Role Of Compressibility And Slip In Blood Flow Through A Local Constriction

Abstract

One type of blood disease is a narrowing of a tubular structure, known as constriction or stenosis and high cholesterol is one of the main causes for this. Suitable mathematical models are important to describe this phenomenon, and to study the problem analytically and numerically. An approximate analytical solution and a recently developed particle-based method called multi-particle collision dynamics (MPC) is used to simulate the weakly compressible steady flow through a three-dimensional constricted axisymmetric cylinder. The particle collisions in

Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

“…To simulate isothermal flow conditions, a thermostat is applied to the system, so as to remove the energy that the external force pumps into the system. The velocity of each particle is rescaled according to a profile-unbiased Galilean invariant thermostat first introduced by [36], the details of which can be found in [8,9,16].…”

“…In [7], slip was incorporated for incompressible, Newtonian flow through a local constriction. Weakly compressible flow with slip was later considered by [8,9], who also allowed for a flow geometry that is not necessarily symmetric about the location of maximum constriction. The results presented here are extensions of the results given in [8,9], giving more accurate expressions for the axial velocity profile.…”

“…All of these works are for incompressible flows as they are applied to blood flow studies. Particle-based numerical methods, such as the Lattice-Boltzmann method [20], dissipative particle dynamics (DPD) [21,22] and multiparticle collision (MPC) dynamics [8,9,16], have more recently led to numerical solutions for flow through a local constriction. The Lattice-Boltzmann method has also recently been used for blood flow studies in complex flow geometries for realistic cardiovascular flow domains [23][24][25].…”

“…The method has been reviewed recently in [26], and its use for complex flows has been reviewed in [27]. Except for [8,9], the results are numerical. Since compressible flows through constrictions can exhibit significant compressibility effects and since particle-based methods have compressibility built-in, such methods are ideal numerical means for simulating compressible flow through local constrictions.…”

“…In this paper, the Karman-Pohlhausen method is used to develop the axial velocity distribution for steady, Newtonian flow through a stenosed vessel, allowing for slip at the wall, as well as compressibility. The analysis is a natural extension of [1] and an improvement to the results given in [8,9]. The flow geometry considered is axisymmetric, but asymmetric about the location of maximum constriction.…”