建議

1. 本實驗之光源使用單一鹵素燈由流道斜上方打光，因此拍攝之影像亮度並不

均勻，而且在實驗時需要耗費許多時間在調整光線入射之角度與位置，同時 有嚴重的反光問題，建議其他研究者嘗試使用其他種類的打光方式或是調整 光源入射的角度與方式，減少影像之雜訊、並避免粒子照光不均勻產生的形 狀偏差。

2. 拍攝粒子之影像時，避免挑選位置太過接近壁面之粒子，以免粒子在拍攝過

程中因沉降至流道底部而靜止不動，或是因為受到壁面摩擦之影響而量測到 不正確的位移量。

3. 當實驗之溫度逐漸增加時，因為流體之氣體溶解度逐漸的下降，因此在流道

內會有小氣泡產生，其反光會影響影像之品質，建議其他研究者在實驗之前 先取出實驗所需體積之奈米金溶液，並加熱至實驗條件之最高溫度，以去除 流體內溶解之氣體。

4. 本實驗在進行影像分析之前，需要花費許多時間來手動進行影像裁剪與處

理，因此在有限時間內限制了分析之粒子的數量，建議其他研究者撰寫可直 接由拍攝之原始影像自動進行粒子追蹤與分析之程式，來縮短影像處理之時 間，並增加粒子取樣數量來降低實驗誤差。

5. 本實驗中因為奈米金粒子會沉降的特性，使得實驗具有時間限制，而降低實

驗之成功機率，建議其他研究者嘗試尋找可避免粒子沉降之機制，或是改良 加熱平台使整體系統能在更短的時間內達到熱平衡。

6. 本實驗中粒子流道內溫度估算使用體積較大之 k 型熱電偶，使得流道無法完 整的密封，因此隨著實驗溫度的升高，流道內流體將更快的蒸發，同樣也限 制了實驗之時間，建議其他研究者可以嘗試使用微機電元件製作微型溫度感 測元件，增加流道密封性以避免流體之蒸發並降低流體溫度估算之不確定 性。

7. 目前的實驗並未研究物鏡放大倍率以及不同次像素位置估算之演算法對於系 統與隨機誤差所產生的影響，建議其他研究者可以嘗試研究這些實驗條件所 產生之影響，以便更完整了解此溫度估算技術最佳之實驗參數。

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表 2.1 不同粒子密度下，奈米金溶液粒子密度之不確定性 particle density

( ml^-1 )

image size ( px )

systematic error( ml^-1 )

random error( ml^-1 )

relative uncertainty 10⁵ 1920×1080 3.64×10⁴ 4.79×10⁴ 60.13%

10⁶ 1080×960 3.99×10⁵ 4.21×10⁵ 58.03%

10⁷ 960×540 5.35×10⁵ 3.22×10⁶ 32.64%

10⁸ 300×300 1.47×10⁷ 9.12×10⁶ 17.34%

表 3.1 不同溫度之流體黏滯係數、粒子擴散係數

temperature ( °C )

viscosity of fluid[51]

( Pa·s )

diffusivity of particles by Eq(1.3) ( m² s^-1 )

30 797.22 3.71×10^-12

35 719.13 4.18×10^-12

40 652.73 4.68×10^-12

50 546.52 5.77×10^-12

60 466.03 6.98×10^-12

70 403.55 8.30×10^-12

表 3.2 時間間隔Δt=1 s 時，不同溫度之粒子 MSD 與 RMSD

temperature ( °C )

MSD by Eq(1.7) ( m² )

MSD ( px² )

RMSD ( m )

RMSD ( px )

