Microsoft Word - .s doc

Size: px

Start display at page:

Download "Microsoft Word - .s........-2.doc"

琰鉴武
7 years ago
Views:

1 臺灣二 O O 六年國際科學展覽會科別 : 物理科作品名稱 :Self Assembly Mechanism of Water Drotlets 得獎獎項 : 佳作學校 / 作者 : 臺北市立中山女子高級中學王啟芸臺北市立和平高級中學王啟倫

2 圖左為王啟倫, 圖右為王啟芸我很喜歡做一些可以自己 DIY 的事情, 像美工方面之類所以以前有得過土工北市第二和紙工校內第一當然我也很喜歡運動, 尤其是籃球 ; 在我國中的時候是再興的籃球隊隊長, 高中部球隊教練有想找我入隊一起練球, 但是因為爸媽反對, 所以我還是把籃球當作一項休閒活動另外我從小學二年級每年都有作科展直到現在, 雖然有時實驗的進展不是很順利, 但只要有了新發現而且是自己動腦想出來的話, 就會非常有成就感這次我覺得實驗做的滿完整的, 希望評審教授也能給予意見與指導 ( 王啟倫 ) 從小喜歡探索問題, 從生活中的小地方, 發現無限的奧秘我從小對繪畫和美工有很大的興趣, 常常是學校海報設計的常勝軍, 國二時, 得到學生美展版畫類第三名平時, 除了讀書之餘, 喜歡到郊外踏青, 擁抱大自然, 或是到博物館美術館參觀欣賞國中開始和弟弟一起作科展, 從中不但和弟弟的感情更好, 對設計實驗思考問題撰寫報告也更上一層樓了 ( 王啟芸 )

有成就感這次我覺得實驗做的滿完整的, 希望評審教授也能給予意見與指導 ( 王啟倫 ) 從小喜歡探索問題, 從生活中的小地方, 發現無限的奧秘我從小對繪畫和美工有很大的興趣, 常常是學校海報設計的常勝軍, 國二時, 得

3 作品目錄作品摘要 P.2~3 實驗裝置 P.4~8 分析與討論 P.9 結論 P.21 參考資料 P.22~27 2

4 Self Assembly Mechanism of Water Droplets 3

5 作品摘要這是一系列關於水蒸氣冷凝為極細微小水珠的長程實驗其中可以分為下列三個階段 : 第一階段是基礎實驗將水氣導入至潔淨的光滑表面上 ( 蓋玻片 ), 觀察水珠冷凝的機制第二階段是在外加磁場及電場作用下, 將水氣導入至潔淨的光滑表面 ( 蓋玻片 ), 觀察水珠冷凝的機制這部分的實驗推翻了一般水分子是電中性, 在電場或磁場中不受影響的刻板觀念! 實驗所呈現出來的冷凝水珠, 不但有明確的自我組成模式 ( Self assembly pattern) 並且發現 : 電場會增速凝結水珠的成長 (Aggregation), 而磁場則會抑制凝結水珠的成長第三階段是將水蒸氣導引至超聲波的環境中 : 我們先將超聲波訊號產生器 ( 變頻定頻 ) 面向於載台旁, 再讓水氣導入至潔淨的光滑表面上 ( 蓋玻片 ), 觀察冷凝水珠的機制當使用固定頻率超聲波波源, 我們發現 : 在超聲波場中水珠的成長會受到抑制, 且成長速率會隨著頻率的升高而逐漸減小第一階段與第二階段的實驗結果與討論已分別發表於 2004 年及 2005 年的台灣國際科學展覽報告中, 本作品將詳述第三階段 4

實驗所呈現出來的冷凝水珠, 不但有明確的自我組成模式 ( Self assembly pattern) 並且發現 : 電場會增速凝結水珠的成長 (Aggregation), 而磁場則會抑制凝結水珠的成長第三階段是將水蒸氣導引至超聲波的環境中 : 我們先將

