capillary tube — Fig. 2. The capillary top was located 13 mm away from the bath bottom. The water in the capillary rose at an observable stable rate and reached a maximum height of 60 mm above the normal bath level under ultrasonication. By contrast, the water increased extremely slowly, and only 2 mm of a water head was observed in the absence of ultrasonication. Acoustic pressure in water outside and inside the capillary was then measured by using an acoustic pressure meter, and the results are illustrated in Fig. 13. The data exhibited variance to a certain extent. However, the acoustic pressure from the outside to the inside of the capillary considerably declined. At the same time, the acoustic pressure in the capillary decreased with increased capillary height. These results indicate that the distinct capillary rise of liquid under ultrasonic agitation may be attributed to the decline in acoustic pressure gradient from the entrance of the capillary to the capillary surface. For a glass tube located in an ultrasonically agitated liquid bath (Fig. 14), most of the ultrasonic waves were reflected by the end of the tube when travelling to liquid/tube interfaces. Only a small part of the ultrasonic waves were transmitted into and propagated in the capillary by the prefilled liquid (this liquid fills into the capillary under the hydrostatic pressure). The propagation of ultrasonic waves in the capillary induced liquid flow. The viscous resistance of the liquid itself and the friction forces of the liquid on the capillary wall promoted the gradual dissipation of ultrasonic energy through conversion into heat energy, which led to ultrasonic attenuation. The propagation of acoustic waves in a capillary can be expressed as follows: where P is the acoustic pressure at a traveling distance x in the capillary, P0 is the initial acoustic pressure at the entrance of the capillary, is the angular velocity, k is the wave number in the capillary, and is the attenuation coefficient. can be expressed as where d is the capillary diameter, C is the acoustic velocity, and μ and are the dynamic viscosity and density of the liquid, respectively (Refs. 24, 25). Equation 2 shows that the coefficient of acoustic attenuation is proportional to the square root of liquid viscosity and acoustic frequency, and inversely proportional to the diameter of the capillary. These characteristics indicate that a higher frequency and smaller capillary size correspond to an acoustic energy with a higher dissipation ratio. Thus, immersing a capillary with a diameter of hundreds of micrometers in an ultrasonically agitated liquid decreases the acoustic energy from the outside to the inside of the capillary and leads to the formation of a decreasing gradient of acoustic energy along the capillary. In consequence, capillary rise of the liquid occurs to compensate for this acoustic energy difference (as acoustic pressure difference) regardless of the wetting status of the liquid to the capillary material. In other words, the liquid is ultrasonically pumped into the capillary without the driving force of surface tension. When a capillary end is located in a developed cavitation zone, the capillary rise would be considerably higher than that in the noncavitation zone because of the great acoustic pressure difference between the outside and the inside of the capillary. Previous studies (Refs. 13, 20, 21) have shown that a sharp increase in liquid pressure at the base of a capillary, which manifests in the presence of cavitation bubbles, is unilaterally responsible for nonwet- = 1 dC μ 2 (2) P = P0e x e j(tkx ) (1) WELDING RESEARCH 270-s WELDING JOURNAL / JULY 2016, VOL. 95 Fig. 15 — Variation in acoustic attenuation coefficient with the capillary diameter d for the solder Sn9Zn. Fig. 14 — Model for the propagation of ultrasonic waves in the capillary.
Welding Journal | July 2016
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