臺灣博碩士論文加值系統

本文利用分子動力模擬的方法針對不同的參數，探討真空環境下單顆液滴撞擊固體面上薄膜的行為及影響。影響液滴撞擊行為的參數主要分為液滴撞擊速度、液滴尺寸、薄膜厚度及材質(本文採用氦、氬、氙三種材質)。主要的結果利用可視化程式呈現在內容中。當撞擊速度大時，液滴在表面上會有飛濺的現象，而撞擊速度小的時候，液滴趨於圓球的形狀。不同的薄膜厚度對於液滴的後期發展有較大的影響。在不同的液滴尺寸中，較大的液滴可以快速的攤開達到欲噴灑的表面，但也伴隨著較高的王冠狀液滴發生。所以建議採用較小的液滴，可以得到較平滑的面。在模擬系統中主要採許同樣的溫度及密度，但由於三種惰性氣體在同樣溫度、密度下不是所期望的狀態，由結果可知氦在撞擊過程中已經趨於氣體的狀態，然而氙已經趨於固體狀態，故內容討論主要針對氬作液滴行為上的討論。

摘要 I
Contents II
List of Tables VI
List of Figuers VII
Chapter 1 Introduction 1
1.1 Motivation 1
1.1.1 Droplet collision dynamics 1
1.1.2 Continuum scale 1
1.1.3 Atomic scale 2
1.2 Background 3
1.2.1 Droplet-solid collision 3
1.2.1.1Droplet stick 3
1.2.1.2 Droplet bounce 3
1.2.1.3 Droplet spread (absorption) 3
1.2.1.4 Droplet splash 4
1.2.2 Governing parameters 4
1.2.2.1 Weber number ( ) 4
1.2.2.2 Non-dimensional film thickness ( ) 5
1.3 Literature review 5
1.4 Objectives 7
Chapter 2 Numerical method 8
2.1 Basic molecular dynamics 8
2.2 Equation of motion 9
2.3 Interaction potentials 11
2.3.1 Lennard-Jones potential 12
2.4 Force computations 13
2.4.1 All pairs 13
2.4.2 Cell subdivision 14
2.4.3 Neighbor lists 15
2.4.4 Neighbor list + link-cell 16
2.5 Boundary conditions 16
2.5.1 Periodic boundary conditions 16
2.5.2 Wall boundary conditions 16
2.6 Parallel molecular dynamics method 18
2.6.1 Atomic–decomposition algorithm 18
2.6.2 Force–decomposition algorithm 19
2.6.3 Spatial–decomposition algorithm 19
2.6.4 PCMD (Parallel Cellular Molecular Dynamics) algorithm 20
Chapter 3 Results and discussion 23
3.1 Simulation model 23
3.1.1 The substrate 23
3.1.2 The droplet 24
3.2 The effect factors 24
3.2.1 Impact velocity 24
3.2.1.2 Results 25
3.2.2 The film thickness 25
3.2.2.2 Results 26
3.2.3 The droplet size 26
3.2.3.2 Results 27
3.2.4 The atom species 27
3.2.4.2 Results 27
Chapter 4 Conclusions 28
Chapter 5 Recommendations of future work 30
References 31
Tables 35
Figures 36



































List of Tables
Table 2.1 System of units used in soft-sphere molecular dynamics programs 35
Table 2.2 The physical parameters of helium, argon and xenon in Lennard-Jones potential 35

























