Abstract
In this thesis, a recently developed particle-based method called multiparticle collision dynamics (MPC) is used to simulate steady flows through three-dimensional constricted axisymmetric cylinders. The work is motivated by complex particle interactions in blood flow such as aggregation and the need to be able to capture these effects in physiologically relevant complex flow geometries. This is the first time that MPC dynamics has been applied to simulate flows though constrictions. The particle collisions in MPC dynamics are numerically more efficient than other particle-based simulation methods. Particle interactions with the cylinder walls are modeled using bounce-back (BB) and loss in tangential, reversal of normal (LIT) boundary conditions. BB is an analog of the macroscopic no-slip boundary condition, and LIT gives slip. Finally, an averaging procedure is employed to make a connection with the solution to the Navier-Stokes equations. Interesting differences have been found in the velocity profiles obtained using MPC with BB and LIT, compared to Navier-Stokes.
Highlights
1.1 Biological MotivationsThe complex nature of blood flow can largely be attributed to the cellular components of blood and the complex physiological geometries
The slip can be seen in the case of loss in tangential (LIT), and the BB data points are in good agreement with Navier-Stokes
In case of the LIT, particle density is higher near the wall and in case of BB, the density profile is fairly uniform across the cross-section
Summary
1.1 Biological MotivationsThe complex nature of blood flow can largely be attributed to the cellular components of blood and the complex physiological geometries. The RBC aggregates can create a solid core, and in order to break up this core for blood to flow, a minimum amount of stress is required. This minimum stress is known as the yield stress [2] and is a non-Newtonian property. It has been shown that with an appropriate averaging procedure, macroscopic rate laws for chemical reactions can be recovered Complex geometries, such as local constrictions in blood vessels, can cause RBC aggregation. Rolling, tumbling and twisting motions of red blood cells were observed due to the flow choking characteristics in the stenotic region [5] These aspects can only be captured by using discrete particle-based simulation methods. Results of all these simulations have been found to be in good agreement with empirical data and the Navier-Stokes equations
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