30 14.9 28.43 3.85 5.33

35 16.7 31.86 4.09 5.64

40 18.7 35.68 4.33 5.97

50 23.1 44.07 4.81 6.63

60 27.9 53.23 5.28 7.29

70 33.2 63.34 5.76 7.95

表 3.3 不同粒子密度與溫度下，連續拍攝 10 秒，平均影像重疊率 Nc

Temperature ( °C )

particle density, p_{( ml}^-1 ₎

10⁵ 10⁶ 10⁷ 10⁸

30 0.005 0.045 0.45 4.48

35 0.005 0.048 0.48 4.76

40 0.005 0.051 0.51 5.04

50 0.006 0.056 0.56 5.60

60 0.006 0.062 0.61 6.14

70 0.007 0.067 0.67 6.70

power supply

high-speed camera

objective 10X data acquisition

instrument

thermocouples computer

halogen lamp light guide

T

cover glass

tape channel slide glass copper plate Peltier heater working fluid with

nanoparticles

acrylic enclosure

圖 2.1 實驗架構圖

tape (3M, Scotchrap 50) glass slide

clear nail polish cover glass surface cleaning

tape attaching

tape cutting and removal

coating of clear nail polish

cover glass bonding

圖 2.2 試片製作程序

10

10

2

channel depth : 500 μm

5

unit : mm

圖 2.3 試片上視圖

acrylic enclosure acrylic cover

Peltier heater cover glass

copper plate glass slide tape channel working fluid with

nanoparticles

thermocouple T

圖 2.4 加熱平台與試片示意圖

= 10⁵ ml^-1

ρp ρp= 10⁶ ml^-1

= 10⁸ ml^-1 ρp

= 10⁷ ml^-1 ρp

(a) (b)

(c) (d)

圖 2.5 不同粒子密度下拍攝之影像

圖 2.6 粒子之原始影像與處理後之影像

(b) (a)

ra ndom e rr or , δT

rand

( °C )

imposed temperature, T

_i

(°C)

20 30 40 50 60 70 80

0 1 2 3 4

p = 2× 3 px p = 2× 5 px p = 2× 7 px

20 30 40 50 60 70 80

0 1 2 3 4 5 6

imposed temperature, T

i

(°C)

sy st e m a ti c e rr or , δT

sys

( °C )

p = 2× 3 px p = 2× 5 px p = 2× 7 px

圖 2.7 不同溫度下，使用不同數量資料點進行 Gaussian fit 分析之 (a) 系統誤差與 (b) 隨機 誤差

(時間間隔t= 0.06 s，觀察時間t = 10 s，粒子密度_tr p= 10⁶ ml^-1)

x y

x y

(a)

(b)

x position (px)

-1 0 1

normalized intensity value, Ĩ

0.0 0.5 1.0

Xpeak = -0.2438

y position (px)

-1 0 1

0.0 0.5 1.0

Ypeak = -0.2301

normalized intensity value, Ĩ

圖 2.8 粒子位置分析示意圖 (a) x 方向上影像強度 array 與回歸分析所得之擬合曲線 (b) y 方 向上影像強度 array 與回歸分析所得之擬合曲線

True

False

Start Image

acquisition

Image normalization

Image cropping

Position analysis of particle (2x3 Gaussian fit )

Calculate MSD from Eq. (1.1)

If | T-T_i | < 0.01 Calculate temperature, T

end

Calculate viscosity of working fluid

   Ti Assign

time interval t &

tracking time t _tr

Particle radius, rp

Assign initial temperature, T_i

Ti = Ti + 0.01 Image pre-processing

Temperature estimation

Output temperature, T

圖 2.9 粒子位置分析與溫度估算流程圖

displacement in x, x (px)

PDF

Ti = 30°C

displacement in y, y (px)

PDF

Ti = 30°C

displacement in y, y (px)

PDF

T_i = 50°C

displacement in x, x (px)

PDF

T_i = 50°C

displacement in y, y (px)

PDF

Ti = 70°C

displacement in x, x (px)

PDF

displacement in x, x (px)

PDF

Ti = 30°C

displacement in y, y (px)

PDF

Ti = 30°C

displacement in y, y (px)

PDF

T_i = 50°C

displacement in x, x (px)

PDF

T_i = 50°C

displacement in y, y (px)

PDF

Ti = 70°C

displacement in x, x (px)

