Effective governing equations for dual porosity Darcy-Brinkman systems subjected to inhomogeneous body forces and their application to the lymph node

Girelli, A., Giantesio, G., Musesti, A. and Penta, R. (2023) Effective governing equations for dual porosity Darcy-Brinkman systems subjected to inhomogeneous body forces and their application to the lymph node. Proceedings of the Royal Society Series A: Mathematical, Physical and Engineering Sciences, 479(2276), 20230137. (doi: 10.1098/rspa.2023.0137)

Abstract

We derive the homogenised governing equations for a double porosity system where the fluid flow within the individual compartments is governed by the coupling between the Darcy and the Darcy-Brinkman equations at the microscale, and are subjected to inhomogeneous body forces. The homogenised macroscale results are obtained by means of the asymptotic homogenization technique and read as a double Darcy differential model with mass exchange between phases. The role of the microstructure is encoded in the effective hydraulic conductivities which are obtained by solving periodic cell problems whose properties are illustrated and compared. We conclude by solving the new model by means of a semi-analytical approach under the assumption of azimuthal axisymmetry to model the movement of fluid within a lymph node.

• Item Type: Articles
• Additional Information: This work was partially supported by National Group of Mathematical Physics (GNFM-INdAM).R.P. is partially funded by EPSRC grant nos. EP/S030875/1 and EP/T017899/1.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Penta, Dr Raimondo
• Authors: Girelli, A., Giantesio, G., Musesti, A., and Penta, R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the Royal Society Series A: Mathematical, Physical and Engineering Sciences
• Publisher: The Royal Society
• ISSN: 1364-5021
• ISSN (Online): 1471-2946
• Published Online: 02 August 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Proceedings of the Royal Society Series A: Mathematical, Physical and Engineering Sciences 479(2276):20230137
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
303232		EPSRC Centre for Multiscale soft tissue mechanics with MIT and POLIMI (SofTMech-MP)	Xiaoyu Luo	Engineering and Physical Sciences Research Council (EPSRC)	EP/S030875/1	M&S - Mathematics
308255		The SofTMech Statistical Emulation and Translation Hub	Dirk Husmeier	Engineering and Physical Sciences Research Council (EPSRC)	EP/T017899/1	M&S - Statistics