Measurement of the fractal order of wall void fraction during nucleate boiling

The fractal nature of hydrodynamic features during nucleate boiling is illustrated in this study. Earlier reports in the literature explored the fractal nature of the thermal features in pool boiling. In these studies typically the time-delay technique was used to obtain chaos quantifiers in boiling from wall temperature fluctuation measurements. In this study experiments were performed at different wall superheats to obtain the images of voids (bubbles) on micro-heaters during nucleate boiling. This study quantifies boiling chaos based on the geometrical features of the voids (e.g., area and perimeter). The fractal order of the geometrical features was obtained by digital image processing. The fractal order (correlation dimension) was computed using the box-counting technique. The experimental apparatus consisted of an array of individually controlled micro-heaters which were used in conjunction with a total internal reflection technique to visualize the wetted area during boiling of FC-72. Images of the voids (bubbles) were captured with a high speed camera. The resulting images were analyzed using the image processing toolbox in MATLABR®. Temporal fluctuations observed in the values of the fractal order (for different images in a sequence) were found to remain within distinct bounds with only marginal overlap between the values computed from experimental data obtained at different wall superheats. The fractal order of the voids (based on area, Dc2) was found to increase with the wall superheat. This implies that the complexity of the boiling system (represented by the fractal order of the system) increases with wall superheat in nucleate boiling. The fractal order based on perimeter (edge lengths, Dc1) of the voids was found to reach a maxima with wall superheat. Furthermore, the plot of Dc2 versus Dc1 was found to mimic the conventional boiling curve (wall heat flux versus wall superheat). This shows that Dc2 and Dc1 are intrinsically related to wall superheat and heat flux, respectively. Further, it implies that the liquid–vapor contact line plays a major role in modifying pool boiling heat flux compared to the size of the voids (bubbles).