PDF

displacement in x, x (px)

displacement in y, y (px)

PDF

Ti = 30°C

displacement in y, y (px)

PDF

displacement in x, x (px)

PDF

displacement in y, y (px)

PDF

displacement in x, x (px)

PDF

displacement in x, x (px)

PDF

Ti = 30°C

displacement in y, y (px)

PDF

Ti = 30°C

displacement in y, y (px)

PDF

Ti = 50°C

displacement in x, x (px)

PDF

Ti = 50°C

displacement in y, y (px)

PDF

T_i = 70°C

displacement in x, x (px)

PDF

displacement in x, x (px)

PDF

T_i = 30°C

displacement in y, y (px)

PDF

T_i = 30°C

displacement in y, y (px)

PDF

T_i = 50°C

displacement in x, x (px)

PDF

T_i = 50°C

displacement in y, y (px)

PDF

Ti = 70°C

displacement in x, x (px)

PDF

displacement in x, x (px)

PDF

T_i = 30°C

displacement in y, y (px)

PDF

T_i = 30°C

displacement in y, y (px)

PDF

T_i = 50°C

displacement in x, x (px)

PDF

T_i = 50°C

displacement in y, y (px)

PDF

Ti = 70°C

displacement in x, x (px)

PDF

time intereval, Δ t (s) MSD ( m

2

)

0.00 0.05 0.10 0.15 0.20

0

0.00 0.05 0.10 0.15 0.20

0

time intereval, Δ t (s)

0.00 0.05 0.10 0.15 0.20

0

0.00 0.05 0.10 0.15 0.20

0

time intereval, Δ t (s)

0.00 0.05 0.10 0.15 0.20

0

0.00 0.05 0.10 0.15 0.20

0

systematic error, δTe,sys (°C)

time interval, Δt (s)

0.00 0.04 0.08 0.12 0.16 0.20

0

0.00 0.04 0.08 0.12 0.16 0.20

0 5 10 15 20

systematic error, δTe,sys (°C)

time interval, Δt (s)

0.00 0.04 0.08 0.12 0.16 0.20

0 5 10 15 20

systematic error, δTe,sys (°C)

time interval, Δt (s)

10 15 20

systematic error, δTe,sys (°C)

time interval, Δt (s)

0.00 0.04 0.08 0.12 0.16 0.20

0 5

systematic error, δTe,sys (°C)

time interval, Δt (s)

0.00 0.04 0.08 0.12 0.16 0.20

0 5 10 15 20

0.00 0.04 0.08 0.12 0.16 0.20

systematic error, δTe,sys (°C)

time interval, Δt (s)

0

systematic error, δTe,sys (°C)systematic error, δTe,sys (°C)systematic error, δTe,sys (°C) systematic error, δTe,sys (°C)systematic error, δTe,sys (°C)systematic error, δTe,sys (°C) time interval, Δt (s)

time interval, Δt (s)

time interval, Δt (s)

time interval, Δt (s)

time interval, Δt (s)

time interval, Δt (s)

0.00 0.04 0.08 0.12 0.16 0.20

0 5 10 15 20

0.00 0.04 0.08 0.12 0.16 0.20

0 5 10 15 20

0.00 0.04 0.08 0.12 0.16 0.20

0 5 10 15 20

0.00 0.04 0.08 0.12 0.16 0.20

0 5 10 15 20

0.00 0.04 0.08 0.12 0.16 0.20

0 5 10 15 20

0.00 0.04 0.08 0.12 0.16 0.20

0

(a) (b)

(c) (d)

(e) (f)

time interval, Δt (s)

0.00 0.04 0.08 0.12 0.16 0.20

random error, δTe,rand (°C) ^{Ti = 30°C}

time interval, Δt (s)

0.00 0.04 0.08 0.12 0.16 0.20

random error, δTe,rand (°C)

0

time interval, Δt (s)

0.00 0.04 0.08 0.12 0.16 0.20

random error, δTe,rand (°C)

0

time interval, Δt (s) random error, δTe,rand (°C)

