National Sun Yat-sen University Institutional Repository:Item 987654321/39416

對流及濃度效應對固化過程氣泡成長之影響(2/3)

計畫類別： 個別型計畫

計畫編號： NSC92-2212-E-110-007-

執行期間： 92 年 08 月 01 日至 93 年 07 月 31 日

執行單位： 國立中山大學機械與機電工程學系(所)

計畫主持人： 魏蓬生

計畫參與人員： 黃昶誠

報告類型： 精簡報告

處理方式： 本計畫可公開查詢

中 華 民 國 93 年 5 月 20 日

3:55 PM, May 20, 2004

行政院國家科學委員會補助專題研究計畫成果報告

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對流及濃度效應對固化過程氣泡成長之影響

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計畫類別：X 個別型計畫 □整合型計畫

計畫編號：NSC 92-2212-E-110-007

執行期間： 92 年 8 月 1 日 至 93 年 7 月 31 日

計畫主持人：魏蓬生

共同主持人：

計畫參與人員：黃昶誠

本成果報告包括以下應繳交之附件：

□赴國外出差或研習心得報告一份

□赴大陸地區出差或研習心得報告一份

□出席國際學術會議心得報告及發表之論文各一份

□國際合作研究計畫國外研究報告書一份

執行單位：國立中山大學機械與機電工程學系

中 華 民 國 93 年 5 月 日

3:55 PM, May 20, 2004

行政院國家科學委員會專題研究計畫期中成果報告(2/3)

對流及濃度效應對固化過程氣泡成長之影響

計畫編號：NSC 92-2212-E-110-007

執行期限：92 年 8 月 1 日至 93 年 7 月 31 日

主持人：魏蓬生 國立中山大學機械與機電工程學系

計畫參與人員：黃昶誠 國立中山大學機械與機電工程學系

一、中文摘要

微米加工或機械製造譬如鑄造, 銲接,

及晶體成長等過程, 工件中經常發生氣孔.

氣孔之分佈及尺寸大小, 決定了工件之美

觀,更直接影響加工品質. 此計畫分為三年.

第一年為規劃採購設置干涉儀.工作原理是

利用濃度,溫度差異造成雷射相位差,以量

測觀察濃度,溫度,流場分佈.第二年為以既

有之顯微鏡及數位照相機,同時連續觀察單

一及多個氣泡,因水中氧氣及二氧化碳氣體

濃度過飽和而成核, 成長,及陷於固體冰過

程,受環繞濃度流場分佈影響之動態變形.

關鍵詞：氣泡動力學､固化過程､製造加

工產生之氣孔

Manufacturing processes such as casting, welding, and crystal growth are usually accompanied with porosities in workpieces. The distribution, size, shape, and volume fraction of porosities determine the extent of any degradation in mechanical properties. The first year of this three years’ project is to setup an interferometer to measure flow patterns, distributions of solute gas and temperature around the bubbles on the solidification front. This study is the second year of this project. The work is to use a microscopy accompanying with a CCD camera to observe unsteady dynamic growth of pores in solid after the bubbles are nucleated from supersaturation of oxygen and carbon dioxide gases on the solidification front.

Keywords: Bubble dynamics, solidification process, pores induced in manufacturing

二、緣由與目的

Porosity has been regarded as defects that degrade the mechanical properties of the products. It is one of the most serious problems commonly occurring in the MEMS, materials and manufacturing processings, and biosciences. Since gas solubility in the solid is usually much less than that in the liquid, gas accumulation ahead of the solidification front readily results in nucleation of bubbles on the solidification front. Pore formation in solids is a consequence of the bubbles trapped by the solidification front [1-10].

To understand pore formation in solid, water is often used as a medium not only for an easy visualization but also for solidification similar to that of metals [11]. Chalmers [1] interpreted that air rejected by the solidification front accumulated in water near the interface until concentration was high enough for bubbles to nucleate. The bubble grew because air diffused into it. If the interface continued to move forward, the bubble cannot grow laterally but forward to form a cylindrical pore, known as an ice worm. The ice worm that frequently looked like a string of pearls was proposed to be due to the fluctuations of the freezing rate. When freezing was slow, bubbles were bigger because more air diffused into them. During fast growth there was less time for diffusion and the bubble decreased in cross section. The formation of ice worms therefore was suppressed and the ice contained a large number of very small, round pores. Very slow freezing permitted the rejected air to diffuse away from the interface. Neither bubbles nor ice worms appeared. It is noted that the above interpretations were exclusively focused on conservation of mass. This leads to a mis-interpretation for that an increase of air diffusion into a bubble resulted from a decrease of the freezing rate was responsible for an increase in the size of the bubble. In fact, the radius of an elongated bubble is increased by decreasing gas pressure in order to satisfy momentum balance on the cap. The decrease in gas pressure is due to a decrease

in the freezing rate reducing solute accumulation and diffusion into the bubble [12-16].

