  This work focuses on inferring the molecular state of the polymer chain
required to induce elasto-capillary stress relaxation and the accurate measure
of the polymer relaxation time in uniaxial stretching of dilute polymer
solutions. This work is facilitated by the discovery that constant velocity
applied at early times leads to initial constant extension rate before reaching
the Rayleigh-Plateau instability. Such constant rate experiments are used to
correlate initial stretching kinematics with the thinning dynamics in the
elasto-capillary Regime. We show that there is a minimum initial strain-rate
required to induce rate independent elastic effects. Below the minimum
extension rate, insufficient stretching of the chain is observed before
capillary instability, such that the polymer stress is comparable to the
capillary stress at long times and true stress relaxation is not achieved.
Above the minimum strain-rate, the chain reaches a critical stretch before
instability, such that during the unstable filament thinning the polymer stress
is significantly larger than the capillary stress and true stress relaxation is
observed. Using a single relaxation mode Oldroyd-B model, we show that the the
minimum strain rate leads to a required initial stretch of the chain before
reaching the Rayleigh Plateau limit. Along with the accurate measure of
relaxation time, this work introduces a characteristic dimensionless group,
called the stretchability factor, that can be used to quantitatively compare
different materials based on the overall material deformation/kinematic
behavior, not just the relaxation time. Overall, these results demonstrate a
useful methodology to study the stretching of dilute solutions using a constant
velocity stretching scheme.