0.00 0.04 0.08 0.12 0.16 0.20

0

time interval, Δt (s) random error, δTe,rand (°C)

0.00 0.04 0.08 0.12 0.16 0.20

0

time interval, Δt (s) random error, δTe,rand (°C)

0.00 0.04 0.08 0.12 0.16 0.20

0

random error, δTe,rand (°C)random error, δTe,rand (°C)random error, δTe,rand (°C)

0.00 0.04 0.08 0.12 0.16 0.20

0.00 0.04 0.08 0.12 0.16 0.20 0.00 0.04 0.08 0.12 0.16 0.20

random error, δTe,rand (°C)random error, δTe,rand (°C)random error, δTe,rand (°C)

0.00 0.04 0.08 0.12 0.16 0.20 0.00 0.04 0.08 0.12 0.16 0.20

0.00 0.04 0.08 0.12 0.16 0.20

time interval, Δt (s)

time interval, Δt (s) time interval, Δt (s)

time interval, Δt (s)

time interval, Δt (s) time interval, Δt (s)

(a) (b)

(a) (b)

2 4 6 8 10 0

5 10 15 20

tracking time, t

tr

(s)

sys te m a ti c e rror , δT

sys

( °C )

_T

i = 30°C

= 10⁸ ml^-1 ρ_p

t = 1 s t = 2 s t = 3 s t = 4 s

t = 8 s t = 7 s

t = 6 s t = 5 s

t = 9 s t = 10 s

(a)

(b)

圖 3.18 粒子密度 = 10p ⁸ ml^-1，Ti = 30°C 時 (a)不同時間下之粒子影像 (b) 觀察時間與溫度 估算系統誤差之關係

tracking time, t

_tr

(s) sy st e m a ti c e rr or , δT

e,sys

( °C )

0 2 4 6 8 10

0 2 4 6 8

圖 3.19 觀察時間對於溫度估算系統誤差之影響 ( 時間間隔t= 0.06 s，所有粒子密度與溫度下之平均 )

(a) (b)

(c) (d)

tracking time, t _tr (s)

= 10⁵ ml^-1 ρ_p

random error, δTe,rand (°C)

tracking time, t tr (s)

= 10⁷ ml^-1 ρ_p

random error, δTe,rand (°C)

tracking time, t _tr (s)

= 10⁶ ml^-1 ρ_p

random error, δTe,rand (°C)

tracking time, t tr (s)

ρ_{p= 10}⁸ _ml^-1

random error, δTe,rand (°C)

0 2 4 6 8 10

tracking time, t

_tr

(s) ra ndom e rr or , δT

e,rand

( °C )

0 2 4 6 8 10

0 2 4 6 8

圖 3.21 觀察時間對於溫度估算隨機誤差之影響 ( 時間間隔t= 0.06 s，所有粒子密度與溫度下之平均 )

image

p r

rc

DOF

2 r

c ^{2 RMSD}

(a)

(b)

圖 3.22 (a)粒子之有效碰撞半徑計算 (b)在觀察時間間隔內，有效碰撞面積劃過的空間

30 40 50 60 70

imposed temperature, T

i

(°C)

ra ndom e rr or , δT

e,rand

( °C )

^{= 10}

sy st e m a ti c e rr or , δT

e,rand

( °C )

imposed temperature, T

_i

(°C)

= 10⁵ ml^-1

(a) (b)

(c) (d)

(e) (f)

RMSD (px)

Ti = 30°C

systematic error, δTe,sys (°C)

0 1 2 3 4

RMSD (px) sy st e m a ti c e rr or , δT

e,sys

( °C )

= 10⁵ ml^-1 ρ_p

0 1 2 3 4

0 5 10 15

20 Ti = 30°C

Ti = 35°C Ti = 40°C Ti = 50°C Ti = 60°C Ti = 70°C

圖 3.25 粒子密度 =10p ⁵ ml^-1時，RMSD 與溫度估算系統誤差之關係 ( 觀察時間t = 10 s ) _tr

RMSD (px) sy st e m a ti c e rr or , δT

e,sys

( °C )

