Most people think nothing of it when their desktop ink jet printer spews out page after page of documents, or how the characters are formed, letter after letter, line after line. The hum of the cartridge moving across the page is their only concern. But what if users knew the real mechanism by which those characters, each made up of thousands of minuscule dots squirted out of tiny nozzles, were produced? What if they knew that hundreds of microscopic pads were heated at rates of almost 1 billion degrees per second? Why, people might even be amazed - both by the temperatures involved and that they even could be measured.

"The bubble-jet printing process is undoubtedly a significant achievement in design and ingenuity, drawing upon concepts in boiling of liquids, electronics, heat transfer and fluid mechanics," said C. Thomas Avedisian, Cornell University professor of mechanical and aerospace engineering who led a study on the thermal ink jet process.

But what Avedisian and his colleagues found surprised even them: In confiming the mechanism by which the process works, they measured the highest recorded heating rate on the smallest surface in a boiling process, almost 1 billion degrees per second.

"We knew that the print heads would have to be heated very fast to avoid forming multiple bubbles and that we would be at the edge of prior experimental art with measuring such fast transients, but we were surprised by just how high the heating rates actually were," Avedisian said.

Here is how the process works: Tiny droplets of ink are propelled onto paper from print heads that are about 60 microns square (1 micron = .00004 inches). These droplets may form characters or other images. The droplets are created and propelled by heating the ink in contact with the printheads so fast that the liquid boils sharply, almost explosively.

The vapor bubble, of steam in the experiment's case but of ink vapor in a printer, squeezes the liquid above the bubble partially through a nozzle. Then the bubble collapses extremely rapidly when the power is turned off, pinching off the liquid and forming the droplet. In the commercial product, about 100 of the tiny print heads, or resistors, made of a mixture of tantalum and aluminum, sit on a 1/4-inch silicon chip. The researchers are studying just one of these tiny heaters in their experiments.

For the process to work effectively, a single bubble must be produced on the print head when it is heated. "If the resistor is heated too slowly, multiple bubbles can form on it much the same way that water boils in a teapot, and that decreases print quality," Avedisian said. Increasing the heating rate suppresses the familiar teapot-like boiling in favor of the more preferred mode - by molecular density fluctuations in the liquid, which create only one bubble.

To achieve this, the ink must be heated to well above its normal boiling point (212ûF for water at atmospheric pressure). The researchers anticipated that temperatures close to 570ûF would have to be reached, which is a theoretical limit for water (the "critical point" of water is about 705ûF, and it is not possible to maintain the liquid state at higher temperatures at any pressure). For the liquid to reach such high temperatures above the boiling point without boiling, the researchers calculated that surface heating rates higher than 100 million degrees per second would have to be realized for the bubble jet print head.

"No one had previously measured heating rates this high for such tiny surfaces in a boiling process. Higher heating rates have, however, been measured for laser heating solids in air," Avedisian said.

"The importance of knowing the surface temperature is that it establishes physical mechanisms for boiling, and models can be formulated based on such mechanisms for improving printers," Avedisian said. A major ink jet printer manufacturer, Hewlett Packard Co. (HP), also wanted to know the answer. Thus began a quest that took six years, working with several students, some of whom now are employed by HP.

With funding from HP, which donated all the equipment, the Cornell researchers designed an experiment to study the short duration transient heating process. The team consists of Avedisian, who is an expert in heat transfer and fluid mechanics, and Francis D. McLeod Jr., lecturer in electrical engineering and an expert in circuit theory and design. The two devised an exquisite experiment to measure surface temperature and the time it takes for a bubble to form under conditions found within office desk-jet printers.

A student, Bill Osborne, an HP employee on a one-year company fellowship from HP's Vancouver, Wash., Printer Operation Laboratory, completed the project this year. Osborne earned his master of engineering degree at Cornell in 1996 in part with his report, "Nucleation Experiments with Thermal Ink Jet Thin Film Resistors," typed, of course, on an HP DeskJetPrinter.

The problem for the researchers was to measure the surface temperature on the time scale of the heating process, about 5 microseconds (1 microsecond= 10-6 seconds), and to acquire enough data during the transient to draw meaningful conclusions.

The researchers used a relatively simple concept for measuring surface temperature: They first measured the electrical resistance of the heater pad during the time it takes for a bubble to form and collapse, and then calibrated the heater resistance with temperature. But it wasn't easy.

"We had to solve a whole host of problems. We had to find a way to measure and store the print head temperature on a very small time scale and a microscale surface. We had to be able to identify when during the transient heating process a bubble formed. We also had practical problems, such as how to eliminate electrical noise in the output signal. Data storage was a problem because of the small time scales and the necessity of acquiring enough data to draw meaningful conclusions. A final problem was the need for calibratingthe electrical resistance of the tiny print head against temperature toconvert the measured electrical resistance to average surface temperature."

The critical elements needed to finish the project were computerizing the data acquisition system, completed by graduate student Charles Curley as part of his master of engineering project in 1995 and Osborne's work this year in developing a method for calibrating the print head electrical resistance with temperature.

The result: They found that these minature power plants are heated at rates close to 1 billion degrees per second under some conditions, all in that little office printer spewing out page after page, letter after letter . . .