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Measuring Flux Distributions for Diffusion in the Small-Numbers Limit

Seitaridou, Effrosyni and Inamdar, Mandar M. and Phillips, Rob and Ghosh, Kingshuk and Dill, Ken (2007) Measuring Flux Distributions for Diffusion in the Small-Numbers Limit. Journal of Physical Chemistry B, 111 (9). pp. 2288-2292. ISSN 1520-6106. PMCID PMC3261839. doi:10.1021/jp067036j. https://resolver.caltech.edu/CaltechAUTHORS:20170526-112238161

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Abstract

For the classical diffusion of independent particles, Fick's law gives a well-known relationship between the average flux and the average concentration gradient. What has not yet been explored experimentally, however, is the dynamical distribution of diffusion rates in the limit of small particle numbers. Here, we measure the distribution of diffusional fluxes using a microfluidics device filled with a colloidal suspension of a small number of microspheres. Our experiments show that (1) the flux distribution is accurately described by a Gaussian function; (2) Fick's law, that the average flux is proportional to the particle gradient, holds even for particle gradients down to a single particle difference; (3) the variance in the flux is proportional to the sum of the particle numbers; and (4) there are backward flows, where particles flow up a concentration gradient, rather than down it. In addition, in recent years, two key theorems about nonequilibrium systems have been introduced:  Evans' fluctuation theorem for the distribution of entropies and Jarzynski's work theorem. Here, we introduce a new fluctuation theorem, for the fluxes, and we find that it is confirmed quantitatively by our experiments.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1021/jp067036jDOIArticle
http://pubs.acs.org/doi/abs/10.1021/jp067036jPublisherArticle
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3261839/PubMed CentralArticle
ORCID:
AuthorORCID
Phillips, Rob0000-0003-3082-2809
Additional Information:© 2007 American Chemical Society. Received: October 26, 2006; In Final Form: December 27, 2006. Publication Date (Web): February 13, 2007. We thank S. Blumberg, F. Brown, D. Drabold, P. Grayson, L. Han, C. Jarzynski, J. Kondev, H. J. Lee, H. Qian, S. Quake, S. Ramaswamy, U. Seifert, T. Squires, Z. G. Wang, E. Weeks, and D. Weitz for helpful and stimulating comments and discussions. K.D. and M.M.I. would like to acknowledge support from NIH Grant No. R01GM34993, E.S. acknowledges support from the Betty and Gordon Moore Fellowship, and R.P. acknowledges support from NSF Grant No. CMS-0301657, CIMMS, the Keck Foundation, NSF NIRT Grant No. CMS-0404031, and NIH Director's Pioneer Award Grant No. DP1 OD000217.
Funders:
Funding AgencyGrant Number
NIHR01GM34993
Gordon and Betty Moore FoundationUNSPECIFIED
NSFCMS-0301657
W. M. Keck FoundationUNSPECIFIED
NSFCMS-0404031
NIHDP1 OD000217
Issue or Number:9
PubMed Central ID:PMC3261839
DOI:10.1021/jp067036j
Record Number:CaltechAUTHORS:20170526-112238161
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170526-112238161
Official Citation:Measuring Flux Distributions for Diffusion in the Small-Numbers Limit Effrosyni Seitaridou, Mandar M. Inamdar, Rob Phillips, Kingshuk Ghosh, and Ken Dill The Journal of Physical Chemistry B 2007 111 (9), 2288-2292 DOI: 10.1021/jp067036j
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77813
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 May 2017 19:06
Last Modified:15 Nov 2021 17:34

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