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 -