List of Figuers
Fig.1.1 The various impingement of regions identified in the spray-film interaction model 36
Figure 2.1 Molecular Dynamics flow chart 37
Figure 2.2 The Lennard-Jones pair potential and pair force for argon, helium and xenon.The units here are and 38
Figure 2.3 The different approaches to computing interactions: all pairs, cell subdivision, and neighbor lists 38
Figure 2.4 The neighbor lists method 39
Figure 2.5 The neighbor list + link-cell method 39
Figure 3.1 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =7 for 4 film thickness. Time increment: 1 time step 41
Figure 3.2 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =7 for 4 film thickness. Time increment: 1 time step 41
Figure 3.3 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =7 for 4 film thickness. Time increment: 1 time step 42
Figure 3.4 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =11 for 4 film thickness. Time increment: 1 time step 42
Figure 3.5 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =11 for 4 film thickness. Time increment: 1 time step 43
Figure 3.6 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =11 for 4 film thickness. Time increment: 1 time step 43
Figure 3.7 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =14.5 for 4 film thickness. Time increment: 1 time step 44
Figure 3.8 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =14.5 for 4 film thickness. Time increment: 1 time step 44
Figure 3.9 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =14.5 for 4 film thickness. Time increment: 1 time step 45
Figure 3.10 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =7 for 4 film thickness. Time increment: 1 time step 45
Figure 3.11 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =7 for 4 film thickness. Time increment: 1 time step 46
Figure 3.12 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =7 for 4 film thickness. Time increment: 1 time step 46
Figure 3.13 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =11 for 4 film thickness. Time increment: 1 time step 47
Figure 3.14 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =11 for 4 film thickness. Time increment: 1 time step 47
Figure 3.15 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =11 for 4 film thickness. Time increment: 1 time step 48
Figure 3.16 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =14.5 for 4 film thickness. Time increment: 1 time step 48
Figure 3.17 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =14.5 for 4 film thickness. Time increment: 1 time step 49
Figure 3.18 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =14.5 for 4 film thickness. Time increment: 1 time step 49
Figure 3.19 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =7 for 4 film thickness. Time increment: 1 time step 50
Figure 3.20 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =7 for 4 film thickness. Time increment: 1 time step 50
Figure 3.21 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =7 for 4 film thickness. Time increment: 1 time step 51
Figure 3.22 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =11 for 4 film thickness. Time increment: 1 time step 51
Figure 3.23 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =11 for 4 film thickness. Time increment: 1 time step 52
Figure 3.24 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =11 for 4 film thickness. Time increment: 1 time step 52
Figure 3.25 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =14.5 for 4 film thickness. Time increment: 1 time step 53
Figure 3.26 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =14.5 for 4 film thickness. Time increment: 1 time step 53
Figure 3.27 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =14.5 for 4 film thickness. Time increment: 1 time step 54
Figure 3.28 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =7 for 8 film thickness. Time increment: 1 time step 54
Figure 3.29 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =7 for 8 film thickness. Time increment: 1 time step 55
Figure 3.30 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =7 for 8 film thickness. Time increment: 1 time step 55
Figure 3.31 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =11 for 8 film thickness. Time increment: 1 time step 56
Figure 3.32 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =11 for 8 film thickness. Time increment: 1 time step 56
Figure 3.33 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =11 for 8 film thickness. Time increment: 1 time step 57
Figure 3.34 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =14.5 for 8 film thickness. Time increment: 1 time step 57
Figure 3.35 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =14.5 for 8 film thickness. Time increment: 1 time step 58
Figure 3.36 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =14.5 for 8 film thickness. Time increment: 1 time step 58
Figure 3.37 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =7 for 8 film thickness. Time increment: 1 time step 59
Figure 3.38 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =7 for 8 film thickness. Time increment: 1 time step 59
Figure 3.39 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =7 for 8 film thickness. Time increment: 1 time step 60
Figure 3.40 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =11 for 8 film thickness. Time increment: 1 time step 60
Figure 3.41 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =11 for 8 film thickness. Time increment: 1 time step 61
Figure 3.42 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =11 for 8 film thickness. Time increment: 1 time step 61
