Jump to ContentJump to Main Navigation
Brownian Motion$
Users without a subscription are not able to see the full content.

Robert M. Mazo

Print publication date: 2008

Print ISBN-13: 9780199556441

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199556441.001.0001

EINSTEIN–SMOLUCHOWSKI THEORY

Chapter:
(p.46) 4 EINSTEIN–SMOLUCHOWSKI THEORY
Source:
Brownian Motion
Author(s):

Robert M. Mazo

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199556441.003.0004

This chapter begins the study of the physical study of Brownian motion. The theory of Smoluchowski is based on a kinetic model of colliding spheres, at first for an ambient dilute gaseous medium. This result is then generalized, approximately to a dense ambient medium. It is indicated how fluctuations may give an appreciable effect when the effect of an individual collision is negligible. Essentially the same result is obtained by Einstein's theory, using probabilistic, instead of kinetic reasoning. The relation of the friction constant to the diffusion coefficient is obtained. The Langevin equation, expressing the foregoing ideas in dynamical terms is discussed.

Keywords:   Einstein, Smoluchowski, Langevin equation, Stokes–Einstein, rotation, fluctuation, viscosity, root-mean-square displacement, random force, friction

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.