Low frequency of a deforming capillary vibration, part 1: Mathematical model:

The capillary effect has wide applications from biology and textile engineering to nanotechnology especially the micro-electromechanical systems and microfluidics device. The capillary vibration significantly affects its mass transmission. This paper establishes a nonlinear oscillator of a deforming capillary tube. The geometric potential theory is used to estimate the capillary force. The paper reveals that the low-frequency property of capillary vibration plays an important role not only in life but also engineering applications.