Next Article in Journal
Fractional Derivatives with the Power-Law and the Mittag–Leffler Kernel Applied to the Nonlinear Baggs–Freedman Model
Next Article in Special Issue
A Fractional B-spline Collocation Method for the Numerical Solution of Fractional Predator-Prey Models
Previous Article in Journal / Special Issue
Towards a Generalized Beer-Lambert Law
Article Menu

Export Article

Open AccessArticle
Fractal Fract 2018, 2(1), 9; https://doi.org/10.3390/fractalfract2010009

Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms

Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802, USA
Received: 16 October 2017 / Revised: 1 February 2018 / Accepted: 2 February 2018 / Published: 6 February 2018
(This article belongs to the Special Issue Fractional Dynamics)
Full-Text   |   PDF [628 KB, uploaded 7 February 2018]   |  

Abstract

Cerebral aneurysms and microaneurysms are abnormal vascular dilatations with high risk of rupture. An aneurysmal rupture could cause permanent disability and even death. Finding and treating aneurysms before their rupture is very difficult since symptoms can be easily attributed mistakenly to other common brain diseases. Mathematical models could highlight possible mechanisms of aneurysmal development and suggest specialized biomarkers for aneurysms. Existing mathematical models of intracranial aneurysms focus on mechanical interactions between blood flow and arteries. However, these models cannot be applied to microaneurysms since the anatomy and physiology at the length scale of cerebral microcirculation are different. In this paper, we propose a mechanism for the formation of microaneurysms that involves the chemo-mechanical coupling of blood and endothelial and neuroglial cells. We model the blood as a non-local non-Newtonian incompressible fluid and solve analytically the Poiseuille flow of such a fluid through an axi-symmetric circular rigid and impermeable pipe in the presence of wall slip. The spatial derivatives of the proposed generalization of the rate of deformation tensor are expressed using Caputo fractional derivatives. The wall slip is represented by the classic Navier law and a generalization of this law involving fractional derivatives. Numerical simulations suggest that hypertension could contribute to microaneurysmal formation. View Full-Text
Keywords: fractional calculus; non-Newtonian fluid; Poiseuille flow; cerebral aneurysms; microaneurysms fractional calculus; non-Newtonian fluid; Poiseuille flow; cerebral aneurysms; microaneurysms
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Drapaca, C.S. Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms. Fractal Fract 2018, 2, 9.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Fractal Fract EISSN 2504-3110 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top