Fractals -- jagged, chaotic geometrical arrays that never smooth out, no matter how closely you look at them -- best describe the liquid-gas interface of a spray, according to a four-person team led by Antonio Sarmiento-Galan of the Mathematics Institute at Mexico's National University. While studying the fractal nature of sprays, the researchers claim they discovered how to increase the efficiency of spray application processes used, say, in coating electrical connections with copper films to improve conductivity. Another example is the application of metals to substrates -- such as ceramic or glass -- to make flexible electrical circuits.

"The total efficiency of a spray grows as the 'fractality' of the liquid increases," Sarmiento-Galan told NewsFactor. The more fractal -- or chaotic -- the spray, then, the better.

Ragged Reality

Introduced by the Polish mathematician Benoit Mandelbrot, fractals research attempts to express the "raggedness" of the real world in concise mathematical terms. Seashores, snowflakes and an atomized perfume spritz all exhibit uneven edges and fractional, rather than integral, dimensions.

Fractional dimensions express the approximate "roughness" of fractal curves. While a line has a dimension of 1, a rough line that zigs and zags adds almost -- but not quite -- another dimension to its wanderings. Roughness, then, is a fractional increase in dimension: A rough line has a dimension between 1 and 2 -- 1 1/4, say -- and a rough surface has a dimension between 2 and 3.

Atomized and Visualized

"In most spray processes, the particle stream arriving at the substrate is not uniform," University of Minnesota mechanical engineering professor Joachim Heberlein told NewsFactor. "The particles are not all following the same trajectories on their way to the substrate," he explained. Heberlein directs the university's high temperature and plasma technology laboratory and studies the mechanics of spray processes.

Observing the chaotic dynamics of sprays posed challenges that Sarmiento-Galan and his team overcame with a so-called "shadow graph technique" that photographs transparent objects, such as air and water. Illuminating the spray from behind so the light striking the spray passed through it, the team photographed the atomization process, "which occurs as a result of the interaction between the liquid state and the surrounding air and involves several stages through which the liquid becomes an aerosol," Sarmiento-Galan explained.

Fast-Moving Clouds

Initially, the fluid leaves the atomizer as "thin laminar waves that are gradually converted by aerodynamic forces into thin ligaments," Sarmiento-Galan said. "Downstream, these ligaments are broken up into a cloud of small droplets that continue to move with an average velocity of several meters per second." (continued...)

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