Tear-free hair brushing? All you need is math
Researchers develop a mathematical understanding of detangling that could
be used for textile manufacturing, robotic hairdressers
Date:
April 13, 2022
Source:
Harvard John A. Paulson School of Engineering and Applied Sciences
Summary:
Scientists explore the mathematics of combing and explain why the
brushing technique used by so many is the most effective method
to detangle a bundle of fibers.
FULL STORY ==========================================================================
As anyone who has ever had to brush long hair knows, knots are a
nightmare. But with enough experience, most learn the tricks of detangling
with the least amount of pain -- start at the bottom, work your way up to
the scalp with short, gentle brushes, and apply detangler when necessary.
==========================================================================
L. Mahadevan, the Lola England de Valpine Professor of Applied
Mathematics, of Organismic and Evolutionary Biology, and of Physics,
learned the mechanics of combing years ago while brushing his young
daughter's hair.
"I recall that detangling spray seemed to work sometimes, but I still
had to be careful to comb gently, by starting from the free ends," said Mahadevan. "But I was soon fired from the job as I was not very patient."
While Mahadevan lost his role as hairdresser, he was still a scientist
and the topology, geometry and mechanics of detangling posed interesting mathematical questions that are relevant to a range of applications
including textile manufacturing and chemical processes such as polymer processing.
In a new paper, published in the journal Soft Matter, Mahadevan
and co-authors Thomas Plumb Reyes and Nicholas Charles, explore the
mathematics of combing and explain why the brushing technique used by
so many is the most effective method to detangle a bundle of fibers.
To simplify the problem, the researchers simulated two helically entwined filaments, rather than a whole head of hair.
"Using this minimal model, we study the detangling of the double helix via
a single stiff tine that moves along it, leaving two untangled filaments
in its wake," said Plumb-Reyes, a graduate student at SEAS. "We measured
the forces and deformations associated with combing and then simulated it numerically." "Short strokes that start at the free end and move towards
the clamped end remove tangles by creating a flow of a mathematical
quantity called the 'link density' that characterizes the amount that
hair strands that are braided with each other, consistent with simulations
of the process" said Nicholas Charles, a graduate student at SEAS.
The researchers also identified the optimal minimum length for each
stroke - - any smaller and it would take forever to comb out all the
tangles and any longer and it would be too painful.
The mathematical principles of brushing developed by Plumb-Reyes, Charles
and Mahadevan were recently used by Professor Daniela Rus and her team
at MIT to design algorithms for brushing hair by a robot.
Next, the team aims to study the mechanics of brushing curlier hair
and how it responds to humidity and temperature, which may lead to a mathematical understanding of a fact every person with curly hair knows:
never brush dry hair.
This research was supported by funds from the US National Science
Foundation, and the Henri Seydoux Fund.
========================================================================== Story Source: Materials provided by Harvard_John_A._Paulson_School_of_Engineering_and_Applied
Sciences. Original written by Leah Burrows. Note: Content may be edited
for style and length.
========================================================================== Journal Reference:
1. Thomas B. Plumb-Reyes, Nicholas Charles, L. Mahadevan. Combing
a double
helix. Soft Matter, 2022; 18 (14): 2767 DOI: 10.1039/D1SM01533H ==========================================================================
Link to news story:
https://www.sciencedaily.com/releases/2022/04/220413203128.htm
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