The Oldroyd-B model is a constitutive model used to describe the flow of
viscoelastic fluids.
This model can be regarded as an extension of the
upper-convected Maxwell model and is equivalent to a fluid filled with elastic bead and spring dumbbells.
The model is named after its creator
James G. Oldroyd.[1]
is the total
viscosity composed of solvent and polymer components, ;
is the deformation rate tensor or rate of strain tensor, .
The model can also be written split into polymeric (viscoelastic) part separately from the solvent part:[2]
where
Whilst the model gives good approximations of viscoelastic fluids in shear flow, it has an unphysical singularity in extensional flow, where the dumbbells are infinitely stretched. This is, however, specific to idealised flow; in the case of a cross-slot geometry the extensional flow is not ideal, so the stress, although singular, remains integrable, i.e. the stress is infinite in a correspondingly infinitely small region.[3]
^Oldroyd, James (Feb 1950). "On the Formulation of Rheological Equations of State". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 200 (1063): 523–541.
Bibcode:
1950RSPSA.200..523O.
doi:
10.1098/rspa.1950.0035.
^Owens, R. G.; Phillips, Timothy N. (2002). Computational Rheology. Imperial College Press.
ISBN978-1-86094-186-3.