= 10⁶ ml^-1 ρ_p

0 1 2 3 4

0 5 10 15

20 Ti = 30°C

Ti = 35°C Ti = 40°C Ti = 50°C Ti = 60°C Ti = 70°C

圖 3.26 粒子密度 =10p ⁶ ml^-1時，RMSD 與溫度估算系統誤差之關係 ( 觀察時間t = 10 s ) _tr

RMSD (px) sy st e m a ti c e rr or , δT

e,sys

( °C )

= 10⁷ ml^-1 ρ_p

0 1 2 3 4

0 5 10 15

20 Ti = 30°C

Ti = 35°C Ti = 40°C Ti = 50°C Ti = 60°C Ti = 70°C

圖 3.27 粒子密度 =10p ⁷ ml^-1時，RMSD 與溫度估算系統誤差之關係 ( 觀察時間t = 10 s ) _tr

= 10⁸ ml^-1 ρ_p

RMSD (px) sy st e m a ti c e rr or , δT

e,sys

( °C )

0 1 2 3 4

0 5 10 15

20 Ti = 30°C

Ti = 35°C Ti = 40°C Ti = 50°C Ti = 60°C Ti = 70°C

圖 3.28 粒子密度 =10p ⁸ ml^-1時，RMSD 與溫度估算系統誤差之關係 ( 觀察時間t = 10 s ) _tr

RMSD (px) sy st e m a ti c e rr or , δT

e,sys

( °C )

0 1 2 3 4

0 5 10 15

20 Ti = 30°C

Ti = 35°C Ti = 40°C Ti = 50°C Ti = 60°C Ti = 70°C

圖 3.29 RMSD 與溫度估算系統誤差之關係 ( 觀察時間t = 10 s，所有粒子密度下之平均) _tr

RMSD (px) sy st e m a ti c e rr or , δT

e,sys

( °C )

= 10⁵ ml^-1

sy st e m a ti c e rr or , δT

e,sys

( °C )

= 10⁶ ml^-1

RMSD (px) sy st e m a ti c e rr or , δT

e,sys

( °C )

= 10⁷ ml^-1

RMSD (px)

sy st e m a ti c e rr or , δT

e,sys

( °C )

_{Ti = 30°C}

T_i = 35°C T_i = 40°C T_i = 50°C Ti = 60°C Ti = 70°C

0 1 2 3 4

0 5 10 15 20

圖 3.34 RMSD 與溫度估算系統誤差之關係 ( 影像數量 Nf = 50 frames，所有粒子密度下之平均 )

(a) (b)

RMSD (px) RMSD (px)

RMSD (px) RMSD (px)

Ti = 35°C

Ti = 40°C Ti = 50°C

Ti = 60°C Ti = 70°C

random error, δTe,rand (°C) random error, δTe,rand (°C)

random error, δTe,rand (°C) random error, δTe,rand (°C)

random error, δTe,rand (°C) random error, δTe,rand (°C)

0 1 2 3 4

RMSD (px)

= 10⁵ ml^-1 ρ_p

ra ndom e rr or , δT

e,rand

( °C )

0 1 2 3 4

0 2 4 6

Ti = 30°C Ti = 35°C Ti = 40°C Ti = 50°C Ti = 60°C Ti = 70°C

圖 3.36 粒子密度 =10p ⁵ ml^-1時，RMSD 與溫度估算隨機誤差之關係 ( 觀察時間t = 10 s ) _tr

RMSD (px)

ra ndom e rr or , δT

e,rand

( °C )

^{= 106 ml-1ρp}

0 1 2 3 4

0 2 4 6

Ti = 30°C Ti = 35°C Ti = 40°C Ti = 50°C Ti = 60°C Ti = 70°C

圖 3.37 粒子密度 =10p ⁶ ml^-1時，RMSD 與溫度估算隨機誤差之關係 ( 觀察時間t = 10 s ) _tr

RMSD (px)

ra ndom e rr or , δT

e,rand

( °C )

