Pumping the fizz into simulations.

A freshly poured soft drink foams and crackles as bubbles of carbon dioxide rise to the surface and burst. Each pop churns a little liquid into the air, tickling the nose of anyone who tries to sip the beverage too soon after pouring.

Applying an innovative approach to the computer simulation of gas bubbles rising inside a liquid, two mathematicians have now obtained results that show how the movements of bubbles disturb the liquid. Analyzing such flows in detail may make possible the development of a new theory of turbulence based on molecular interactions, says Donald Greenspan of the University of Texas at Arlington.

Mark S. Korlie of Montclair State University in Upper Montclair, N.J., described the findings last week at the Joint Mathematics Meetings in San Diego.

Instead of modeling the bubbles and liquid as flowing fluids, which are continuous, Korlie and Greenspan focused on the behavior of the individual molecules responding to gravity and the electric forces between them. The molecules move about erratically, colliding and rebounding like billiard balls.

To simplify the simulation, the researchers clumped the huge number of molecules present in a typical container into a relatively small number of larger units called quasimolecules, or particles (SN: 7/9/88, p. 21). Applying Newton's laws of motion, they computed how a collection of these randomly moving particles would behave. When the simulation included a mixture of carbon dioxide and water particles, the carbon dioxide particles acted like tiny bubbles, rising to the liquid's surface. By initially placing all the carbon dioxide particles next to each other to represent a single large bubble, the mathematicians could also observe oscillations of the rising bubble and the flow of water in its wake. They noted additional turbulent motion at the liquid's surface as the bubble broke apart and carbon dioxide escaped.

Korlie and Greenspan did their simulations in two dimensions. However, "we can extend the method directly to the three-dimensional case," Korlie says.