E. L.
Bouzarth's Research Page
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 My research combines fluid dynamics and numerical analysis to study physical problems often motivated by biology.
Immersed Semi-Flexible Elastic FilamentsMany physical and biological systems involve inextensible fibers immersed in a fluid; examples include cilia, polymer suspensions, and actin filament transport. In such systems, the dynamics of the immersed fibers may play a significant role in the observed macroscale fluid dynamics. In this study, we simulate the dynamics of an approximately inextensible semi-flexible fiber immersed in a two-dimensional cellular background flow. The system is modeled as an immersed boundary problem with the fluid dynamics described using the Stokes equations. The motion of the immersed fiber is computed by means of the method of regularized Stokeslets, which allows one to calculate fluid velocity, pressure, and stress in the Stokes fluid flow regime due to a collection of regularized point-forces without computing fluid velocities on an underlying grid. Simulations results show that, for some parameter values, the fiber may buckle when approaching a stagnation point. These results provide insight into the stretch-coil transition and macroscale random walk behavior that have been reported in mathematical and experimental literature. An
immersed semi-flexible elastic filament immersed in cellular Stokes
flow near a hyperbolic stagnation point. The white arrows depict
fluid velocity while the color contour plot relates to stress.
Hydrodynamics of CiliaMy doctoral research was inspired by the Virtual Lung Project at the University of North Carolina at Chapel Hill. In this endeavor, a diverse interdisciplinary group of researchers is studying a variety of components of the human lung. The goal is to develop a computational model that will allow future scientific breakthroughs pertaining to the prevention, treatment, and cure of pulmonary malfunction, specifically, cystic fibrosis. Of the many research aspects of the Virtual Lung Project, investigating the hydrodynamic effects of cilia on surrounding liquid is the area most closely related to my work. Cilia in the lung are small whip-like protrusions responsible for moving mucus and contaminants out of the lung. Besides pulmonary cilia, primary nodal cilia precess conically and are responsible for the development of left-right asymmetry in embryos.  Sketches of pulmonary (left) and primary nodal (right) cilia motion. (left image courtesy of http://www.p-c-d.org/en/brochure) Implementing regularized singularities to model Stokes flow generated by a precessing rod is intended to numerically simulate a situation for which colleagues have exact mathematical solutions and experimentalists have corresponding laboratory studies on the micro- and macro-scales. By strategically distributing regularized singularities in a fluid domain to mimic an immersed boundary, one can compute the velocity and trajectory of the fluid at any point of interest. In addition, a no-slip plane can be created with additional regularized singularities to better match the experimental setup. The exact solution allows for careful error analysis and the experimental studies provide new applications for the numerical model. Spectral deferred correction methods are used to alleviate time stepping restrictions in trajectory calculations. Quantitative and qualitative comparisons to theory and experiment have shown that a numerical simulation of this nature can generate insight into fluid systems that are too complicated to fully understand via experiment or exact numerical solution independently. Mechanics of RunningRunning is a topic that interests researchers in many fields, including sociology, anthropology, sports medicine, anatomy, physics, and mathematics. Running shoe technology and its effect on the evolution of the human running stride is a topic of current conversation in scientific and anthropological studies. In collaboration with an undergraduate student as part of the Duke University PRUV Program, we developed a simple model of the lower leg, foot, and ankle to study various aspects of running. The structure of the model developed from fundamental principles of physics: force, torque, momentum, and energy. This research investigates the force distribution before, during, and after ground impact, which may provide insight into injury prevention. By looking at the transfer and loss of energy during a running stride, one may be able to make observations relating to factors affecting efficiency and performance. Incorporating different foot-strike patterns, physiological parameters, shoes, and running surfaces into our model provides an opportunity to address questions of efficiency and injury prevention. Research Publications:
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