Bari and Hallett [5] observed the growths of air and helium bubbles trapped in ice. It was found that bubbles grew as cylindrical pores for solidification

rate below 5 µm/s, while they became egg-shaped

with the narrow ends toward the interface at higher solidification rates. Geguzin and Dzuba [7] divided bubbles and pores into well-type, semi-closed, closed inclusions, boundary containing gas-saturated liquid, and isolated gas bubble in solid near the solidification front. It was proposed that a bubble is not captured, captured as an elongated inclusion, and isolated pore as the solidification front is, respectively, less, equal, and greater than the rate of displacement of the top surface of the growing bubble. Murakami and Nakajima [10] observed and measured the radii and periodic distances between columnar pores for different growth rates and supersaturations of a water-carbon dioxide solution. Although the shapes and sizes of the bubbles in solid versus solidification rate are known, a detailed and quantitative in-situ observation and interpretation of the bubbles generated and trapped in solids as pores has not been presented. This becomes the objective of this work.

Geguzin and Dzyuba [6] observed the bubbles to be arisen chiefly in the region of coarse distortions of the solidification front, at which a local increase in gas concentration exists. Wei et al [12] conducted the first experiments and analysis to study bubble nucleation on a solidification front. In view of an increase in solute content resulting in a decrease in free energy barrier at the advancing interface, the critical radii and the number of nucleating bubbles decrease and increase, respectively, in an early stage of solidification. Since solidification rates decreased in later stages of freezing, interfacial solute content and free energy barrier were decreased and increased, respectively.

A simple analysis for a growth of a bubble trapped in solid was proposed by Wei et al. [13]. It was shown that since gas in liquid highly accumulates at cap surface of the bubble by increasing solidification rate, mass transport to the bubble is enhanced and gas pressure in the bubble is increased. A satisfaction of momentum balance leads to a decrease of cap radius. When the solidification rate decreases in the course of freezing, cap radius increases with time. Solidification rates play an important role in pore formation. The growth of the cap radius is found to be a result of the decreasing rate of gas pressure overriding that of hydrostatic pressure on the cap. As the decreasing rate of gas pressure becomes of the same order as that of

hydrostatic pressure in later times, the wall of the pore readily corrugates. Since the cap angle significantly affects the shape of the pore, more realistic shapes and growths of bubbles with deformed caps in solids have been predicted [14].

The present work is to conduct an in-situ observation of the shapes of the bubbles trapped in solid after nucleation on the solidification front during an upward solidification. Bubble formation is resulted from supersaturation of oxygen gas in the water near the solidification front. From providing exploratory analysis to interpret experimental observations, the major factors affecting and controlling this complex bubble dynamics in the solid during the freezing process is presented.

三、實驗量測

The experimental apparatus and setup are the same as a previous work conducted by Wei et al. [12]. The system includes a glass tube, constant-temperature bath, zoom microstereoscope, and charge-coupled device (CCD) camera, as illustrated in Fig. 1. The glass tube (PYREX) has outer and inner radii of 0.027 and 0.025 m and length 0.5 m, respectively. The glass tube was poured by a degassed and deionized water in a height of 0.2 m. After the water was exposed by a chosen dissolvable gas for one hour, the free surface

was sealed by wax (melting point is 50

°

tube was then placed on the constant temperature sink for cooling. Gas concentration and temperature were measured by using a hand-held dissolved oxygen gas system and thermocouples, respectively. Locations of the solidification front and shapes of the bubbles on the interface and in the solid were photographed from the zoom stereo microscope accompanied with the CCD camera. The major components used for the experiment was as follows:

1. Constant temperature sink (LC-10H,

WISDOM, Apparatus Mfg. Co., Kaohsiung, Taiwan, Republic of China): The thermal sink maintains a chosen constant temperature at the bottom of the glass tube. The temperature range for measurement is -30 to + 20 °C with precision of

±

°

2. Zoom stereo microscope (Olympus Model SZ60, Olympus Optical Co., Tokyo, Japan). In order to obtain a long focal distance and clear image of bubbles, a zoom of 1-6.3 X, C-Mount TV Adapter, Eyepiece GSWH 10X with two pieces was chosen. To remove inherent errors induced by the curvature of the glass tube, real sizes of bubbles were determined by comparing photographed bubbles and a ruler inserted in the water.

