The beads-on-string structure of viscoelastic threads

Abstract

By adding minute concentrations of a high molecular weight polymer, liquid jets or bridges collapsing under the action of surface tension develop a characteristic shape of uniform threads connecting spherical fluid drops. In this paper, high-precision measurements of this beads-on-string structure are combined with a theoretical analysis of the limiting case of large polymer relaxation times, for which the evolution can be divided into two distinct regimes. This excludes the very late stages of the evolution, for which the polymers have become fully stretched. For times smaller than the polymer relaxation time, over which the beads-on-string structure develops, we give a simplified local description, which still contains the full complexity of the problem. At times much larger than the relaxation time, we show that the solution consists of exponentially thinning threads connecting almost spherical drops. Both experiment and theoretical analysis of a one-dimensional model equation reveal a self-similar structure of the corner where a thread is attached to the neighbouring drops.

Influence of viscoelasticity on drop deformation and orientation in shear flow. Part 2: Dynamics

“…Further increase in the capillary number leads to an increase in the length of the initial neck region and coalescence does not occur. The neck typically develops into a beads-on-string formation reminiscent of viscoelastic jets [49,50], together with end-pinching.…”

Constant force extensional rheometry of polymer solutions

“…With Weissenberg numbers W i = λd ln L/dt ≫ 1 the constant force pull ultimately imposes an almost affine deformation on the microstructural elements in the polymeric sample towards their finite extensibility limit. In contrast to this in capillary breakup (CABER) type experiments the Weissenberg number remains in the elastocapillary balance regime constant at W i = 2/3 [12,9] and the polymeric chains are not deforming affinely with the flow [23,16]. Although the polymer chains will also in a Caber experiment eventually approach their finite extensibility limit, this requires higher strains than for the affine deformation with the CFP technique.…”

Extensional rheometry of cellulose ether solutions: flow instability

“…These infinitely stretchable springs impart elastic stress to the fluid. Provided all the dumbbells have springs with identical force constants, the fluid exhibits a single relaxation time (Clasen et al 2006a).…”

“…These instabilities refer to the growth of satellite fluid droplet(s) connected to either of or both the fluid hemispheres through the filament. The formation of so called 'bead-on-string' structures in the capillary thinning of filaments and jets has been investigated extensively (Chang et al 1999;Stelter et al 2000;Li and Fontelos 2003;Clasen et al 2006a). 'Bead-onstring' flow instabilities in uniaxial extensional flows have been reported to be primarily caused by either (1) inertia or (2) elasticity.…”

“…Also, since cellulosic polymers are widely used as rheology modifiers, an understanding of this flow instability for the systems containing cellulosic polymers is very important due to their potential applications in the commercial processes such as roll-coating, fertilizer spraying, paint-leveling, bottle-filling, misting and inkjet printing (Clasen et al 2006a;Oliveira and McKinley 2005). These processes have a significant component of free surface extensional deformation and the presence of droplets could potentially affect the quality of the end product.…”