Bubble Trouble

Heather Fletcher
January 01, 2000
four silver bubbles side by side

Silvery air bubbles rising up a capillary tube filled with a polymer solution demonstrate the premise of Eisa Almatroushi and Robert Johnson's mathematical model: that bubbles in capillaries change shape when the thickness and density of the surrounding solution changes.

It might have been the bubbles in your beer. Or the fat, lazy, colorful blobs in your lava lamp. Perhaps even raindrops tapping on your windowpane during an otherwise perfectly good summer afternoon. But whatever it was that drew you in, you likely have stopped to contemplate the peculiar behavior of bubbles.

Some bubbles collide and bounce away. Others meet and melt into each other in a process that engineers call coalescence. At Penn State, chemical engineering doctoral students Eisa Almatroushi and Robert Johnson are working on a mathematical model that describes these bubble-to-bubble interactions.

Coalescence, Almatroushi notes, can occur in everything from blood to shampoo. "I recently read that medical researchers were trying to develop a drug that will prevent coalescence of blood gases in divers who resurface too quickly." This condition, known as the bends, can result in one large bubble that can stop a diver's heart. A surprisingly similar situation arises in oil pipelines when small bubbles of natural gas come together to form large pockets. These can cause technical difficulties by requiring increased pressures to resume the flow of oil or by causing the pumps to operate dry. "And if, at the store, you see a bottle of shampoo that has separated into two layers," he says, "you won't buy it."

Bubbles experience forces that both attract them to each other and drive them apart. In a large tank, there is no guarantee that two bubbles will ever come close enough to collide. So Almatroushi and Johnson have confined their study to a capillary system—a narrow vertical tube. The capillary tube lines the bubbles up so that collision is inevitable, provided the bubbles are moving at the appropriate speed.

Bubble speed in a capillary is dramatically influenced by drag forces. Drag forces along the walls of the tube work in opposition to the buoyancy forces that push bubbles up to the top of a container of liquid. As a bubble increases in size and gets closer to the wall of the capillary, the effect becomes dramatic. By injecting a large bubble first and following it with a smaller, faster one, collision is guaranteed to occur.

From his cubical on the first floor of Fenske Building, Johnson uses his IBM workstation to manipulate the complex system of differential equations that mathematically govern the motion of a bubble in a capillary. Upstairs, Almatroushi works with the real thing. A glass tube less than one centimeter in diameter is clamped vertically into place and filled with a thick, dense liquid—often a glycerin solution. A syringe is used to inject air bubbles or drops of a different liquid through a one-way valve near the bottom of the capillary. Almatroushi uses a digital camera that is mounted on a motor-driven stage to film the drops and bubbles as they float up the tube. Two plastic flashlights strapped onto the camera platform with electrical tape provide the lighting. ("Somewhere there is a much more expensive piece of equipment that might work a little better for this," Johnson shrugs, "but this works, so why change it?") The bubble footage is replayed frame by frame, and Almatroushi imports selected data into an image analysis software program.

Johnson and Almatroushi's model predicts the size, shape, and speed of the drop relative to the size of the tube and the viscosity, density, and surface tension of the two fluids. To test it, they gathered data for a four-drop series first computationally, and then experimentally. What they got each time were four shapes that looked something like an egg on its side, a sphere, a gumdrop, and a gourd. "It was almost a perfect match," Johnson recalls. The second part of their model still has some bugs. Johnson and Almatroushi want to correlate the radius of the disk that forms between two touching bubbles with the time it takes the bubbles to coalesce, but so far the experimental data don't match the computational results. "The model we were using," remarks Almatroushi, "was just too simple."

Manipulating bubble coalescence in real-life systems is the ultimate application of Johnson and Almatroushi's model, once they have perfected it. Soil can be thought of as a series of capillaries, so in the ground, just as in the lab, the size of a drop determines the extent to which drag forces slow its movement.

"Sometimes, pores in the soil trap oil globules that have broken up into very small drops," their adviser, chemical engineer Ali Borhan, explains. If you could adjust the size of the drop, you could encourage the oil to coalesce into a larger pocket, which you could then pump out more easily. Johnson has already begun to study mathematically how large, soapy molecules called surfactants can make drops smaller and more flexible by reducing the surface tension. Presumably, the desired change in coalescence behavior results. "You ought to be able to use surfactants to wash the oil from the dirt just like you wash your clothes," Almatroushi says, "but that will have to be the subject of another student's dissertation."

Eisa A. Almatroushi and Robert A. Johnson are Ph.D. candidates in chemical engineering in the College of Engineering. Their adviser is Ali Borhan, Ph.D., associate professor of chemical engineering, 104 Fenske Lab, University Park, PA 16802; 814-865-7847; borhan@psu.edu. Almatroushi can be reached at 208 Fenske; 814-863-1388; mailto:eam156@psu.edu">eam156@psu.edu and Johnson at 102 Fenske; 814-863-8087; raj6@psu.edu. Johnson's research is funded by the Petroleum Research Fund of the American Chemical Society; Almatroushi receives his support from the United Arab Emirates University.

Last Updated January 01, 2000