Capillary Break-up Rheometry of Low-Viscosity Elastic Fluids

Lucy E.
Rodd^{1,3}, Timothy P.
Scott^{3
}

^{1}Dept. of Chemical
and Biomolecular Engineering,

The University of Melbourne, VIC 3010, Australia

^{2}Division of Chemical
Engineering,

The University of Queensland, Brisbane, QLD 4072,
Australia

^{3}Hatsopoulos
Microfluids Laboratory, Dept. of Mechanical Engineering,

Massachusetts
Institute of Technology, Cambridge, MA 02139, USA

July 28, 2004

We investigate the
dynamics of the capillary thinning and break-up process for low viscosity
elastic fluids such as dilute polymer solutions. Standard measurements of the
evolution of the midpoint diameter of the necking fluid filament are augmented
by high speed digital video images of the break up dynamics. We show that the
successful operation of a capillary thinning device is governed by three
important time scales (which characterize the relative importance of inertial,
viscous and elastic processes), and also by two important length scales (which
specify the initial sample size and the total stretch imposed on the sample). By
optimizing the ranges of these geometric parameters, we are able to measure
characteristic time scales for tensile stress growth as small as 1 millisecond
for a number of model dilute and semi-dilute solutions of polyethylene oxide
(PEO) in water and glycerin. If the aspect ratio of the sample is too small, or
the total axial stretch is too great, measurements are limited, respectively, by
inertial oscillations of the liquid bridge or by the development of the
well-known beads-on-a-string morphology which disrupt the formation of a uniform
necking filament. By considering the magnitudes of the natural time scales
associated with viscous flow, elastic stress growth and inertial oscillations it
is possible to construct an “operability diagram” characterizing successful
operation of a capillary break-up extensional rheometer. For Newtonian fluids,
viscosities greater than approximately 70 mPa.s are required; however for dilute
solutions of high molecular weight polymer the minimum viscosity is
substantially lower due to the additional elastic stresses arising from
molecular extension. For PEO of molecular weight 10^{6} g/mol, it is
possible to measure relaxation times of order 1 ms in dilute polymer solutions
of viscosity 2 – 10 mPa.s.