3. Charge-coupled device (CCD) camera (Pixera Professional, Pixera Co., Los Gatos, CA) with magnification of 1: 2.1 and 4 passes/2 s. The position of the solidification front is tracked by using a CCD camera.

4. A hand-held dissolved oxygen system (OXI 330, Wissenschaftlich-Technische Werkstatten GmbH & Co., KG, Weilheim, Germany). The hand-held dissolved oxygen system was utilized to determine concentration of oxygen gas in a degassed and deionized water produced from Ultrapure Water System (Barnstead model D4741, Barnstead/Thermolyne Co., Dubuque, IA).

四、結果討論

In this work, the bubbles trapped in solid after nucleation on a solidification front during the freezing of a water containing a dissolvable gas is experimentally and quantitatively observed. From a comparison between observations and predictions, the physical mechanisms of bubble growths are revealed. Figs. 2(a)-(h) show photographs of the growths of bubbles on the solidification front at different locations near 0.01 m during the freezing of water containing an oxygen gas of 0.0041 g/100 g at a cold

temperature of -25

°

as the solidification front passes through a location x = 0.01 m, a bubble pointed by an arrow with "a" is nucleating on the interface. The time is considered to be a reference time of zero. Nucleation takes place if the Helmholtz free energy reaches the maximum, namely, the free energy barrier. Bubble a becomes trapped and grows in size at a later time of 5 s, as shown in Fig. 2(b). The shape of the bubble is still spherical. The contact angle representing the inclination angle of the cap on solidification front

decreases from around 180 to 150ο. At a time of 20 s,

the length of the bubble in solid increases to

1.2×10−4 m, while the radius reaches the maximum

value of around 5 ×10−5 m at contact angles of

around 90ο, as shown in Fig. 2(c). The increase in the

length of the bubble is attributed to advancement of the solidification front [13, 14]. The maximum radius

of the bubble for a contact angle of 90οshould be

identical to the critical radius of the nucleating bubble. However, the maximum radius is found to be significantly larger than the critical radius. This is attributed to that the difference in pressures across the cap is lower than that of the bubble at the critical state. Similar to homogeneous nucleation and subsequent growth to macroscopic sizes of a bubble in a saturated solution, the mass flux of the dissolved gas from the

liquid to a spherical bubble decreases the difference in pressures across the surface. As a consequence, an account for a regime of a spherical growth after nucleation is required. The shape of the bubble in solid is traced by tangential lines of the cap at the triple point from previous times [14]. From dynamic adjustments between the spherical growth of the bubble and advancement of the solidification front [17], the radii near the bottom of the bubble in solid in the spherical growth regime are increased. The spherical growth is ended and the maximum radius of the bubble is reached, as the contact angle decreases

to around 90ο. The reason for the maximum radius

greater than the critical radius can also be affected by a decrease in the solidification rate [13]. Other reason seems to be the melting of the bubble in the solid. Heat transfer from the liquid above the cap into the interior of a bubble and to the surrounding solid. Since the bottom of the bubble in solid is observed to maintain nearly the same shape (see Figs. 2(a) through (c)), heat transfer between the bubble and the surrounding solid is slight.

A bubble denoted by "b" is seen to be nucleated

on the solidification front at a time of 60 s, as shown in Fig. 2(d). In contrast to bubble a, bubble b is necked at the solidification front, as shown in Fig. 2(e) at a time of 120 s. The neck is a consequence of an increase in gas pressure from an enhanced gas content on the cap. The increase in interfacial gas content is a result of an instantaneous increase in solidification rate, or relative velocity between the liquid and solidification front. Even though the solidification front is varied within 10 percent, the change of the radius can be around one radius [14]. The necked bubble b is trapped in solid at a time of 150 s as shown in Fig. 2(f). A third bubble denoted by "c" is also seen to nucleate and grow on the solidification front as shown in Fig. 2(g) at a time of 180 s. The

length of bubble a continuously increases to 10−3 m.

