A Study of Factors that Affect Capillarity: a Designed Experiment

DOE Course Project

Team 1: 杨路怡 陆泓宇 陈驰

Introduction

Capillarity is pervasive and widely applied.

Keen academic interest in HEIGHT Actively researched Theoretical Formula Limitations:

Inadequate assumptions Inaccurate in characterizing capillarity Fails to consider a number of significant

factors

gdh

cos4

Purpose of the Study

To identify significant factors that affect capillarity height and their potential interactions

To provide insight for practical application and future study

Design of Experiment

Design of Experiment

A 25 (five factors, two levels, 32 tests) full factorial design

Five Factors: Solution type, tube diameter,

experimental method, moisture, angle of inclination

The response variable: Capillarity Height

Design of Experiment

Factor Low Level (-) High Level (+) Note

Solution type water ethanol drink water, pure ethanol

Tube diameter thin thick thin:0.5mm ; thick: 1mm

Experimental method descending ascending

Moisture dry wet

Inclination angle 45 。 90 。

Conducting the Experiment

Date: 2011/5/14Time:19:00-22:00Equipment ：pipette, capillary tubes, beaker, Dixie cup, ruler, protractor

Analysis and Results

Main Effects

1-1

40

35

30

25

20

1-1 1-1

1-1

40

35

30

25

20

1-1

溶液

平均值

管直径 上升下降

是否浸润 倾斜角

Hei ght（mm） 主效应图数据平均值

Analysis and Results

Interactions

50

30

10

1-1

1-1 1-1

50

30

1050

30

1050

30

10

1-1

50

30

101-1

溶液

管直径

上升下降

是否浸润

倾斜角

-11

溶液

-11

管直径

-11

下降上升

-11

浸润是否

-11

倾斜角

Hei ght（mm） 交互作用图数据平均值

Analysis and Results

Identify significant factors Solution Type (A), Tube Diameter (B),

Experimental Method (C), AC, ABC

1050- 5- 10- 15- 20- 25

99

9590

80706050403020

105

1

效应

百分比

A 溶液B 管直径C 上升下降D 是否浸润E 倾斜角

因子 名称

不显著显著

效应类型

ABC

AC

BA

效应的正态图（响应为 Hei ght（mm），Al pha = . 05)

Lenth 的 PSE = 2. 83125

C

ABC

AC

B

A

9876543210

项

标准化效应

2. 056A 溶液B 管直径C 上升下降

因子 名称

标准化效应的 Pareto 图（响应为 Hei ght（mm），Al pha = . 05)

Analysis and Results

ANOVA table for the reduced modelSource DF Seq SS SS Adj MS F P

Main effects 3 7306.3 7306.3 2435.43 47.80 0.000

2-factor interaction 1 556.1 556.1 556.11 10.92 0.003

3-factor interaction 1 367.2 367.2 367.21 7.21 0.012

Residual 26 1324.7 1324.7 50.95

Lack of fit 2 360.8 360.8 180.38 4.49 0.022

Pure error 24 963.9 963.9 40.16

Total 31 9554.3

Analysis and Results

Residual Check

20100-10-20

99

90

50

10

1

残差

百分比

604530150

20

10

0

-10

拟合值残差

1680-8

10. 0

7. 5

5. 0

2. 5

0. 0

残差

频率

3230282624222018161412108642

20

10

0

-10

观测值顺序

残差

正态概率图 与拟合值

直方图 与顺序

Hei ght（mm） 残差图

Analysis and Results

Effects of solution type

1- 1

40

35

30

25

20

溶液

平均值

Hei ght（mm） 主效应图数据平均值

1- 1

50

45

40

35

30

25

20

15

溶液

平均值

-11

下降上升

Hei ght（mm） 交互作用图数据平均值

溶液

上升下降

1. 00. 50. 0- 0. 5- 1. 0

1. 0

0. 5

0. 0

- 0. 5

- 1. 0

管直径 - 1是否浸润 - 1倾斜角 - 1

保持值

> – – – < 20

20 3030 4040 50

50

Hei ght（mm）

Hei ght（mm） 与 上升下降, 溶液 的等值线图

120

40

60

- 10

0- 11

Hei ght（mm）

上升下降溶液

管直径 - 1是否浸润 - 1倾斜角 - 1

保持值

Hei ght（mm） 与 上升下降, 溶液 的曲面图

Analysis and Results

Effects of the tube diameter The thinner, the higher Height proportional to the reciprocal of

diameter Consistent with the theoretical formula No two-factor interaction

1- 1

40

35

30

25

20

管直径

平均值

Hei ght（mm） 主效应图数据平均值

Analysis and Results

Effects of the experimental method Higher capillarity achieved by

descending method Interaction with the solution type

1- 1

32

31

30

29

28

27

26

25

上升下降

平均值

Hei ght（mm） 主效应图数据平均值

1- 1

50

45

40

35

30

25

20

15

上升下降

平均值

-11

溶液

Hei ght（mm） 交互作用图数据平均值

Analysis and Results

Effects of moisture No significant effect Conjectures of the unexpectedness▪ Difficult to quantify, limited number of tubes,

hair dryer▪ Descending method nullifies the effect▪ Large measurement error

Analysis and Results

Effects of the angle of inclination 90 。 slightly higher than 45 。 Not significant Practical implication:▪ Incline the tube to let more liquid in

Analysis and Results Three-factor

interaction the best scenario is the

combination of water (inorganic solution), thinner tube and descending method.

The worst case occurs with ethanol (organic solution), thicker tube and ascending method.

Cube plot

Best case

Worst case

Analysis and Results

Regression model R-Sq = 86.14% R-Sq （ Prediction ） = 79.00% R-

Sq （ Adjusted ） = 83.47% Indicate model adequacy

Comments Two outliers with thin tubes Futile Rerun with used tubes: large

variability Impurity and water vacuoles Thick tubes more resistant to such

adverse effects

ABCACCBAy 39.317.410.379.908.1143.28ˆ

Conclusion Mains effects of the solution type, tube

diameter and the experimental method Interaction between solution type and the

experimental method Three-factor interaction of solution type,

tube diameter and experimental method No significant effects of moisture and angle Highlight

identify the experimental method as a significant factor and the interaction effects

THANK YOU!

DOE Course ProjectA Study of Factors that Affect Capillarity: a Designed Experiment

Team 1: 杨路怡 陆泓宇 陈驰