What is Linearization

The chapter explores the dynamics of liquid penetration in a closed end vertical capillary. This model is very important for impedance spectroscopy methodology where oxidized porous silicon provides an in vitro medium, and one important criteria of this methodology is the liquid penetration depth inside the silicon pores as the impedance is greatly affected by this penetration depth. This problem is also important in order to understand how the presence of entrapped air inside a micro pore can influence the dynamics of capillary flow. For this purpose, the model is studied both analytically and numerically. In this study, different pore size (500 nm and 2 µm diameter) with equal pore depth (~10 µm) have been used. Finally, the analytical solution is compared with the numerical results. In addition, the linearization of the system is also investigated and found the critical viscosity of which demarcates the over-damped and under-damped regimes. Further, this study is extended by incorporating the dynamic contact angle effects on the meniscus dynamics.