In Fig. 2(h) at a time of 206 s, bubble a is escaped through the solidification front to the liquid and left a pore or a channel in the solid. Only two minor bubbles are left in the pore. In contrast to bubbles, the existence of pores is only vaguely seen.

五、結論

1. Development of bubble or pore shapes in solid during the freezing can be divided into five regimes: (1) nucleation of a bubble on the solidification front, (2) spherical growth on the interface, (3) solidification rate-controlled elongation, (4) disappearance in the solid, and (5) formation of the pores.

2. The bubbles nucleated at different locations on the solidification front at the same time may exhibit different shapes, which strongly influence the final shapes of the pores in solid.

3. The spherical growth of the bubble on the solidification front in regime (2) is similar to the growth after nucleation to a macroscopic size of a bubble in a super-saturated solution.

4. Different phenomena during the

solidification rate-controlled elongation of the bubble in regime (3) are possible: (a) the bubble can be elongated and maintained a relatively constant radius associated with slight variations; (b) the bubble can be necked, broken at the solidification front and trapped in solid; (c) the bubble can be aggregated with other bubbles in the solid; and (d) the bubble in the solid can be separated into several bubbles. Cases (a) and (b) have been systematically interpreted from accumulation of the solute gas, mass transport of the dissolved gas to the bubble, changes in gas pressure and radius at the cap.

5. In contrast to spherical growth, the gas pressure in the bubble in the solidification rate-controlled elongation regime may increase or decrease in the course of solidification.

6. The bubbles in the solid remain the relatively same shapes in most cases.

7. More detailed and accurate investigations of five regimes involving different mechanisms of growths and shapes of the bubbles in the solid are essentially required.

REFERENCES

1. B. Chalmers: Scientific American, 1959, vol. 200, pp. 114-122.

2. J. D. Fast: Interaction of Metals and Gases, translated from Dutch by M. E. Mulder-Woolcock, Academic Press, New York, 1965, .

3. S. Kou: Welding Metallurgy, Wiley, New York, 1987.

4. A. E. Carte: Proceedings Physical Society London, 1961, vol. 77, pp. 757-768.

5. S. A. Bari and J. Hallett: J. Glaciology, 1974, vol. 13, pp. 489-520.

6. Ya. E. Geguzin and A. S. Dzyuba: Soviet Physics, Crystallography, 1977, vol. 22, pp. 197-199 (from Kristallografiya,1977, vol. 22, pp. 348-353).

7. Ya. E. Geguzin and A. S. Dzuba: J. Cryst. Growth, 1981, vol. 52, pp. 337-344.

8. G. Lipp, Ch. Korber, S. Englich, U. Hartmann, and G. Rau: Cryobiology, 1987, vol. 24, pp. 489-503.

9. K. Tagavi, L. C. Chow, and O. Solaiappan: Experimental Heat Transfer, 1990, vol. 3, pp. 239-255.

10. K. Murakami and H. Nakajima: Materials Transactions, 2002, vol. 43, pp. 2582-2588.

11. K. A. Jackson and J. D. Hunt: Acta Metall.,1965, vol. 13, pp. 1212-1215.

12. P. S. Wei, C. C. Huang, and K. W. Lee: Metall. Mater. Trans. B, 2003, vol. 34B, pp. 321-332. 13. P. S. Wei, Y. K. Kuo, S. H. Chiu, and C. Y. Ho: Int. J. Heat Mass Transfer, 2000, vol. 43, pp. 263-280.

14. P. S. Wei and C. Y. Ho: Metall. Mater. Trans. B., 2002, vol. 33B, pp. 91-100.

15. W. A. Tiller, K. A. Jackson, J. W. Rutter, and B. Chalmers: Acta Metallurgica, 1953, vol. 1, pp. 428-437.

16. M. V. A. Bianchi and R. Viskanta: Int. J. Heat Mass Transfer, 1997, vol. 40, pp. 2035- 2043. 17. C. C. Huang: Master thesis, Dept. Mechanical and Electro-Mechanical Eng., National Sun Yat-Sen University.

LIST OF FIGURES

Fig. 2 Photographs of heterogeneous nucleation, growth and disappearance of bubbles trapped in solid at different times or locations near the location of 1 cm (a) 0, (b) 5, (c) 20, (d) 60, (e) 120, (f) 150, (g) 180, and (h) 206 s during the freezing of water containing oxygen gas content of 0.0041 g/100 g and temperature