Pranav Bhagirath

154 Chapter 8 Note the close correspondence between lines [1] and [2] of the code and equation [6] by substituting them in equation LHS = RHS. Computing platform All analyses were performed on a 2.4 GHz quadcore laptop running Windows 8 OS. Solving the potential equations was delegated to a an Ubuntu 12.10 virtual machine running on this laptop, communicating with the activation modelling software by the use of synchronised message file sharing. Reference times were computed using a single core. RESULTS Rectangular tank Figure 2 shows the 3D mesh of the tank. A potential of 4V peak to peak was observed in the middle of the tank. The computations using a tetrahedral mesh with 1.5 cm edge length, demonstrated a deviation of the 4V plane from the middle by about one grid cell. By refining the mesh to an edge length of 0.5 cm, this deviation was expected to diminish. Paradoxically, the deviation from the middle actually increased by about 2.5 cm, to a total deviation about 10 times larger than the mesh size ( figure 2a ). Figure 2b and c reveal the potential gradients to increase near to the electrode. This is caused by the small contact area between the fluid and the electrodes introducing a high resistivity: R = 1 / (area x sigma) [Ohm/m]. Because R is large, the potential drop U is large according to Ohms law. Moreover, a relative misrepresentation of the electrode area by 5% leads to a relative error in this potential drop in the same order of magnitude. Figure 2d illustrates that minor errors in the potential drop near the electrodes yield large deviations in the 4V equipotential plane. In the middle of the tank the x coordinate varies rapidly with small potential changes. By using volume information, the counterintuitive effect shown in figure 2a can be understood. For large electrodes, misrepresentations of their area by the mesh are relatively small. This should render the position of the 4V equipotential plane insensitive to the mesh cell size ( figure 2e ).