^{= 107 ml-1ρp}

0 1 2 3 4

0 2 4 6

Ti = 30°C T_i = 35°C T_i = 40°C Ti = 50°C T_i = 60°C T_i = 70°C

圖 3.38 粒子密度 =10p ⁷ ml^-1時，RMSD 與溫度估算隨機誤差之關係 ( 觀察時間t = 10 s ) _tr

RMSD (px)

ra ndom e rr or , δT

e,rand

( °C )

^{= 10}

8 ml^-1 ρ_p

0 1 2 3 4

0 2 4 6

Ti = 30°C Ti = 35°C Ti = 40°C Ti = 50°C Ti = 60°C Ti = 70°C

圖 3.39 粒子密度 =10p ⁸ ml^-1時，RMSD 與溫度估算隨機誤差之關係 ( 觀察時間t = 10 s ) _tr

RMSD (px) ra ndom e rr or , δT

e,rand

( °C )

0 1 2 3 4

0 2 4 6

Ti = 30°C Ti = 35°C Ti = 40°C Ti = 50°C Ti = 60°C Ti = 70°C

圖 3.40 RMSD 與溫度估算隨機誤差之關係 ( 觀察時間t = 10 s，所有粒子密度下之平均 ) _tr

20 30 40 50 60 70 80 90 100

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

number of frames, Nf (frame)

RMSD (px)

unit : °C

圖 3.41 RMSD、影像數量與溫度估算隨機誤差之關係 ( 所有粒子密度下之平均 )

imposed temperature, Ti (°C)

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

圖 3.42 粒子密度 =10p ⁵ ml^-1時，觀察時間間隔與流體溫度對於溫度估算系統誤差之影響

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

imposed temperature, Ti (°C)

time interval, Δt (s)

= 10⁶ ml^-1,

ρ_p t_{tr= 10 s} unit : °C

圖 3.43 粒子密度 =10p ⁶ ml^-1時，觀察時間間隔與流體溫度對於溫度估算系統誤差之影響 ( 觀察時間t = 10 s ) _tr

30 35 40 45 50 55 60 65 70

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

imposed temperature, Ti (°C)

time interval, Δt (s)

= 10⁷ ml^-1,

ρ_{p ttr= 10 s unit : °C}

圖 3.44 粒子密度 =10p ⁷ ml^-1時，觀察時間間隔與流體溫度對於溫度估算系統誤差之影響 ( 觀察時間t = 10 s ) _tr

30 35 40 45 50 55 60 65 70

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

imposed temperature, Ti (°C)

time interval, Δt (s)

= 10⁸ ml^-1,

ρ_{p ttr= 10 s unit : °C}

圖 3.45 粒子密度 =10p ⁸ ml^-1時，觀察時間間隔與流體溫度對於溫度估算系統誤差之影響 ( 觀察時間t = 10 s )

6

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

imposed temperature, Ti (°C)

time interval, Δt (s)

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

imposed temperature, Ti (°C)

time interval, Δt (s)

= 10⁶ ml^-1,

ρ_p N_f= 50 frames ^{unit : °C}

圖 3.47 粒子密度 =10p ⁶ ml^-1時，觀察時間間隔與流體溫度對於溫度估算系統誤差之影響 ( 影像數量 Nf = 50 frames )

30 35 40 45 50 55 60 65 70

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

imposed temperature, Ti (°C)

time interval, Δt (s)

= 10⁷ ml^-1,

ρ_p N_f= 50 frames _{unit : °C}

圖 3.48 粒子密度 =10p ⁷ ml^-1時，觀察時間間隔與流體溫度對於溫度估算系統誤差之影響

圖 3.48 粒子密度 =10p ⁷ ml^-1時，觀察時間間隔與流體溫度對於溫度估算系統誤差之影響

在文檔中 應用奈米金粒子布朗運動結合粒子追蹤測速之溫度量測參數最佳化 (頁 56-119)