Startup and cessation of steady shear and extensional flows: Exact analytical solutions for the affine linear PhanThienTanner fluid model
Abstract
Exact analytical solutions for startup and cessation flows are obtained for the affine linear PhanThienTanner fluid model. They include the results for startup and cessation of steady shear flows, of steady uniaxial and biaxial extensional flows, and of steady planar extensional flows. The solutions obtained show that at startup of steady shear flows, the stresses go through quasiperiodic exponentially damped oscillations while approaching their steadyflow values (so that stress overshoots are present); at startup of steady extensional flows, the stresses grow monotonically, while at cessation of steady shear and extensional flows, the stresses decay quickly and nonexponentially. The steadyflow rheology of the fluid is also reviewed, the exact analytical solutions obtained in this work for steady shear and extensional flows being simpler than the alternative formulas found in the literature. The properties of steady and transient solutions, including their asymptotic behavior at low and high Weissenberg numbers, are investigated in detail. Generalization to the multimode version of the PhanThienTanner model is also discussed. Thus, this work provides a complete analytical description of the rheology of the affine linear PhanThienTanner fluid in startup, cessation, and steady regimes of shear and extensional flows.
 Publication:

Physics of Fluids
 Pub Date:
 August 2020
 DOI:
 10.1063/5.0017326
 arXiv:
 arXiv:2006.04116
 Bibcode:
 2020PhFl...32h3105S
 Keywords:

 Physics  Fluid Dynamics;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 38 pages, 7 tables, 7 figures