An Oldroyd-B solver for vanishingly small values of the viscosity ratio: Application to unsteady free surface flows

Author(s)

Viezel, C. ^[1] ; Tome, M. F. ^[1] ; Pinho, F. T. ^[2] ; McKee, S. ^[3]

Affiliation

^[1] Univ Sao Paulo, Dept Appl Math & Stat, BR-13560970 Sao Paulo, SP - Brazil

^[2] Univ Porto, Fac Engn, Dept Mech Engn, CEFT, Rua Dr Roberto Frias S-N, P-4200465 Porto - Portugal

^[3] Univ Strathclyde, Dept Math & Stat, 26 Richmond St, Glasgow G1 1XH, Lanark - Scotland

• Document type: Journal article
• Source: Journal of Non-Newtonian Fluid Mechanics; v. 285, NOV 2020.
• Web of Science Citations: 0

Abstract

This work is concerned with time-dependent axisymmetric free surface flows of Oldroyd-B fluids for any value of beta, the ratio of solvent to total viscosities. The Oldroyd-B constitutive equation is dealt with by employing a novel technique to calculate the conformation tensor while an EVSS transformation allows the solution of the momentum equations coupled with the free surface stress conditions: this avoids numerical instabilities that can arise when using small values of beta. The convergence of this new methodology is verified on pipe flow and also by comparing results from the literature for the time-dependent impacting drop problem. This approach is then used to predict the time-dependent free surface flow after a viscoelastic drop impacts a solid surface for beta values in the range {[}0, 1]. The impacting drop problem is investigated for polymer solutions containing a small solvent contribution (beta -> 0) or without any solvent viscosity (beta = 0). In addition, a study of the bouncing drop problem for different values of beta, Weissenberg and Reynolds numbers is undertaken. (AU)

• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC