# Transient Phenomena of Dynamic Contact Angle in Micro Capillary Flows +
## 3 Experimental Apparatus  
Figure 2 shows the schematic of the experimental setup. A drop of liquid is dispensed at the edge of a glass plate by a syringe pump, and then the glass plate is attached to a capillary tube in order to fill the liquid in by only the capillary force. The motion of the flow meniscus is observed using a fluorescence microscope (Nikon, Eclipse Ti, Tokyo, Japan) with a 4\(\times\) objective lens. A halogen lamp is used as an illuminating light source and a high-speed CCD camera (SVSI) captures the images. The capillary tube is made of borosilicate glass with an inner diameter of 200 \(\upmu\)m. The tube diameter is selected considering the typical gap height of the underfill process by capillary force in flip chip packaging. Careful attention was paid to tube cleaning because dust on the surface can distort the contact angle, or the wet surface can alter the interfacial force. In the cleaning process, the tube was kept immersed in water for six hours and then in a mixture of ammonium hydroxide, hydrogen peroxide, and water for one hour. Again, it was immersed in water for more than 24 h. Finally, it was dried in an electrolysis desictor for 24 h. By changing the volume fraction of the glycerin-water mixture, the viscosity of the operating liquid is controlled. A small amount of water added to the mixture significantly changes the viscosity of the mixture. In the present study, the volume fractions of glycerin are 85.7%, 93.75%, 96.87%, and 99% at room temperature 20 \({}^{\circ}\)C, which yields the viscosity to be \(\mu=\) 0.21, 0.54, 0.82, and 1.36 Pa-s, respectively. The viscosity was measured by a rheometer (Brookfield DVIII + ULTRA). However, the fluid density \(\rho\) and surface tension coefficient \(\sigma\) are not sensitive to the small amount of added water [19; 20]. Thus, \(\rho=\) 1260 kg/m\({}^{3}\) and \(\sigma=\) 0.063 N/m are used for all the glycerin-water mixtures.  
In order to measure the dynamic contact angle, the thickness \(T\) of the shadow image of the flow meniscus is obtained as shown in Figure 3. If the interfacial shape is assumed to be a part of a circle, the contact angle \(\theta\) can be calculated by \(\theta=2\tan^{-1}(0.5D/T)-\pi/2\)[21]. The spatial resolution for the contact angle measurement is enhanced by a high magnification microscope. The scale factor in image plane is 3.0 \(\upmu\)m/pixel. The static equilibrium contact angle \(\theta_{s}\) is evaluated from the image when there is no fluid motion. Table 1 shows the values measured in this experiment. The dynamic contact angle, however, varies during the meniscus movement. The measurement length of the micro tube is 0-10 mm, so that the CCD camera cannot capture the whole field of view at one time. Thus, the measurement length is divided into three sub-sections, and then their data are combined successively. During the experiments, the tube inlet and the end of the camera screen are aligned on the same line after positioning the tube on the stage. Then, images are captured by incrementally moving the stages at intervals of 3.5 mm using a micro-axis transfer device. For each case, five experiments are conducted to obtain an average value. Since the interface movement depends on surface condition, all tubes are washed and dried for several hours. The careful cleaning of the tube surface assures the convergence of experimental data.