6 Abstract This experiment explores the basic nature of the condensation of water vapor into droplets on the surfaces of cover glasses. This condensation occurs because of the difference in temperature between the water vapor and the cover glass. The condensation process is observed under a microscope. The growth of the droplets can be described as: nucleation, aggregation (piling up) and coalescence. The growth is irrelevant to surfaces or environments. It is found that the temperature difference of moist air over the cover glass do not affect the nucleation size of the droplets in simple plain surroundings; while the change of flow rate does. In general, the coalescence is speeded up at higher temperatures. Furthermore, the effects of electric fields magnetic fields and ultrasonic waves are also studied. It can be observed that the size of water droplets become smaller and grow more uniformly under magnetic fields or imposed ultrasonic waves; also, the aggregation rate is decreased by imposed magnetic fields or ultrasonic waves, and it is increased by imposed electric fields. These effects of magnetic fields electric fields and imposed ultrasonic waves might be related to the flow conditions and the vibration of surrounding air in the system. This experiment provides the first step in the understanding of the formation of water droplets and their self assembly mechanism in different environment. 5

The growth of the droplets can be described as: nucleation, aggregation (piling up) and coalescence. The growth is irrelevant to surfaces or environments.

7 壹實驗動機這是一個長期系列性研究冷凝極細水珠的整體實驗承接去年所作的實驗 ( 第二階段 ), 我們發現, 當傳送水氣時, 外加電場及磁場會影響水氣冷凝的過程由於電場及磁場屬於超距力場, 為了釐清空氣在其中所扮演的角色, 我們嘗試外加超聲波, 觀察是否會影響水氣冷凝的過程貳研究目的 ( 一 ) 探討超聲波 ( 變動頻率 ) 對冷凝過程的影響 ( 二 ) 探討超聲波 ( 固定頻率 ) 對冷凝過程的影響參實驗方法將潔淨過的蓋玻片 ( 選用蓋玻片是為了透光性良好和擺置的便利性 ) 置於不同變因的實驗板上 ( 我們將環境設為 normal condition ( control ) ultrasonic) 裝置示意圖, 如 ( 圖一 ) ( 圖四 ): 6

探討超聲波 ( 變動頻率 ) 對冷凝過程的影響 ( 二 ) 探討超聲波 ( 固定頻率 ) 對冷凝過程的影響參實驗方法將潔淨過的蓋玻片 ( 選用蓋玻片是為了透光

8 CCD 水氣輸出口恆溫箱圖 ( 一 ) 超聲波發射喇叭積水排出閥氮氣輸入口示波器超聲波波源顯示螢幕顯微鏡圖 ( 二 ) 7

9 95mm 4.5Xmm 21mm 105mm magnets N Normal Magnetic Electric 25m Copper plate 45mm 95mm 21mm 105mm Ultrasonic Field 圖 ( 三 ) 不同變因的台裝置 8

10 V Water droplets Outlet Cover glass Microscope 圖 ( 四 ) 吹送示意圖 9

11 用鐵氟龍做成一個 mm 3 的清洗載體所用的蓋玻片大小為 mm 2 戴手套將蓋玻片放入清洗載體之凹槽中 1. 35%HCl 超音波震 5 min 2. 絕對酒精超音波震 5 min Ω 去離子水超音波震動 5min 將清洗完畢的蓋玻片先放入充滿 18.3Ω 去離子水的培養皿中儲存待要用時, 戴手套將其一取出用氮氣將其吹乾後使用圖 ( 五 ) 清洗流程 10

12 肆實驗結果與討論 ( 一 )1 標準對照組 (Control) 最初 0.2 秒內 T=0.134 s T=0.167 s T=0.2 s 11

13 2 外加超聲波 ( 變動頻率 )55kHz 65kHz 最初 0.2 秒內 T=0.134 s T=0.167 s ( 二 )1 Normal conditio T=0.2 12

14 ( 二 )1 Normal condition ( control ) 最初 0.2 秒內 T=0.134 s T=0.167 s T=0.2 s 13

15 2 外加超聲波 ( 固定頻率 ) 30kHz 最初 0.2 秒內 T=0.134 s T=0.167 T=0.2 s 14

16 3 外加超聲波 ( 固定頻率 ) 40k 最初 0.2 秒內 T=0.134 s T=0.167 s T=0.2 s 15

17 4 外加超聲波 ( 固定頻率 ) 50k 最初 0.2 秒內 T=0.134 s T=0.167 s T=0.2 s 16

18 5 外加超聲波 ( 固定頻率 ) 60k 最初 0.2 秒內 T=0.134 s T=0.167 s T=0.2 s 17

19 ( 三 ) 外加超聲波變動頻率 (from 55K to 65K) 與標準對照組 : (1) 經過 0.2 秒之後, 外加超聲波 ( 變頻 ) 的冷凝水珠的直徑成長速率部份開始趨緩, 而標準對照組則加速 ; 這表示冷凝水珠在 Aggregation 過程會受到超音波場的影響 : 逐漸變慢 Early Time Late Time 1.1 Diameter ( mm ) Ultrasonic Pest Repeller ( from 50 khz to 65 KHz) Control Time ( sec ) ( 2 ) 以 0.1 sec 為界, 將 < 0.1 sec 作為 Early Time, 將 > 0.1 sec 作為 Late Time 在 Early Time 時,Ultrasonic Peat Repeller ( 50~60 khz ) 的成長速率較快於 Control 的成長速率 ; 但是, 在 Late Time 時, 則相反 18

慢 1.3 1.2 Early Time Late Time 1.1 Diameter ( mm ) 1.0 0.9 0.8 0.7 0.6 0.5 Ultrasonic Pest Repeller ( from 50 khz to 65 KHz) Control 0.00 0.

20 ( 四 ) 外加超音波固定頻率 (from 30K to 65K) 與標準對照組 : Diameter ( 30u x mm) Control 30 khz 35 khz 40 khz 45 khz 50 khz 55 khz 60 khz 65 khz Time ( sec ) 7 6 Diameter/ Time Frequency ( khz ) 19

8 Control 30 khz 35 khz 40 khz 45 khz 50 khz 55 khz 60 khz 65 khz 0.10 0.

21 利用直徑變化對時間作圖得到不同頻率的斜率, 以此斜率作為成長速率 ( Growth Rate ) 趨勢漸向下, 表示, 外加超聲波, 當頻率越強, 水珠的成長速率減緩此部份主要是探討 Late Time ( > 0.1 sec ) ΔR= 直徑變化,Δt= 時間變化,ΔR= 直徑平均值利用 ΔR /Δt/ ΔR 可求出水珠相對成長速率 ( Size Growth Rate ), 此趨勢也是向下, 代表外加超聲波的頻率越大, 水珠的成長速減緩此部份主要是探討 Late Time ( > 0.1 sec ) 20

22 ΔV= 體積變化假設體積為半球體 ( 1 4 π r ), 一次微分後得 4πr 2, 則 4πr 2 R 為水珠體積成長速率此趨勢也是向下, 即可表示, 水珠成長隨超聲波頻 t 率的增強而減緩的趨勢此部份主要是探討 Late Time ( > 0.1 sec ) 以 R / t/ R 和 V/ t 分別作圖, 可相互印證, 外加超聲波, 當頻率越大, 水珠成長速率 ( Growth Rate ) 也隨之減緩在外加超聲波的情況下, 其成長模式可分為兩種, 分別為 Early Time ( < 0.1 sec ) 和 Late Time( > 0.1 sec) 推論 : 21

