Fourth-order analysis of a diffusive lattice Boltzmann method for barrier coatings

Kyle T. Strand, Aaron J. Feickert, and Alexander J. Wagner
Phys. Rev. E 95, 063311 – Published 20 June 2017

Abstract

We examine the applicability of diffusive lattice Boltzmann methods to simulate the fluid transport through barrier coatings, finding excellent agreement between simulations and analytical predictions for standard parameter choices. To examine more interesting non-Fickian behavior and multiple layers of different coatings, it becomes necessary to explore a wider range of parameters. However, such a range of parameters exposes deficiencies in such an implementation. To investigate these discrepancies, we examine the form of higher-order terms in the hydrodynamic limit of our lattice Boltzmann method. We identify these corrections to fourth order and validate these predictions with high accuracy. However, it is observed that the validated correction terms do not fully explain the bulk of observed error. This error was instead caused by the standard finite boundary conditions for the contact of the coating with the imposed environment. We identify a self-consistent form of these boundary conditions for which these errors are dramatically reduced. The instantaneous switching used as a boundary condition for the barrier problem proves demanding enough that any higher-order corrections meaningfully contribute for a small range of parameters. There is a large parameter space where the agreement between simulations and analytical predictions even in the second-order form are below 0.1%, making further improvements to the algorithm unnecessary for such an application.

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  • Received 20 March 2017

DOI:https://doi.org/10.1103/PhysRevE.95.063311

©2017 American Physical Society

Physics Subject Headings (PhySH)

Polymers & Soft Matter

Authors & Affiliations

Kyle T. Strand*, Aaron J. Feickert, and Alexander J. Wagner

  • Department of Physics, North Dakota State University, NDSU Dept. 2755, P. O. Box 6050, Fargo, North Dakota 58108-6050, USA

  • *kyle.t.strand@ndsu.edu
  • aaron.feickert@ndsu.edu
  • alexander.wagner@ndsu.edu

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Issue

Vol. 95, Iss. 6 — June 2017

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