Diffusion and Brownian motion in Lagrangian coordinates

Marios M. Fyrillas, Keiko K. Nomura

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper we consider the convection-diffusion problem of a passive scalar in Lagrangian coordinates, i.e., in a coordinate system fixed on fluid particles. Both the convection-diffusion partial differential equation and the Langevin equation are expressed in Lagrangian coordinates and are shown to be equivalent for uniform, isotropic diffusion. The Lagrangian diffusivity is proportional to the square of the relative change of surface area and is related to the Eulerian diffusivity through the deformation gradient tensor. Associated with the initial value problem, we relate the Eulerian to the Lagrangian effective diffusivities (net spreading), validate the relation for the case of linear flow fields, and infer a relation for general flow fields. Associated with the boundary value problem, if the scalar transport problem possesses a time-independent solution in Lagrangian coordinates and the boundary conditions are prescribed on a material surface/interface, then the net mass transport is proportional to the diffusion coefficient. This can be also shown to be true for large Ṕclet number and time-periodic flow fields, i.e., closed pathlines. This agrees with results for heat transfer at high Ṕclet numbers across closed streamlines.

Original languageEnglish
Article number164510
JournalJournal of Chemical Physics
Volume126
Issue number16
DOIs
Publication statusPublished - 2007
Externally publishedYes

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Brownian movement
diffusivity
flow distribution
boundary value problems
Flow fields
convection
scalars
partial differential equations
Initial value problems
diffusion coefficient
heat transfer
tensors
boundary conditions
Boundary value problems
Partial differential equations
Tensors
gradients
fluids
Mass transfer
Boundary conditions

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Diffusion and Brownian motion in Lagrangian coordinates. / Fyrillas, Marios M.; Nomura, Keiko K.

In: Journal of Chemical Physics, Vol. 126, No. 16, 164510, 2007.

Research output: Contribution to journalArticle

Fyrillas, Marios M. ; Nomura, Keiko K. / Diffusion and Brownian motion in Lagrangian coordinates. In: Journal of Chemical Physics. 2007 ; Vol. 126, No. 16.
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