1. I-beams are widely used construction components as they provide good strength for weight ratios. This project will investigate how the shape profile of an I-beam (see Figure 1) influences its strength. You will be asked to choose a number of different profiles (all with the same cross-sectional area) and find the one that has the greatest strength under a uniform loading. (Strength will be assessed by the maximum von Mises equivalent stress.)
2. The corrosion (rusting) of iron and steel is a complex process. A simple description involves two spatially separated electrochemical reactions: the dissolution of the metal (Fe) at anodic sites and the reduction of oxygen (O2) at the cathodic sites to produce hydroxyl ions (OH-). The dissolved metal and hydroxyl ions in solution then precipitate out and form surface deposits that we call rust. The basic requirements for surface corrosion are therefore threefold: moisture in contact with the surface to provide an aqueous environment for the reactions; oxygen present in the water for the reduction reaction to occur; and a conduction path for the electrons from the anodic to cathodic sites. A common situation where all these requirements are met is when small water droplets form on exposed metal surfaces due to environmental phenomena such as mist or sea-spray. (See Figure 2.)
In this situation oxygen is supplied from the atmosphere, but the oxygen must first diffuse through the water droplet in order to reach the cathodic reaction sites. The availability of oxygen at these cathodic sites is often the critical factor determining corrosion rate. In this project you will be asked to investigate how the size of a droplet and its shape, as described by the contact angle θ with the surface, affects how readily oxygen is available at the cathodic corrosion sites.
3. One of the major tasks of our body's circulatory system is to distribute oxygen from our lungs to the many different tissues in our body. Oxygen-rich blood is supplied by the arteries through their smaller branches, the arterioles, to the capillary networks within the tissues of the body. De-oxygenated blood then drains from the capillaries into the venules and then ultimately into the body's venous system. Along this pathway, oxygen is released primarily in the capillaries and is transported within the surrounding tissues by diffusion. The tissues make use of the oxygen for the various aerobic metabolic processes (respiration) that are essential for life. One of the reasons that we "run out of breath" or feel muscle burn after hard physical exertion is that this oxygen transport process within our muscle tissues is not able to keep up.
A simplified description of oxygen transport is that oxygen exists in two forms in muscle tissue, either as molecular oxygen (O2) dissolved in the intercellular medium, which is primarily aqueous (water), or as oxygen chemically bound to a protein called myoglobin. (Myoglobin is chemically closely related to hemoglobin, which is the oxygen carrier within the bloodstream.) As the solubility of molecular O2 is relatively low, the presence of myoglobin with its ability to readily bind with oxygen facilitates the transport of oxygen in muscle tissue. Muscle tissues often have high oxygen requirements and associated metabolic rates, and so optimising oxygen transport would seem an important physiological requirement.
In this project you will consider a simple two-dimensional model of a tissue with multiple parallel capillaries and you will investigate how the various factors such as spacing between capillaries, oxygen content of the incoming blood and diffusivity of the tissue influence the achievable metabolic rate of the tissue.