Cookies on this website
We use cookies to ensure that we give you the best experience on our website. If you click 'Continue' we'll assume that you are happy to receive all cookies and you won't see this message again. Click 'Find out more' for information on how to change your cookie settings.

Summary We investigate the behaviour of flux-driven flow through a single-phase fluid domain coupled to a biphasic poroelastic domain. The fluid domain consists of an incompressible Newtonian viscous fluid while the poroelastic domain consists of a linearly elastic solid filled with the same viscous fluid. The material properties of the poroelastic domain, that is permeability and elastic parameters, depend on the inhomogeneous initial porosity field. We identify the dimensionless parameters governing the behaviour of the coupled problem: the ratio between the magnitudes of the driving velocity and the Darcy flows in the poroelastic domain, and the ratio between the viscous pressure scale and the size of the elastic stresses in the poroelastic domain. We consider a perfusion system, where flow is forced to pass from the single-phase fluid to the biphasic poroelastic domain. We focus on a simplified two-dimensional geometry with small aspect ratio and perform an asymptotic analysis to derive analytical solutions. The slender geometry is divided in four regions, two outer domains that describe the regions away from the interface and two inner domains that are the regions across the interface. Our analysis advances the quantitative understanding of the role of heterogeneous material properties of a poroelastic domain on its mechanical response when coupled with a fluid domain. The analysis reveals that, in the interfacial zone, the fluid and the elastic behaviours of this coupled Stokes—poroelastic problem can be treated separately via (i) a Stokes–Darcy coupling and (ii) the solid skeleton being stress free. This latter finding is crucial to derive the coupling condition across the outer domains for both the elastic part of the poroelastic domain and the fluid flow. Via specification of heterogeneous material properties distribution, we reveal the effects of heterogeneity and deformability on the mechanics of the poroelastic domain.

Original publication

DOI

10.1093/qjmam/hbab014

Type

Journal article

Journal

The Quarterly Journal of Mechanics and Applied Mathematics

Publisher

Oxford University Press (OUP)

Publication Date

10/12/2021

Volume

74

Pages

411 - 439