Modeling Viscoelastic Flow in Three-Dimensional Geometries

Polymer fluids exhibit non-Newtonian behavior, which may include but is not limited to: shear-dependent viscosity, exceptional die swell, elastically driven recirculation flow, high elongational viscosity, and elastic instabilities. An understanding of the development of these structures and the ability to predict/prevent them is very valuable for the polymer processing industry, in particular in die design and fiber spinning.

Modeling polymer fluid mechanics is difficult and requires specialized numerical techniques. The problems are characterized by a huge number of unknowns, so simplification through reduction of dimensionality has been a common practice in modeling efforts. However, there is a need to expand models to be three-dimensional in order to handle arbitrary geometry, capture edge effects, and make predictions for non-axisymmetric shapes. In the case of the 4DG^TM fiber in Figure 1, the high surface area of the cylindrical fiber contributes to its useful transport properties. This problem is inherently three-dimensional. Furthermore, two-dimensional simulations are unable to predict elastically driven flow instabilities that cause flow to become three-dimensional; these transitions have been observed in a variety of flow experiments. Figure 2 shows an example of a three-dimensional instability in a cylindrical fiber.

Figure 1: Artist's rendition of a 4DGTM fiber. The fiber has special properties because of its grooved shape. It can "spontaneously move fluids,'' ''store and trap substances,'' has a ''large surface area per unit volume,'' and it fills more volume than a cylindrical fiber.

Figure 2: Example of an instability arising in the extrusion of a single strand polymer filament. Steady flow is shown in (a), evolving into a shark-skin instability in (b)-(e), and finally gross melt fracture in (f) and (g). Extrudates of a polymer melt at 70o C. Shear rates are (a) 1.36 s-1, (b) 2.72 s-1, (c) 6.81 s-1, (d) 13.6 s-1. (e) 34.1 s-1, (f) 68.1 s-1, and (g) 136 s-1. Fiber is roughly 1 mm in diameter. Copied from the thesis of Scott Phillips, MIT PhD.