Constant force extensional rheometry of polymer solutions

Abstract

We revisit the rapid stretching of a liquid filament under the action of a constant imposed tensile force, a problem which was first considered by Matta & Tytus [JN-NFM vol. 35, pp 215-229, 1990]. A liquid bridge formed from a viscous Newtonian fluid or from a dilute polymer solution is first established between two cylindrical disks. The upper disk is held fixed and may be connected to a force transducer while the lower cylinder falls due to gravity. By varying the mass of the falling cylinder and measuring its resulting acceleration, the viscoelastic nature of the elongating fluid filament can be probed. In particular, we show that with this constant force pull (CFP) technique it is possible to readily impose very large material strains and strain rates so that the maximum extensibility of the polymer molecules may be quantified. This unique characteristic of the experiment is analyzed numerically using the FENE-P model and two alternative kinematic descriptions; employing either an axially-uniform filament approximation or a quasi two-dimensional Lagrangian description of the elongating thread. In addition, a second order pertubation theory for the trajectory of the falling mass is developed for simple viscous filaments. Based on these theoretical considerations we develop an expression that enables estimation of the finite extensibility parameter characterizing the polymer solution in terms of quantities that can be extracted directly from simple measurement of the time-dependent filament diameter.

An analytic solution for capillary thinning and breakup of FENE-P fluids

“…It will be of future interest to see whether degradation in the molecular weight of the MUC5B chains can be systematically monitored and modelled using the finite breakup time derived from the FENE-P model presented herein and tested against results from CaBER experiments. Care must be taken when extracting molecular weight values at various stages of degradation from the values of b extracted from filament thinning measurements, as previous work has shown that the FENE-P model can substantially overpredict the true tensile stress in strong transient elongational flows [29,30]. However, in the quasi-steady FENE limit in which the chains are close to fully stretched, much better agreement with the values expected from molecular theory can be obtained [31].…”

Jetting behavior of polymer solutions in drop-on-demand inkjet printing

“…Similarly, recent experiments to determine the value of extensibility, L, by Szabo et al (2012) using a falling plate technique suggest that in practice this is significantly shorter than suggested by molecular theory. However, these experiments were performed with much higher molecular weight PS than that considered here.…”

“…Underestimation of relaxation time [Clasen et al (2006); Vadillo et al (2012)] and overestimation of extensibility [Szabo et al (2012)] both increase the likelihood of the occurrence of regime III behavior in fast polymer ink-jet printing applications.…”

Extensional Flow and Relaxation of Semi‐dilute Solutions of Schizophyllan

“…For high viscosity systems, rheometers have been designed by Meissner,1 Münstedt,2, 3 and recently by Sentmanat et al4 that explore the possibilities to mechanically grab and hold a sample. For lower viscosities down to η ≈ 1 Pa · s, filament stretching devices have been developed over the last two decades that rely on the adhesion of a sample to two surfaces between which the fluid is stretched 5–9. For viscosities below 1 Pa · s, recently the capillary breakup extensional rheometer (CaBER) was proposed as a method to determine the transient extensional viscosity as well as the extensional relaxation time of viscoelastic fluids 10–21.…”