When elastic fibers are immersed in a Newtonian fluid, the behavior of the system, or the "fiber suspension" becomes non-Newtonian. Understanding the dynamics of such systems is of particular interest in a wide variety of fields, including locomotion of microorganisms, paper and pulp industry, microfluidics etc. When these fibers are immersed in the fluid at low Reynolds number, the elastic equation for the fibers couples to the Stokes equations, which greatly increases the computational complexity of the problem. I have simulated buckling behavior of a single fiber suspended in a shear flow and have applied two numerical method, a slender body approximation known as Local Drag model and a regularized Boundary Integral method known as Regularized Stokeslet method. We have extended the Local Drag model to simulate naturally bent fibers based on the target or resting curvature of the fibers. Microorganisms possess fiber-like organs known as the appendages and swim by flapping these organs. We have also simulated swimming motion of a simple microorganism model by imposing a time dependent resting curvature of these fibers.

This research is a thorough numerical investigation and critical analysis of lateral migration of a deformable particle settling in a vertical weak shear flow. Under the vertical weak shear fluid, the deformable particle may move either to the coagulation area, or the dispersion area, depending on Reynolds numbers, shear Reynolds number, fiber flexibility, and aspect ratio. In this study, a lattice Boltzmann equation is used to solve Navier-Stokes equation and a flexible particle method is employed to attack the problem of motion of a flexible fiber. A bounce-back rule is used to deal with moving boundaries interacting with fluids. Several simulations are first conducted at the same shear Reynolds number, particle settling Reynolds number and aspect ratio except that the rigidity is varied at different levels. It is found that the rigidity plays a critical role, may change particle lateral migration direction, either migrate toward a coagulation area, or toward a dispersion area, depending the value of the rigidity. It shows that the rigidity may alter the fiber inertia, in turn, convert coagulation to dispersion. In other words, flexibility may alter the stability of fiber suspension. At a low settling Reynolds number, as the vertical shear flow increases the fiber dispersion trend increases and the lower rigid fiber has a larger tendency to disperse.

The behavior of solid particles in a fluid has become an important topic. The need to improve our understanding of the mechanisms of fluid-particle interaction is the motivation for the present work. The characteristics of fibers suspensions depend on the many variables such as flexibility, Reynolds numbers, density and aspect ratio. The aim of this work is to probe effects of these variables on sedimentation behavior by using a fiber-level simulation technique. In this techniques, a D3Q15 model in a lattice Boltzmann equation with a Bhatnagar-Gross-Krook (BGK) approximation is used to simulate motion of fluids, where Navier-Stokes equations are solved equivalently. Meanwhile, a lattice spring model is utilized to mimic the deformation of flexible fibers. The interaction between fluid and solid fiber is handled by an immersed boundary method. Dynamic motion of a single flexible fiber and two flexible fibers settling in an infinite long fluid column at low and moderate Reynolds numbers are numerically simulated in a three dimensional space. The fiber flexibility and density are varied at different levels and their effects on sedimentation are studied. In the simulations, cuboid and cylindrical fibers at different aspect ratios are considered. It is demonstrated that the fiber flexibility has an important impact on fiber position, settling velocities, and fluid structures, where the drafting, kissing, and tumbling (DKT) mechanisms play important roles. The simulation results provide useful information, at a microscopic level, which may not be easily measured in a lab environment.

Results from simulation show the rigid fiber in simple shear flow produces a good agreement for orientation of a fiber relative to the theoretical study by Jeffery (1922). The flexible fiber exhibits an increase on the rotational period from the rigid fiber due to more deformation shape is revealed during rotation. The simulation technique demonstrates the ability to simulate fiber-fiber interactions to further study of relative viscosity of suspensions in shear flow. Simulation results show that fiber orientation and relative viscosity depend on the fiber characteristics (fiber aspect ratio, fiber flexibility, and volume fraction). The results are verified against known experimental measurements and theoretical results.