Tear-free brushing? All you need is math

Anyone who has ever had to brush long hair knows how bad knots can be. If you have enough experience, you can start at the bottom, work your way up to the head with gentle brushes, and apply a detangler when necessary.

L. Mahadevan, the Professor of Applied Mathematics, of Organismic and Evolutionary Biology, and of Physics, learned the mechanics of combing while brushing his daughter's hair.

Mahadevan was fired from the job as he was not very patient.

While Mahadevan lost his job as a hairdresser, he was still a scientist and he had interesting mathematical questions that were relevant to a range of applications including textile manufacturing and chemical processes.

Mahadevan and his co-authors explain the mathematics of combing in a new paper published in the journal Soft Matter.

To simplify the problem, the researchers used two intertwined strands of hair.

A graduate student at SEAS said that they study the detangling of the double helix using a single stiff tine that moves along it.

A flow of a mathematical quantity called the "link density" that characterizes the amount that hair strands that are braided with each other, is created by short strokes that start at the free end and move towards the clamped end.

It would take forever to comb out all the tangles and it would be too painful.

The mathematical principles of brushing developed by Plumb-Reyes, Charles and Mahadevan were recently used by Professor Rus and her team at MIT to design a method for brushing hair by a robot.

Next, the team wants to study the mechanics of brushing curly 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.

More information: Thomas B. Plumb-Reyes et al, Combing a double helix, Soft Matter (2022). DOI: 10.1039/D1SM01533H Journal information: Soft Matter Citation: Tear-free brushing? All you need is math (2022, April 13) retrieved 14 April 2022 from https://phys.org/news/2022-04-tear-free-math.html This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.