Fluid mechanics mystery solved

Date:
June 10, 2020
Source:
Oregon State University
Summary:
An environmental engineering professor has solved a decades-old
mystery regarding the behavior of fluids, a field of study with
widespread medical, industrial and environmental applications.



FULL STORY ==========================================================================
An Oregon State University environmental engineering professor has solved
a decades-old mystery regarding the behavior of fluids, a field of study
with widespread medical, industrial and environmental applications.


==========================================================================
The research by Brian D. Wood, published in the Journal of Fluid
Mechanics, clears a roadblock that has been puzzling scientific minds for nearly 70 years and paves the way to a clearer picture of how chemicals
mix in fluids.

A more complete grasp of that basic principle provides a foundation
for advances in a range of areas -- from how pollutants spread in the atmosphere to how drugs perfuse tissues within the human body.

Funded by the National Science Foundation, Wood's work with dispersion
theory builds on research by one of the most accomplished scientists
in Oregon State history, Octave Levenspiel. A 1952 chemical engineering
Ph.D. graduate and later a longtime faculty member, Levenspiel in 1957 published an important paper on dispersion in chemical reactors on his
way to becoming the college's first inductee to the National Academy
of Engineering.

Even more importantly, the research by Wood bridges a longstanding gap
in one of the fundamental tenets of fluid mechanics: Taylor dispersion
theory. Named for British physicist and mathematician G.I. Taylor,
author of a seminal 1953 paper, the theory concerns phenomena in which fluctuations in a fluid's velocity fields cause chemicals to spread
within it.

"The process of dispersive spreading tends to increase over time until
it reaches a steady level," Wood said. "You can think of it as analogous
to investment in a startup, in which the rates of return can initially
be very large before settling in to a more sustainable level that is
close to constant." Taylor's theory was the first to allow researchers
to predict that steady level of dispersion using what's known as the macroscopic dispersion equation. The equation can describe the net
movement of a chemical species in a fluid - - provided enough time has
elapsed from when the chemical entered the fluid.



========================================================================== "That was a significant revelation at the time," Wood said. "It was on
par with what researchers were doing theoretically in other disciplines,
like quantum mechanics." While Taylor's theory was successful and revolutionary, researchers still struggled with the problem of how
dispersive spreading evolves from its dynamic, early behavior -- what's
termed as its initial condition -- to when it attains the more constant
value predicted by Taylor.

Scientists found some success by adding to the equation a time-dependent dispersion coefficient, but the coefficient created problems of its own,
the primary one being paradoxes.

"For example, if chemical solutes injected into a fluid at two
different times overlap, which time do you assign to the dispersion coefficient?" Wood said.

"Taylor himself understood that, where a time-dependent dispersion
coefficient was adopted, contemporary theories violated basic notions
of causality in physics." Wood and collaborators used another canon,
the theory of partial differential equations, to show that problems
with the time-dependent dispersion coefficient arose from neglecting
the relaxation of the solute -- the chemical injected into the fluid,
or solution -- from its initial condition.



========================================================================== "When chemical species are first injected, their behavior is
not necessarily consistent with a dispersion-type equation," Wood
explained. "Rather, the initial condition first has to 'relax.' During
this time, there is an additional term to account for that was missing
in Taylor's macroscale dispersion equation." In an equation, a term
refers to a single number or a variable, or numbers and variables
multiplied together.

The term Wood added corrects the dispersion equation to account for
the initial configuration of the chemical species moving around in
the fluid. Somewhat surprisingly, Wood said, the theory also resolves
paradoxes in other theories with time-dependent dispersion coefficients.

"In the new theory, there is never a question about what dispersion
coefficient should be used when chemical solutes overlap," he said. "The adjustment to the spreading process is accounted for automatically by
the presence of the additional term."

========================================================================== Story Source: Materials provided by Oregon_State_University. Original
written by Keith Hautala. Note: Content may be edited for style and
length.


========================================================================== Journal Reference:
1. E. Taghizadeh, F. J. Valde's-Parada, B. D. Wood. Preasymptotic
Taylor
dispersion: evolution from the initial condition. Journal of Fluid
Mechanics, 2020; 889 DOI: 10.1017/jfm.2020.56 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/06/200610094116.htm

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