Permeability model for porous transducer with glass spheres packing

A theoretical model is developed for predicting permeability of a porous transducer, which is a crucial component of liquid circular angular accelerometer and sintered by glass microspheres. The proposed permeability model of the transducer is determined with consideration of its shape factor, tortuosity, and particle size distribution (PSD) characterized by equivalent mean diameter and skewness. A novel analytical method for calculating the shape factor for the arbitrary cross-section area is derived. In addition, a tortuosity model is designed by fitting skewness and tortuosity of particle packing beds in a regular tetrahedron microspheres arrangement structure. Together with the analytical model of shape factor, the tortuosity fitting model and a method to determine equivalent diameter from PSD, the permeability model is implemented to compare with Kozeny-Carman (KC) model. The experiments are performed to measure the permeability of four types of porous transducers fabricated with different PSDs and consequently validate the permeability model. The results indicate that the proposed model can be utilized for predicting permeability of porous transducer with higher precision.