Tracking the motion of balloons during inflation and deflation

High-speed videos were recorded at 25 fps during inflation. Python libraries for optical character recognition (OCR) and image segmentation were used to obtain pressure-radius curves. The experimental results shown in pressure vs. radius plots clearly express the underlying behavior of rubber balloons under shear stress. The results agreed with the expected theoretical behavior, and the data were further fitted using the Mooney-Rivlin model.

The Mooney strain-energy function offers a satisfactory match to data for minor deformations. However, the predictions of this theory significantly differ from observations for large deformations in simple tension and, more generally, in biaxial deformation (deformation in
the skin of spherical membrane). Even though the Mooney-Rivlin model can forecast unstable conditions, it cannot capture “the ultimate stiffening effect” with sufficient accuracy. As a result, it cannot fit the second ascending branch of the inflation curve. Experimental data support theoretical results by showing that the internal pressure increases quickly until it reaches a maximum value, then decreases until it reaches a minimum before rising again.

However in some cases, the Ogden strain energy function leading to the three-term Ogden equation has better explained the large deformation behavior of rubber balloons. We discovered that the rubber balloon loses elasticity the more times it is inflated from the cyclic data. The balloon’s rubber stretched after the initial total inflation and increased in size. The inflation pressure to inflate the balloon a second time was lower than the first time, and the same is true for all subsequent cyclic attempts. The digital sensors and experimental techniques we used to extract radius and pressure data to get plots have limitations. In the initial experimental attempt, we used our displacement sensor—Physdisp to obtain radius data and Physbar to retain pressure values, keeping the pressure-radius values coordinated over time. We
discovered a limitation in measuring radius and pressure. The error in the radius data is because the Physdisp uses infrared light to find the closest object, and its values change as the item moves. The balloon size increased as it was inflated and eventually approached Physdisp. Sometimes, during inflating, the balloon was out of alignment with the Physdisp position and could not provide us with accurate displacement.

Therefore, in order to overcome this limitation, in the subsequent experiment, we used optical character recognition to extract pressure data and threshold image segmentation to determine a balloon’s area and volume using the solid revolution formula. This eventually determined the balloon’s effective radius. Furthermore, in planning this endeavor, we wanted to identify the radius and sync it with pressure data obtained from the physbar. The concept of the image processing method allowed us to create contours after marking the balloon’s region of interest to extract the radius from the image. Then, we considered synchronizing the radius and pressure measurements. The rationale
behind synchronizing pressure measurements with the radius was to capture the computer screen and the balloon inflation behavior simultaneously. Using optical character recognition, we read text from images.

The study concludes that the home-built setup, including the sensors and data extraction techniques, is a viable investigation of rubber balloons. Additionally, further experimentation with balloons could lead to a better understanding of the system’s state equation, including state variables such as entropy, pressure, and internal energy.