Stresses of PTT, Giesekus, and Oldroyd-B fluids in a Newtonian velocity field near the stick-slip singularity

Autor(es)

Evans, J. D. ^[1] ; Palhares Junior, I. L. ^{[2, 1]} ; Oishi, C. M. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon - England

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13566590 Sao Carlos, SP - Brazil

^[3] Univ Estadual Paulista, Fac Ciencias & Tecnol, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Physics of Fluids; v. 29, n. 12 DEC 2017.
• Citações Web of Science: 4

Resumo

We characterise the stress singularity of the Oldroyd-B, Phan-Thien-Tanner (PTT), and Giesekus viscoelastic models in steady planar stick-slip flows. For both PTT and Giesekus models in the presence of a solvent viscosity, the asymptotics show that the velocity field is Newtonian dominated near to the singularity at the join of the stick and slip surfaces. Polymer stress boundary layers are present at both the stick and slip surfaces. Byintegrating along streamlines, we verify the polymer stress behavior of r(-4/11) for PTT and r(-5/16) for Giesekus, where r is the radial distance from the singularity. These asymptotic results for PTT and Giesekus do not hold in the limit of vanishing quadratic stress terms for Oldroyd-B. However, we can consider the Oldroyd-B model in the fixed kinematics of a prescribed Newtonian velocity field. In contrast to PTT and Giesekus, this is not the correct balance for the momentum equation but does allow insight into the behavior of the Oldroyd-B equations near the singularity. A three-region asymptotic structure is again apparent with now a polymer stress singularity of r(-4/5). The high Weissenberg boundary layer equations are found to manifest themselves at the stick surface and are of thickness r(3/2). At the slip surface, dominant balance between the upper convected stress and rate-of-strain terms gives a slip boundary layer of thickness r(2). The solution of the slip boundary layer shows that the polymer stress is now singular along the slip surface. These results are supported through numerical integration along streamlines of the Oldroyd-B equations in a Newtonian velocity field. The Oldroyd-B model thus extends the point singularity at the join of the stick and slip surfaces to the whole of slip surface. As such, it does not have a physically meaningful solution in a Newtonian velocity field. We would expect a similar stress behavior for this model in the true viscoelastic velocity field. Published by AIP Publishing. (AU)

• Processo FAPESP: 14/17348-2 - Estabilidade de métodos numéricos para escoamentos viscoelásticos com alto número de Weissenberg
• Beneficiário: Irineu Lopes Palhares Junior
• Linha de fomento: Bolsas no Brasil - Doutorado
• Processo FAPESP: 16/20389-8 - Estudo numérico do tensor na formulação natural para problemas com superfície livre
• Beneficiário: Irineu Lopes Palhares Junior
• Linha de fomento: Bolsas no Exterior - Estágio de Pesquisa - Doutorado
• Processo FAPESP: 15/50094-7 - Asymptotics and simulation of complex fluids
• Beneficiário: José Alberto Cuminato
• Linha de fomento: Auxílio à Pesquisa - Regular