### Eric Scribben, Donald G. Baird, and Peter Wapperom

### The role of transient rheology in polymeric coalescence

* Rheologica Acta* **45** (2006) 825-839

#### Abstract

The initial theory of Frenkel and Eshelby for the coalescence of drops in air
(or sintering) of Newtonian fluids, which equated the work of surface tension
to the work done by viscous stresses while assuming biaxial extensional flow
kinematics, was extended to the case of time dependent material functions
using the Upper Convected Maxwell (UCM) model. A numerical scheme was developed
to solve the ordinary differential equations (ODE) for the stresses which
are embedded in the ODE based on the mechanical energy balance. Initial
conditions required to solve the set of non-linear ODEs were obtained from
visualization experiments of the coalescing drops as the theory for elastic
contact gave unrealistically high values of the initial neck radius. The
transient model predicted that coalescence was accelerated by increasing the
relaxation time, the opposite relationship of what was predicted by the
steady state UCM formulation, and was capable of quantitatively predicting
the experimental coalescence rates at times when viscoelasticity was
important.
#### Keywords

Sintering; Coalescence; polypropylene;
transient viscosity; upper convected Maxwell model