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Fluid Permeation Through A Membrane With Infinitesimal Permeability Under Reynolds Lubrication

Published online by Cambridge University Press:  14 August 2020

Asahi Tazaki ,
Shintaro Takeuchi Open the ORCID record for Shintaro Takeuchi [Opens in a new window] ,
Suguru Miyauchi ,
Lucy T. Zhang ,
Ryo Onishi  and
Takeo Kajishima
Asahi Tazaki
Affiliation:
Dept. of Mechanical Engineering, Osaka University, Osaka, Japan
Shintaro Takeuchi*
Affiliation:
Dept. of Mechanical Engineering, Osaka University, Osaka, Japan
Suguru Miyauchi
Affiliation:
Institute of Fluid Science, Tohoku University, Miyagi, Japan Dept. of Mechanical Engineering, University College London, Torrington Place, London, UK
Lucy T. Zhang
Affiliation:
Dept. of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, New York, USA
Ryo Onishi
Affiliation:
Center for Earth Information Science and Technology, Japan Agency for Marine-Earth Science and Technology, Kanagawa, Japan
Takeo Kajishima
Affiliation:
Dept. of Mechanical Engineering, Osaka University, Osaka, Japan
*
*Corresponding author ([email protected])

Abstract

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To understand the lubrication-dominated permeation through a membrane, numerical simulations of permeation through a moving corrugated permeable membrane is carried out with a fully validated numerical method. Through comparisons between the numerical results and the results of an asymptotic analysis of permeate flux (under an infinitesimal permeability condition) using Reynolds lubrication equation, the effect of permeation on lubrication and its inverse effect (i.e., the dependence of permeation on lubrication) are discussed. The linear and non-linear dependences of the relaxation of the lubrication pressure due to membrane permeation are identified. The effect of the tangential component of the permeate flux is evaluated by a linear analysis, and the limitation of Reynolds-type lubrication is discussed.

Keywords

LubricationPermeable membranePressure discontinuityDiscrete-forcing immersed boundary method
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 5 , October 2020 , pp. 637 - 648
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