Figure 3.43 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =14.5 for 8 film thickness. Time increment: 1 time step 62
Figure 3.44 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =14.5 for 8 film thickness. Time increment: 1 time step 62
Figure 3.45 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =14.5 for 8 film thickness. Time increment: 1 time step 63
Figure 3.46 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =7 for 8 film thickness. Time increment: 1 time step 63
Figure 3.47 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =7 for 8 film thickness. Time increment: 1 time step 64
Figure 3.48 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =7 for 8 film thickness. Time increment: 1 time step 64
Figure 3.49 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =11 for 8 film thickness. Time increment: 1 time step 65
Figure 3.50 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =11 for 8 film thickness. Time increment: 1 time step 65
Figure 3.51 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =11 for 8 film thickness. Time increment: 1 time step 66
Figure 3.52 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =14.5 for 8 film thickness. Time increment: 1 time step 66
Figure 3.53 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =14.5 for 8 film thickness. Time increment: 1 time step 67
Figure 3.54 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =14.5 for 8 film thickness. Time increment: 1 time step 67
Figure 3.55 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =7 for 16 film thickness. Time increment: 1 time step 68
Figure 3.56 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =7 for 16 film thickness. Time increment: 1 time step 68
Figure 3.57 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =7 for 16 film thickness. Time increment: 1 time step 69
Figure 3.58 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =11 for 16 film thickness. Time increment: 1 time step 69
Figure 3.59 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =11 for 16 film thickness. Time increment: 1 time step 70
Figure 3.60 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =11 for 16 film thickness. Time increment: 1 time step 70
Figure 3.61 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =14.5 for 16 film thickness. Time increment: 1 time step 71
Figure 3.62 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =14.5 for 16 film thickness. Time increment: 1 time step 71
Figure 3.63 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =14.5 for 16 film thickness. Time increment: 1 time step 72
Figure 3.64 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =7 for 16 film thickness. Time increment: 1 time step 72
Figure 3.65 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =7 for 16 film thickness. Time increment: 1 time step 73
Figure 3.66 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =7 for 16 film thickness. Time increment: 1 time step 73
Figure 3.67 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =11 for 16 film thickness. Time increment: 1 time step 74
Figure 3.68 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =11 for 16 film thickness. Time increment: 1 time step 74
Figure 3.69 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =11 for 16 film thickness. Time increment: 1 time step 75
Figure 3.70 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =14.5 for 16 film thickness. Time increment: 1 time step 75
Figure 3.71 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =14.5 for 16 film thickness. Time increment: 1 time step 76
Figure 3.72 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =14.5 for 16 film thickness. Time increment: 1 time step 76
Figure 3.73 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =7 for 16 film thickness. Time increment: 1 time step 77
Figure 3.74 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =7 for 16 film thickness. Time increment: 1 time step 77
Figure 3.75 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =7 for 16 film thickness. Time increment: 1 time step 78
Figure 3.76 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =11 for 16 film thickness. Time increment: 1 time step 78
Figure 3.77 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =11 for 16 film thickness. Time increment: 1 time step 79
Figure 3.78 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =11 for 16 film thickness. Time increment: 1 time step 79
Figure 3.79 The evolution of the droplet impinging on the liquid film with the velocity 2000m/s, droplet radius =14.5 for 16 film thickness. Time increment: 1 time step 80
Figure 3.80 The evolution of the droplet impinging on the liquid film with the velocity 1000m/s, droplet radius =14.5 for 16 film thickness. Time increment: 1 time step 80
Figure 3.81 The evolution of the droplet impinging on the liquid film with the velocity 500m/s, droplet radius =14.5 for 16 film thickness. Time increment: 1 time step 81
Figure 3.82 Comparison of non-dimensional deformation radius and height of droplet with different impact velocity (a) 500m/s (b) 1000m/s (c) 2000m/s ( film thickness=8 and droplet size=11 ) 81
Figure 3.83 Comparison of non-dimensional deformation radius and height of droplet with different film thickness (a) 4 (b) 8 (c) 16 ( droplet size=11 and impact velocity=1000m/s ) 82
Figure 3.84 Comparison of non-dimensional deformation radius and height of droplet with different droplet size (a) 7 (b) 11 (c) 14.5 ( film thickness=8 and impact velocity=1000m/s ) 82

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