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Mass transport through interstitial structures

Iwanowska-Chomiak B., Walicka A.

International Journal of Applied Mechanics and Engineering

2019

Vol. 24, no. 4

66--91

Interstitial space, also called interstitum, separating the vital organs of a human body, is the primary source of lymph and is a major fluid compartment in the body. Interstitial space (IS) is filled out by thick collagen (CL) bundles which form lattices represented by a network of capillaries. This network has the structure similar to a sponge porous matrix (SPM) with pores-capillaries of variable cross-section. To analyse the mass transport of interstitial fluids (IFs) through the porous matrix it is assumed that the SPM is composed of an irregular system of pores which may be modelled as a fractal porous matrix. The interstitial fluids can be either bio-suspensions or bio-solutions and therefore they have to be modelled as non-Newtonian fluids. Analysing the fluid flow through the porous matrix it is assumed that the SPM is modelled as capillary tubes of variable radii. Introducing a hindrance factor allowed us to consider the porous matrix as a system of fractal capillaries but of constant radii. Classical and fractal expressions for the flow rate, velocity and permeability are derived based on the physical properties of the capillary model of interstitial structures. Each parameter in the proposed expressions does not contain any empirical constant and has a clear physical meaning, and the proposed fractals models relate the flow properties of the fluids under consideration with the structural parameters of interstitium as a porous medium.