A Generalized Model for Dynamic Contact Angle

Contact angle is an important parameter that characterizes the degree of wetting of a material. While for a static case, estimation and measurement of contact angle has been well established, same can not be said for the dynamic case. There is still a lack of understanding and consensus as to the fundamental factors governing the microscopic dynamic contact angle. With the aim of understanding the physics and identifying the parameters that govern the actual or microscopic dynamic contact angle, we derive a model based on first principles, by performing a force balance around the region containing the contact line. It is found that in addition to the surface tension, the microscopic dynamic contact angle is also a function of surface tension gradient and the jump in normal stress across the interface. In addition to having a significant contribution in determining the microscopic dynamic contact angle, surface tension gradient is also a key cause for contact angle hysteresis.