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Nature of Flow of a Liquid
Published in Wilmer W Nichols, Michael F O'Rourke, Elazer R Edelman, Charalambos Vlachopoulos, McDonald's Blood Flow in Arteries, 2022
The quantity R(ω/v)1/2 is a nondimensional parameter that characterizes kinematic similarities in the liquid motion. It is written as the symbol α: The radius is also made nondimensional by substituting the fractional radius, y = r/R. The solution for the velocity w then converts eqn 3.42 to This gives the velocity of motion of the lamina of liquid at a fraction of the radius, y, from the axis of the tube. The corresponding volume flow is derived by integrating across the tube as was done for Poiseuille flow; the oscillatory volume flow is considered in Chapter 7. Although the terminology and derivation of Womersley (Womersley, 1955a, 1957a) is followed here, the same or essentially similar solutions have previously been achieved by other authors, notably Witzig (1914), Apéria (1940), Iberall (1950), Lambossy (1952a) and Morgan and Kiely (1954). Witzig’s work was in a doctoral thesis and remained unknown until cited by Lambossy (1952a); it is remarkable in that he actually obtained velocity profiles (at values of α of 4.0 and 10), like those illustrated in this chapter, in reference to arterial blood flow. Lambossy also calculated profiles over a range of values of α relevant to the circulation, while Morgan and Ferrante (1955) were more concerned with the limiting cases; Apéria (1940) and Iberall (1950) only dealt with the general mathematical solution.
Red Blood Cell and Platelet Mechanics
Published in Michel R. Labrosse, Cardiovascular Mechanics, 2018
The probably simplest situation one could imagine is a long cylindrical tube through which a fluid is pushed by an externally imposed pressure gradient. This leads to the famous Poiseuille flow profile, in which the flow velocity v is unidirectional along the tube axis (here denominated by x), with a quadratic dependence on the radial position. The flow is given by
Critical design parameters to develop biomimetic organ-on-a-chip models for the evaluation of the safety and efficacy of nanoparticles
Published in Expert Opinion on Drug Delivery, 2023
Mahmoud Abdelkarim, Luis Perez-Davalos, Yasmin Abdelkader, Amr Abostait, Hagar I. Labouta
In the human body, blood flow is governed by fundamental laws of fluid dynamics, and is driven by three main pressure gradients. The most important is the impulsive pressure gradient between arterial and venous circulation, which establishes a unidirectional flow across the capillary beds. The second gradient is the transmural pressure (the difference between intravascular and interstitial pressure); this is the most determinant force over the diameter of the vessels and, thus, over the vascular resistance. The third gradient is the hydrostatic pressure exerted by the column of blood mainly due to its density and gravitational forces [103]. These gradients are responsible for the perfusion of all the organs and tissues; hence, they must be considered and modeled to reproduce physiological conditions into microfluidic chips. The fluid flow inside the microchannel is usually considered the Poiseuille flow, which works when a pressure gradient, 107,120]:
Extraction of patient-specific boundary conditions from 4D-DSA and their influence on CFD simulations of cerebral aneurysms
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2022
Yuya Uchiyama, Soichiro Fujimura, Hiroyuki Takao, Hiroshi Ono, Keigo Katayama, Takashi Suzuki, Toshihiro Ishibashi, Katharina Otani, Kostadin Karagiozov, Koji Fukudome, Yuichi Murayama, Makoto Yamamoto
Our extraction program, which was validated on the basis of the experimental results, was applied to clinical cases. Then, the extracted values were applied as the boundary conditions in CFD simulations. We created a patient-specific vessel geometry and centreline using Amira and VMTK and then extracted the pulse cycle duration and the maximum and minimum velocities from the 4D-DSA images. We approximated that the artery was a cylinder and the velocity distribution followed Hagen–Poiseuille flow. According to the Hagen-Poiseuille flow velocity profile, the averaged velocity over a cross-sectional plane of the artery was half of the velocity at the centreline. Therefore, we set the average velocity at the inlet boundary as half of the extracted velocity. As our program could not directly extract the pulsatile flow velocity waveform, we established the boundary condition by scaling the maximum and minimum velocities and pulse cycle duration of the representative pulsatile waveform reported in a previous study (Karmonik et al. 2008).
Numerical investigation of blood flow and red blood cell rheology: the magnetic field effect
Published in Electromagnetic Biology and Medicine, 2022
Nazli Javadi Eshkalak, Habib Aminfar, Mousa Mohammadpourfard, Muhammed Hadi Taheri, Kaveh Ahookhosh
As mentioned earlier, sometimes external/internal changes can lead to a decrease in the RBC deformability; in other words, it can result in a considerable enhancement in the stiffness/elastic modulus of the RBC membrane. Therefore, in the current study, the motion of an RBC without any deformations is investigated. The Poiseuille flow is assumed Newtonian, viscous, and incompressible, containing a rigid circular red blood cell through a tube with a constant diameter. This case is similar to the case of spherocytosis or Plasmodium-infected RBC, i.e. stiff enough to resist any deformation. In the present study, both the circular and biconcave RBC are discussed. Figure 1 shows the geometry of the present study. As shown in the figure, migration of an RBC without any shape deformation in a straight channel is investigated under the following applied boundary conditions: a parabolic velocity profile at the inlet representing the fully developed flow (i.e. Figure 1. Furthermore, it should be declared that the red blood cell is assumed to move on the centerline of the vessel; in other words, the cell is positioned on the centerline of the vessel and no cell free layer (CFL) effect is observed. In all of the following results, it is assumed that the RBC is moving through an 8-µm channel.