The Role of Porous Media in Modeling Fluid Flow Within Hollow Fiber Membranes of the Total Artificial Lung

Abstract

A numerical study was conducted to analyze fluid flow within hollow fiber membranes of the artificial lungs. The hollow fiber bundle was approximated using a porous media model. In addition, the transport equations were solved using the finite-element formulation based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. A Newtonian viscous fluid model for the blood was used. Different flow models for porous media, such as the Brinkman-extended Darcy model, Darcy’s law model, and the generalized flow model, were considered. Results were obtained in terms of streamlines, velocity vectors, and pressure distribution for various Reynolds numbers and Darcy numbers. The results from this investigation showed that the pressure drop across the artificial lung device increased with an increase in the Reynolds number. In addition, the pressure drop was found to increase significantly for small Darcy numbers.

Evaluation of the path integral for flow through random porous media

“…2 is the level of agreement between the two methods: the Kolmogorov-Smirnov test [37] indicates agreement at a confidence level of 95%. This clearly demonstrates the accuracy of our evaluation of the path integral (7). In addition, there are several noteworthy characteristics of these pressure distributions.…”

“…from which we calculate (4) and in the path integral (7). For ξ = 0.01X (solid blue line), the effect of correlations is small, while, for ξ = 0.5X (broken red line), correlations throughout the system are evident.…”

A Membrane Lung Design Based on Circular Blood Flow Paths

“…The permeability was determined by equation 4. 13–16 $$V_{\mathit{\text{fiber bundle}}}=\pi r_{\mathit{\text{HFM}}}^{2}H{N}_{\mathit{\text{HFM}}}$$ $${𝜖}_P=\frac{V_{\mathit{\text{fiber bundle}}}-V_{\mathit{\text{fibers}}}}{V_{\text{italicfiber bundle}}}$$ $$A_{\mathit{\text{fibers}}}=\pi d_{\mathit{\text{HFM}}}H{N}_{\mathit{\text{HFM}}}$$ $$\kappa =\frac{{{𝜖}_P}^3{d_p}^2}{150{false(1-{𝜖}_{P}false)}^2}$$…”

Pediatric Artificial Lung: A Low-Resistance Pumpless Artificial Lung Alleviates an Acute Lamb Model of Increased Right Ventricle Afterload

“…Computational fluid dynamics (CFD) modeling was carried out on ANSYS CFX software (Ansys Inc., Canonsburg, PA), using previously published methods. 9 Briefly, blood was modeled as an incompressible Navier-Stoked fluid (dynamic viscosity 0.00345 Pa s, density 1060 Kg/m 3 ), and the fiber bundle was modeled as a porous media, governed by Darcy’s Law (permeability 1×10 −10 m 2 , porosity 0.50). The boundary conditions were as follows: blood inlet flow rate = 0.5 L/min, blood outlet pressure = atmospheric pressure and walls = no slip.…”