23 N 2 Control N 2 Early Time (< 0.1 sec) 外加超聲波的水珠成長速率較快推測, 因超聲波增加空氣中的擾動, 而使水珠較容易碰撞, 增加其質量, 並間接加速其下降速率 ( 加速成核速率 ) N 2 Late Time (> 0.1 sec) 外加超聲波的水珠其成長較緩慢推測, 因空氣擾動持續增加, 而使水珠移動範圍加大, 故使冷凝於蓋玻片上的水珠密度下降, 則觀察到的水珠生長速率減緩 22

24 伍結論 1. 成核 (Nucleation) 水珠的成長過程主要是由二部分組成的 : 先堆疊 (Pile up Aggregate) 後合併 (Coalescence) 2. 溫度相同時, 水蒸氣的速度外加磁場強度外加電場強度外加超聲波定頻不同時, 影響成核尺寸 (Nucleation size) 3. 影響凝結水珠散佈於物體表面可能的方式 : (1) 空氣對流機制的影響 (2) 趨向最低能量 (3) 趨向最大亂度 (4) 空氣共振 ( 超聲波 ) 因素影響 4. 影響水珠尺寸的重要因素 : (1) 水蒸氣與凝結表面的溫度差距 (2) 水蒸氣導引的速率 (3) 水蒸氣每秒達凝結表面的數量 (4) 外加超聲波引起空氣共振 5. 外加超聲波,Early Time (< 0.1 sec ) 加速水珠成核速率 Late Time ( > 0.1 sec ) 減緩水珠成長速率 23

25 參考資料 71_f99_10.html PRECIPITATION Precipitation is any form of water (liquid or solid) that falls from a cloud and reaches the ground. There are, obviously, lots of different types of precipitation: rain, snow, hail, sleet, etc. Nucleation : The initiation of a phase change of a substance to a lower thermodynamic energy state. (i.e. vapor to liquid Condensation) American Meteorological Society When water vapor condenses or freezes, it prefers to condense or freeze onto something - it needs a surface (preferable some liquid water or ice already present). Away from the surface of the earth (in the "free atmosphere"), the only available surfaces are tiny solid particles suspended in the air (dust, smoke particles, sea salt, etc.) These are called condensation nuclei. They are generally quite small; typical sizes are 0.01 to 1 micrometers in diameter. The formation of precipitation begins with the process of nucleation, which is the deposition, freezing, or condensation of water vapor in the free air onto condensation nuclei. Let's say you manage to get some water vapor to condense onto a condensation nuclei. What will determine whether this initial water droplet will continue to grow or not? The answer is that the relative humidity of the air around the droplet will determine its growth. If we assume the nuclei is "normal" (i.e. neither attracts nor repels water molecules), then IF RH < 100 % ---> evaporation exceeds condensation > droplet will shrink IF RH = 100 % ---> evaporation equals condensation > droplet will remain same size IF RH > 100 % ---> condensation exceeds evaporation > droplet will grow 24

26 We see that under "normal" circumstances, drop growth by condensation or deposition will only occur when the environment is supersaturated - when RH > 100 %. This is fairly rare. How then will a cloud ever form? The answer is that some condensation nuclei are hygroscopic, they attract water. Because they attract water molecules, hygroscopic nuclei allow drop growth to occur when RH is equal to or less than 100 %. Thus these type of nuclei are very important for cloud formation. It is common to observe tiny droplets of liquid water in clouds even when the temperature is below freezing. When liquid water is present at below freezing temperatures, it is called super-cooled water. Remember that water molecules want to have surfaces to condense (or in this case, to freeze) onto - call them ice nuclei in this case. Since there are very few ice nuclei in a typical cloud, you end up with super-cooled water droplets hanging around looking for something to condense on. If it gets cold enough (below -39 C), these super-cooled water droplets will freeze even in the absence of ice nuclei. This is called spontaneous nucleation. Drop growth by condensation or deposition of water vapor onto appropriate nuclei is very slow. Figure 7.1 in Danielson shows that it takes more than 2 hours to grow a 30-micrometer diameter cloud droplet from a condensation nucleus by condensation alone. We know from routine observations that a thunderstorm can form and produce rain in less time than this. How is this possible, given the fact that drop growth by condensation is so slow? Growth by collision and coalescence (Warm rain process) The handout distributed today shows that typical condensation nuclei are 0.1 to 1 micrometer in diameter. Typical cloud droplets are observed to be 1-30 micrometers in diameter. The smallest precipitation particles are about 0.2 millimeters in diameter (or about 200 micrometers), and they can be up to 5 millimeters (5000 micrometers) in size. Condensation and deposition alone can grow typical cloud droplets in a period of minutes, but you would have to wait almost forever for these processes to produce a 25

