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. 2017 Dec 14;7:17551. doi: 10.1038/s41598-017-17883-0

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Image (a) of a time-dependent droplet concentration c⁻ (y, z, t)profile in a purely diffusional 2D COMSOL model in the y−z plane. In this case the boundary layer is significantly larger and is slower to reach equilibrium. Image (b) of a droplet concentration c⁻(y, z, t) profile in a coupled 2D advection-diffusion physics model that is mixed by a spinning disk at 30 RPM. Qualitatively, it is apparent that the Blasius boundary layer decreases the diffusional UWL thickness. Image (c) of a droplet concentration c⁻ profile in a coupled 2D advection-diffusion physics model that is mixed by a spinning disk at 0, 11, 20, 50, 100 and 200 RPM (snapshot taken at one minute). Qualitatively, the diffusion layer can be seen to be drastically reduced at higher disk rotation speeds. Note that the droplet diameter is set at 1 mm and that the right side donor droplet (+) is truncated for clarity. An intrinsic membrane permeability of P _m = 1.98 × 10⁻⁴ cm s⁻¹ was used in this model.