• Tear-free hair brushing? All you need is

    From ScienceDaily@1:317/3 to All on Wed Apr 13 22:30:44 2022
    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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