# Transient Phenomena of Dynamic Contact Angle in Micro Capillary Flows +
## 1 Introduction  
Liquid penetrates into a narrow gap by capillary action at the gas-liquid interface. This is called a micro capillary flow and has practical importance in a wide range of technology, such as flow through porous materials in micro heat pipes and micro coolers and underfilling process in flip chip packaging [1; 2; 3]. The fundamental research for micro capillary flow is the liquid penetration into a capillary tube. [PERSON] [4] derived a theoretical equation by considering the force balance between capillary force and viscous drag, neglecting gravitation and other effects. To extend [PERSON]'s law, [PERSON] [5] imparted momentum for both length of the tube wetted and velocity of flow. [PERSON] [6] considered the initial period of acceleration when the liquid is attached to the inlet of a tube. For the early stage of the capillary rise, [PERSON] [7] neglected viscous force using a liquid of low viscosity.  
One of the critical drawbacks in these previous studies is the assumption of a constant contact angle at the flow meniscus. In practice, the contact angle does not always keep its equilibrium status but changes dynamically since the flow near the meniscus affects the contact line of the solid-gas-liquid interface [8]. [PERSON] [9] estimated the advancing dynamic contact angle in capillary flow. He presented contact angle versus a function of the capillary number. Based on [PERSON]'s study, more studies for the approximation of the dynamic contact angle were carried out by other researchers [10; 11; 12]. In a molecular approach, [PERSON] et al. [13] attempted to address the change in dynamic contact angle by applying molecular dynamics. In a more advanced study, [PERSON] et al. [14] proposed a self-layered molecular model capable of simulating changes in contact angle resulting from energy dissipation but no one proposed a perfect form, considering that the contact angle decreases as time goes on.  
At the earlier stage of the capillary action, the liquid experiences an acceleration force so that the transient term in the governing equation should be considered. Thus, [PERSON] and [PERSON] [15] and [PERSON] et al. [16] analyzed the dynamic interface motion for circular and rectangular microchannels. They proposed the dimensionless equations of the interface movement in the condition of a wet solid surface. Thereafter, [PERSON] et al. [17] visualized the meniscus of the fluid rising in a wet capillary tube and analyzed the moving speed. Here, it was found that the rising speed of the meniscus increased with the wet thickness of the capillary surface. Despite the great progress in measurement techniques for micro-scale flows, the transient behavior of dynamic contact angle in a capillary channel has not been discussed experimentally.  
The present study focuses on the transient phenomena of the dynamic contact angle in micro capillary flows. With the help of flow visualization and image processing techniques, the wetting distance and meniscus velocity as well as dynamic contact angle are simultaneously measured under the flow. To observe the effect of viscosity on these properties, glycerin-water mixtures with various volume fractions are filled into a circular micro tube. Then, the measured data are compared with the theoretical model, and the dominant force acting on a capillary flow is determined by momentum balance.