References

REFERENCES

Kaazempur-Mofrad, M.R., Wada, S., Myers, J.G. and Ethier, C.R., “Mass transport and fluid flow in stenotic arteries: Axisymmetric and symmetric models,” International Journal of Heat and Mass Transfer, 48, pp. 4510-4517 (2005).CrossRefGoogle Scholar
Balogh, P. and Bagchi, P., “A computational approach to modeling cellular-scale blood flow in complex geometry,” Journal of Com Putational Physics, 334, pp. 280-307 (2017).CrossRefGoogle Scholar
Zhang, L.T., “Shear stress and shear-induced particle residence in stenosed blood vessels,” International Journal of Multiscale Computational Engineering, 6(2), pp.141-152 (2008)CrossRefGoogle Scholar
Gay, M. and Zhang, L.T. “Numerical studies of healthy, stenosed, and stented coronary arteries,” International Journal of Numerical Methods in Fluids, 61, pp.453-472 (2009)CrossRefGoogle Scholar
Cooley, M.D.A. and O’Neill, M.E., “On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or stationary sphere,” Mathematika, 16(1), 37-49 (1969).CrossRefGoogle Scholar
O’Neill, M.E. and Majumdar, S.R., “Asymmetrical slow viscous fluid motions caused by the translation or rotation of two spheres. Part II: asymptotic forms of the solutions when the minimum clearance between the spheres approaches zero,” Zeitschriftf:ur angewandte Mathematik und Physik (ZAMP), 21, Issue 2, pp.180-187 (1970).Google Scholar
Jeffrey, D.J. and Onishi, Y., “Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow,” J. Fluid Mech., 139, pp.261-290 (1984).CrossRefGoogle Scholar
Dance, S. L. and Maxey, M.R., “Incorporation of lubrication effects into the force-coupling method for particulate two-phase flow,” Journal of Computational Physics, 189, pp.212-238 (2003).CrossRefGoogle Scholar
Takeishi, N., Ii, S. and Wada, S. “Blood cells and convective mass transport”, Journal of the Heat Transfer Society of Japan, Vol. 58, No. 242, pp.22-29 (2019) https://www.htsj.or.jp/wp/media/2019_1.pdfGoogle Scholar
Reynolds, O., “On the theory of lubrication and its application to Mr. Beuchamp towers experiments, including an experimental determination of the viscosity of olive oil,” Philosophical Transactions of the Royal Society of London, 177, pp.157-234 (1886).Google Scholar
Gu, J., Sakaue, M., Takeuchi, S. and Kajishima, T., “An immersed lubrication model for the fluid flow in a narrow gap region,” Powder Technology, 329, pp.445-454 (2018). http://doi.org/10.1016/j.powtec.2018.01.040CrossRefGoogle Scholar
Miyauchi, S., Takeuchi, S. and Kajishima, T., “A numerical method for mass transfer by a thin moving membrane with selective permeabilities,” Journal of Computational Physics, 284, pp.490-504 (March 2015). http://doi.org/10.1016/j.jcp.2014.12.048CrossRefGoogle Scholar
Miyauchi, S., Takeuchi, S. and Kajishima, T., “A numerical method for interaction problems between fluid and membranes with arbitrary permeability for fluid,” Journal of Computational Physics, 345, pp.33-57 (2017). http://doi.org/10.1016/j.jcp.2017.05.006CrossRefGoogle Scholar
Kim, Y. and Peskin, C.S., “2-D parachute simulation by the immersed boundary method,” SIAM Journal of Scientific Computing, 28(6), pp. 2294-2312 (2006).CrossRefGoogle Scholar
Layton, A.T., “Modeling water transport across elastic boundaries using an explicit jump method,” SIAM Journal of Scientific Computing, 28(6), pp. 2189-2207 (2006).CrossRefGoogle Scholar
Huang, H., Sugiyama, K. and Takagi, S., “An immersed boundary method for restricted diffusion with permeable interfaces,” Journal of Computational Physics, 228, pp. 5317-5322 (2009).CrossRefGoogle Scholar
Gong, X., Gong, Z. and Huang, H., “An immersed boundary method for mass transfer across permeable moving interfaces,” Journal of Computational Physics, 278, pp. 148-168 (2014).10.1016/j.jcp.2014.08.025CrossRefGoogle Scholar
Breugem, W.-P., “A second-order accurate immersed boundary method for fully resolved simulations of particle-laden flows” Journal of Computational Physics, 231, pp.4469-4498 (2012).CrossRefGoogle Scholar
Sato, N., Takeuchi, S., Kajishima, T., Inagaki, M. and Horinouchi, N., “A consistent direct discretization scheme on Cartesian grids for convective and conjugate heat transfer,” Journal of Computational Physics, 321, pp. 76-104 (2016). http://doi.org/10.1016/j.jcp.2016.05.034CrossRefGoogle Scholar
Takeuchi, S., Fukuoka, H., Gu, J. and Kajishima, T., “Interaction problem between fluid and membrane by a consistent direct discretisation approach,” Journal of Computational Physics, 371, pp. 1018-1042 (2018). http://doi.org/10.1016/j.jcp.2018.05.033CrossRefGoogle Scholar
Takeuchi, S., Tazaki, A., Miyauchi, S. and Kajishima, T., “A relation between membrane permeability and flow rate at low Reynolds number in circular pipe,” Journal of Membrane Science, 582, pp.91-102 (2019). http://doi.org/10.1016/j.memsci.2019.03.018CrossRefGoogle Scholar
Katchalsky, A. and Curran, P.F., “Nonequilibrium Thermodynamics in Biophysics,” Harvard University Press (1966)Google Scholar
Tipei, N., Theory of Lubrication: With Applications to Liquid- and Gas-Film Lubrication, Stanford University Press (1962).Google Scholar
Leal, L. G., Advanced Transport Phenomena: Fluid Mechanics and Convective Transport, Cambridge University Press (2007).CrossRefGoogle Scholar
Takeuchi, S. and Gu, J., “Extended Reynolds lubrication model for incompressible Newtonian fluid”, Physical Review Fluids, Vol.4, No. 11, 114101 (2019) https://doi.org/10.1103/PhysRevFluids.4.114101CrossRefGoogle Scholar
Ikeno, T. and Kajishima, T., “Finite-difference immersed boundary method consistent with wall conditions for incompressible turbulent flow simulations,” Journal of Computational Physics, 226, pp.1485-1508 (2007).CrossRefGoogle Scholar
Mohd-Yusof, J., “Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries,” Annual Research Briefs, Center for Turbulence Research, Stanford University, pp. 317-327 (1997).Google Scholar
Fadlun, E.A., Verzicco, R., Orlandi, P. and Mohd-Yusof, J., “Combined immersed-boundary finite difference methods for three-dimensional complex flow simulations,” Journal of Computational Physics, 161, pp. 35-60 (2000).CrossRefGoogle Scholar