Kim Solves 140-Year-Old Fluid Mechanics Enigma
Sangtae Kim, Distinguished Professor of Chemical
Engineering, has solved a 140-year-old enigma in
fluid mechanics: Why does a simple formula describe
the seemingly complex physics for the behavior of
elliptical particles moving through fluid?
The findings have potential implications for research
and industry because ellipsoid nanoparticles are
encountered in various applications including those
involving pharmaceuticals, foods and cosmetics.
Like a sphere, the oblong ellipsoids undergo "rigid
body motion" when submerged in a fluid, meaning
they do not deform while moving from side to side
and rotating. However, because an ellipsoid is not
perfectly spherical, it is counterintuitive that its rigid-
body motion in a fluid could be described using the
same simple mathematical expression as spheres.
"In general, you would expect a very complicated
expression because an ellipsoid is not a perfect
sphere," said Kim, who first came to Purdue in 2004.
Yet that is not the case, presenting a quandary
that Kim has been pondering since his days as an
undergraduate in the 1970s.
"It has been gnawing at me since then," he said.
MIT chemical engineer Howard Brenner wrote a paper
in 1964 showing the mathematics behind the simple
formula, but it took pages of complex calculations to
arrive at the simple result.
"Dr. Brenner highlighted this simplicity," Kim said. "But
the simplicity of the result could only be shown by
going through 5 to 10 pages of very messy algebra and
calculations. In the end, everything cancels and you get
this final very simple result. It's almost like a miracle,
which has bothered me for a long time."
He has solved the enigma in a new paper appearing
in November in a special issue of the American
Chemical Society (ACS) journal Industrial & Engineering
Chemistry Research. The special issue honors the 50th
anniversary of Purdue's Doraiswami Ramkrishna's
doctoral dissertation, which is considered a landmark
in chemical engineering. Ramkrishna is Purdue’s
(left image) Dr. Sangtae Kim with Purdue President Mitch Daniels. (Inset image) Dr. Kim's research received an editor's choice
distinction in the journal Industrial & Engineering Chemistry Research.
by Emil Venere