maxwell model
KW - Variational principle
UR - http://www.scopus.com/inward/record.url?scp=85145607818&partnerID=8YFLogxK
U2 - 10.1016/j.jnnfm.2022.104948
DO - 10.1016/j.jnnfm.2022.104948
M3 - Article
AN - SCOPUS:85145607818
SN - 0377-0257
VL - 311
JO - Journal of Non-Newtonian Fluid Mechanics
JF - Journal of Non-Newtonian Fluid Mechanics
M1 - 104948
ER -