Ubiquitous Polymers

The plastic in a throwaway pen. Kevlar in a bullet-proof vest. Synthetic rubber in tires. The sturdy shell encasing your desktop computer. Nylon in everything from pantyhose to backpacks. They're all examples of polymers -- materials made from long-chained molecules that, since they were first synthesized in the 1930s, have become a ubiquitous part of our culture.

Making products from these materials involves processing them in liquid form; the polymers flow into molds of the desired size and shape. To get the strength and durability needed for a particular product while keeping a handle on manufacturing cost, it's important to precisely understand how polymers act when they flow. For the past several years, chemical engineer Gary Leal and his colleagues at the University of California, Santa Barbara have been doing that -- complementing experimental studies with computations at the Pittsburgh Supercomputing Center.

In their equilibrium state, when they aren't subjected to the stresses of the manufacturing process, many polymers have a tendency to coil. Others are rod-like but may orient themselves in many different directions. As they flow, the long molecular chains stretch. Think of a ball of spaghetti as it falls from a cooking pot to your plate. "It might get stretched," says Leal, "and it may get less tangled than it was before. If everything gets lined up in one direction, the tendency of the polymer chains to interact with each other will change." These changes, introduced in the molten state during processing, control many properties of the finished product.

Research on polymer flows has only recently begun to approach the complicated geometries that are normal in manufacturing. "For example," says Leal, "when a tire company wants to change the cross-sectional shape of a tire by extruding from a dye, they currently don't have a fundamental basis to predict the shape of the dye. They have a professional dye maker who, after a few tries, gets it right. It costs tens of thousands of dollars, but that's the way they do it. If instead they could use a computer to design prototypes, it would be far less expensive."

Research in this area has changed in recent years for two reasons. On the experimental front, techniques have improved so researchers now are able to probe what happens on a microscopic level. Secondly,
numerical techniques have developed to solve the equations that describe the complex behavior of polymeric liquids in flow. "Materials are going to be a major force in the American economy in the future," says Leal, "and this materials processing research is important to lay the groundwork."

In recent work at Pittsburgh, Leal has developed a modeling approach to polymer flows that allows him to compare computed results with laboratory experiments, and he has achieved good agreement with observed data.

Simulating a Stretched Polymer

These graphics represent simulations of polymer flow in a planar cross-slot device. Dilute polymer solution enters from both sides of the input channel (horizontal axis). The two inflow streams splash into one another, creating a stagnation flow pattern at the center, where they merge and flow out both directions of the cross channel (vertical axis). The black lines indicate flow streamlines. The vertical colored stripe (right) is a closeup of the stagnation region.

Colors emanating from the stagnation point represent how much the polymers stretch with reference to equilibrium state. The polymers enter unstretched, and near the stagnation point stretch out. Since the relaxation process takes time, the polymers remain stretched a distance downstream. With this model (a "dumbbell model," adapted from Hinch and DeGennes), maximum stretch is 300 (dimensionless length squared), compared to two at equilibrium. Thus at the stagnation point, the polymer is stretched nearly to maximum.

"The velocity gradient is approximately constant at the stagnation point," says Leal. "Maximum extension occurs along the outflow axis beginning from the stagnation point, which indicates that polymer conformation is dominated by residence time in this constant velocity gradient region. In other words, conformation depends on the total strain experienced by the polymer molecule, rather than the strain rate."

Researcher: Gary Leal, University of California, Santa Barbara
Hardware: CRAY C90
Software: User-developed code.
Keywords: Polymer, molecule, molecular structure, plastic, synthesized, manufacturing, flow, equilibrium, stress, coils, rods, molecular chains, stretched, polymer flow, materials processing, Deborah number, non-Newtonian fluids, elastic dumbbell model, simulations.

Related Material on the Web:
Projects in Scientific Computing, PSC's annual research report.

References, Acknowledgements & Credits