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We derive a mathematical model and the corresponding computational scheme to study deflection of a two-dimensional elastic cantilever beam immersed in a channel, where one end of the beam is fixed to the channel wall. The immersed boundary method has been employed to simulate numerically the fluid-structure interaction problem. We investigate how variations in physical and numerical parameters change the effective material properties of the elastic beam and compare the results qualitatively with linear beam theory. We also pay careful attention to "corner effects" -- irregularities in beam shape near the free and fixed ends -- and show how this can be remedied by smoothing out the corners with a "fillet" or rounded shape. Finally, we extend the immersed boundary formulation to include porosity in the beam and investigate the effect that the resultant porous flow has on beam deflection.

We apply the immersed boundary (or IB) method to simulate deformation and detachment of a periodic array of wall-bounded biofilm colonies in response to a linear shear flow. The biofilm material is represented as a network of Hookean springs that are placed along the edges of a triangulation of the biofilm region. The interfacial shear stress, lift and drag forces acting on the biofilm colony are computed by using fluid stress jump method developed by Williams, Fauci and Gaver [Disc. Contin. Dyn. Sys. B 11(2):519-540, 2009], with a modified version of their exclusion filter. Our detachment criterion is based on the novel concept of an averaged equivalent continuum stress tensor defined at each IB point in the biofilm which is then used to determine a corresponding von Mises yield stress; wherever this yield stress exceeds a given critical threshold the connections to that node are severed, thereby signalling the onset of a detachment event. In order to capture the deformation and detachment behaviour of a biofilm colony at different stages of growth, we consider a family of four biofilm shapes with varying aspect ratio. Our numerical simulations focus on the behaviour of weak biofilms (with relatively low yield stress threshold) and investigate features of the fluid-structure interaction such as locations of maximum shear and increased drag. The most important conclusion of this work is that the commonly employed detachment strategy in biofilm models based only on interfacial shear stress can lead to incorrect or inaccurate results when applied to the study of shear induced detachment of weak biofilms. Our detachment strategy based on equivalent continuum stresses provides a unified and consistent IB framework that handles both sloughing and erosion modes of biofilm detachment, and is consistent with strategies employed in many other continuum based biofilm models.

We study the settling of solid particles within a viscous incompressible fluid contained in a two-dimensional channel, where the mass density of the particles is slightly greater than that of the fluid. The fluid-structure interaction problem is simulated numerically using the immersed boundary method, with an added mass term that is incorporated using a Boussinesq approximation. Simulations are performed with a single circular particle, and also with two particles in various initial configurations. The terminal settling velocities for the particles correspond closely with both theoretical and experimental results, and the single-particle dynamics reproduce expected behavior qualitatively. The two-particle simulations exhibit drafting-kissing-tumbling dynamics that is similar to what is observed in other experimental and numerical studies.

To better exploit the principles of gas transport and mass transport during the processes of cell seeding of 3D scaffolds and in vitro culture of 3D tissue engineered constructs, the oscillatory cell culture bioreactor provides a flow of cell suspensions and culture media directly through a porous 3D scaffold (during cell seeding) and a 3D construct (during subsequent cultivation) within a highly gas-permeable closed-loop tube. This design is simple, modular, and flexible, and its component parts are easy to assemble and operate, and are inexpensive. Chamber volume can be very low, but can be easily scaled up. This innovation is well suited to work with different biological specimens, particularly with cells having high oxygen requirements and/or shear sensitivity, and different scaffold structures and dimensions. The closed-loop changer is highly gas permeable to allow efficient gas exchange during the cell seeding/culturing process. A porous scaffold, which may be seeded with cells, is fixed by means of a scaffold holder to the chamber wall with scaffold/construct orientation with respect to the chamber determined by the geometry of the scaffold holder. A fluid, with/without biological specimens, is added to the chamber such that all, or most, of the air is displaced (i.e., with or without an enclosed air bubble). Motion is applied to the chamber within a controlled environment (e.g., oscillatory motion within a humidified 37 C incubator). Movement of the chamber induces relative motion of the scaffold/construct with respect to the fluid. In case the fluid is a cell suspension, cells will come into contact with the scaffold and eventually adhere to it. Alternatively, cells can be seeded on scaffolds by gel entrapment prior to bioreactor cultivation. Subsequently, the oscillatory cell culture bioreactor will provide efficient gas exchange (i.e., of oxygen and carbon dioxide, as required for viability of metabolically active cells) and controlled levels of fluid dynamic shear (i.e., as required for viability of shear-sensitive cells) to the developing engineered tissue construct. This bioreactor was recently utilized to show independent and interactive effects of a growth factor (IGF-I) and slow bidirectional perfusion on the survival, differentiation, and contractile performance of 3D tissue engineering cardiac constructs. The main application of this system is within the tissue engineering industry. The ideal final application is within the automated mass production of tissue- engineered constructs. Target industries could be both life sciences companies as well as bioreactor device producing companies.