Extensional deformation of non-Newtonian liquid bridges

Abstract

A numerical method for simulating the extensional dynamics of elongating ®laments of non-Newtonian uids in a ®lament stretching rheometer is presented. The boundary element method, in conjunction with either the Oldroyd-B or the generalized multimode Upper-Convected Maxwell constitutive model, is used to calculate the transient evolution of the liquid interface, the applied force on the stationary end plate and the polymeric stresses. The numerical results are compared to experimental results and are in excellent agreement at low Hencky strains (Newtonian response) but provide less accurate modeling of the stress growth observed in experiments at higher strains. A comparison of different methods for measuring the apparent extensional viscosity from global measurements of the net force and the mid-point radius of the ®lament is presented. At large strains calculations show that the¯uid motion in these devices closely approximates ideal uniaxial elongation.

FILAMENT-STRETCHINGRHEOMETRY OFCOMPLEXFLUIDS

“…More recently, simulations to large Hencky strains have been achieved using adaptive Eulerian finite-element methods for differential viscoelastic constitutive equations (Sizaire & Legat 1997;Sizaire et al 1999;Yao et al , 2000 and a Lagrangian finite-element approach for integral constitutive equations (Kolte et al 1997. Results have also been obtained using a boundary-element method (Gaudet & McKinley 1998) and a hybrid Brownian-dynamics/finite-element (CONNFESSITT) algorithm (J. Cormenzana, A. di Cecca, J. Ramirez, & M. Laso, submitted).…”

Optimised multi-stream microfluidic designs for controlled extensional deformation

“…For studies related to extensional rheological flows of complex fluids, several micro-fabricated designs have been suggested as promising platforms for evaluating extensional material functions such as the extensional viscosity (Galindo-Rosales et al 2013;Haward 2016). In contrast with Newtonian fluids, for viscoelastic fluids, the flow resistance can increase dramatically and in a highly non-linear manner as the strain-rate increases (Gaudet and McKinley 1998). This makes the evaluation of extensional viscosity highly desired.…”

Computational predictions for viscoelastic filament stretching flows: ALE methods and free-surface techniques (CM and VOF)

“…More recently, large Hencky-strains have been achieved with the use of finite element methodology, invoking adaptive Eulerian formulations for differential viscoelastic constitutive equations [3,6,7], and Lagrangian procedures with integral constitutive equations [8,9]. Alternatively, Gaudet and McKinley [10] employed a boundary element method for an Oldroyd-B model predicting the temporal evolution for the liquid interface, the applied force on the stationary end plates and the extensional viscosity. These predictions were tightly corroborated against the experimental results of Spiegelberg et al [11].…”