Beads-on-string formation during filament pinch-off: Dynamics with the PTT model for non-affine motion

Fundamental understanding of the formation and pinch-off of viscoelastic filaments is important in applications involving production of drops (e.g., ink-jet printing. micro-arraying, and atomization). In addition to delaying pinch-off, in some cases, viscoelasticity is known to cause the so-called beads-on-string structure, i.e., a number of small droplets interconnected by thin filaments. In a recent publication [H. Matallah, M.J. Banaai, K.S. Sujatha, M.F. Webster, J. Non-Newtonian Fluid Mech. 134 (2006) 77-104], it was shown that the simulation of an elongating filament modeled by the Phan-Thien/Tanner (PTT) equation with the Gordon-Schowalter (GS) convected derivative, which allows non-affine motion of polymer molecules in the continuum, results in the formation of the beads-on-string structure. On the other hand, such bead formation is not reported in calculations with other viscoelastic models that are also strain-hardening like the M model but do not have the GS convected derivative (see, e.g., [M. Yao, S.H. Spiegelberg. C.H. McKinley,J. Non-Newtonian Fluid Mech. 89(2000) 1-43]). This starkly different behavior of the PTT equation with the GS convected derivative is investigated here. During the elongation of the filament, regions of shear form inside the filament due to its initially curved surface. Because of the presence of the GS convected derivative in the PTT equation - which is known to cause unphysical oscillations in stress in simple step shear flow - the shear stress within the PTT filament exhibits temporal oscillations. The onset of these oscillations coincides with the symmetrical migration of the location of the single maximum in the axial component of the rate-of-strain tensor from the center of the filament to two other locations, one in each half of the filament. This is followed by a similar movement of the location of the maximum in the axial elastic stress inside the filament. These two events eventually lead to the formation of a bead-like structure. The occurrence of the bead is also shown to depend on the extent of the polymer contribution to the total viscosity compared to that of the solvent. (C) 2008 Elsevier B.V. All rights reserved.