27 precipitation-sized particle that is heavy enough to fall. Luckily, there are other ways to produce precipitation-sized particles that work much faster. The growth of precipitation particles beyond the cloud droplet stage can be accomplished by the combined effects of collision and coalescence, and also by the Bergeron process (the three-phase process). Collision and coalescence involve interaction of liquid water droplets with other liquid water droplets - it is most important in clouds with temperatures above freezing - hence the name "warm rain process" (Danielson p. 190). The Bergeron process is most important in clouds with temperatures below freezing. It involves interactions between ice particles, super-cooled water, and water vapor - hence the name "three-phase process"). Collision is self-explanatory. Liquid cloud droplets carried by air motions within a cloud can collide. Obviously, the most effective type of collisions will involve one big droplet moving through a group of smaller droplets. If the droplets are all moving at different speeds, that will also increase the likelihood of collisions. Coalescence refers to the fact that water is "sticky". If two water droplets come into contact (say by collision) then they will stick together and make one larger droplet. Not all droplets that collide will stick together - they could bounce off each other. Therefore, collision and coalescence are not an entirely efficient process. Furthermore, these colliding droplets will tend to limit the size that a precipitation particle can reach - no larger than about 5 millimeters in diameter. 26

28 The free energy of a droplet of radius R is the sum of the energy cost due to the surface tension, 4πσR 2, and the energy gain due to the volume of the new phase, -(4/3)πR 3 f, where ρ is the density (mass per unit volume). Nucleation details When moving into a 2 phase region on phase diagram - how does the new phase form? Two issues: 1. Thermodynamics: Is nucleation possible? (energy minimization) 2. Kinetics: How fast does it happen? (nucleation rate) Homogeneous Nucleation vapor --> liquid (solid) for a pure water Energy minimization involves two terms: volume transition: 1. volume transition 2. surface formation 27

29 where is the atomic volume, PS is the pressure above the liquid (solid), and PV is the pressure in the vapor. We want PV > PS so that ÆG is negative => supersaturation provides the driving force. surface formation: Change in surface energy is always positive when forming surfaces. Total energy change: note: initial formation of nuclei has increase in G => metastable if r < r* then nuclei shrink to lower G if r > r* then nuclei grow to lower G r* is a critical radius for nuclei 28

30 Films will also have an interface term => heterogeneous nucleation (coming soon!) 29

31 評語本作品在今第三年度的研究中, 探討超聲波對水滴形成堆疊的影響雖能從實驗上推論出超聲波會阻礙並降低水滴堆疊的行為, 會有數據顯示超聲波頻率的效應, 但實驗數據較不完整且其廣度應可大幅加強, 以強化支持實驗結論, 在實驗結論機制探討方面, 比較缺乏許多可加強的空間

6-1-1極限的概念

6-1-1極限的概念選修數學 (I-4 多項式函數的極限與導數 - 導數與切線斜率定義. f ( 在的導數 : f ( h 對實函數 f ( 若極限存在 h h 則稱 f ( 在點可微分而此極限值稱為 f ( 在的導數以 f ( 表示 f ( f ( 函數 f ( 在的導數也可以表成 f ( 註 : 為了