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Access type: UnknownSubject: search.filters.subject.Mixed finite element method

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    Two-dimensional nonlinear Brinkman and steady-state Navier–Stokes equations for fluid flow in PCL
    (2024-12-01)
    Phaenchat, Surachai
    ;
    Wuttanachamsri, Kanognudge
    To remove mucus from the human body, periciliary layer (PCL) is an important region found in the human respiratory system. When a human inhales strange particles along with air into the body, goblet cells inside the epithelial cells secrete mucus to catch those particles and form a mucus layer on the top of the PCL. Since the velocity of the fluid in the PCL and cilia residing in the PCL affect the movement of mucus, in this work, we apply two-dimensional nonlinear Brinkman and steady-state Navier–Stokes equations to find the velocity of the fluid in the PCL. In the equations, the velocity of cilia is also contributed in the mathematical model which perturbs the fluid movement instead of the pressure gradient. Because bundles of cilia are considered in this work rather than a single cilium, the governing equations are derived from the hybrid mixture theory (HMT) which are the equations in a macroscopic scale. The numerical solutions are obtained by using a mixed finite element method of Taylor–Hood type and Newton's method. We focus on five different angles of cilia that make with the horizontal plane. The velocity of the PCL fluid is presented for each angle. The numerical solutions obtained in this study can be useful in finding the mucus velocity that can help physicians to treat patients who have massive mucus in their lungs.
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    Effects of Cilia Movement on Fluid Velocity: II Numerical Solutions Over a Fixed Domain
    (2020-09-01)
    Wuttanachamsri, Kanognudge
    ;
    Schreyer, Lynn
    Cilia are hair-like structures that move in unison with the purpose of propelling fluid. They are found, for example, in the human bronchiole respiratory system and molluscs. Here, we validate a novel model of fluid flow due to the movement of cilia in a fixed computational domain. We consider two domains, a porous medium and a free-fluid domain and numerically solve the Stokes–Brinkman system of equations where the cilia geometry and velocity are input and the velocity of fluid due to the movement of cilia is determined. The cilia velocities and geometry are approximated using human lung cilia experimental data available in the literature. We use a mixed finite element method of Taylor-Hood type to calculate the fluid velocities in a three-dimensional domain. The results are validated in a simple case by comparison with an exact solution with good agreement. This problem can be used as a benchmark for the movement of fluid phases due to the self-propelled movement of a solid phase in a porous medium.