兩道可混合液體的並排層流（也稱為水平分層流）是微流體中最常見的兩相流動狀態之一。 此流態在廣泛的應用中提供了獨特的幫助，但它也給這些系統帶來了新的複雜性，而這些系統還沒有被很好地理解。 正確理解這種流態的質傳(物質濃度不均勻而發生的質量轉移過程)和流體動力學是設計高效微流體裝置的先決條件。

在此，使用分析、數值和實驗方法對水平分層流態 (HSFR) 中的側向流動進行了深入研究。 首先，研究了改變模式的橫向流動的根本原因。根據觀察，HSFR 比以前假設的要復雜得多。發現了一系列相互關聯的參數，可以解釋觀察到的側向流動。這一系列參數源於擴散率、質量密度和重力的同時影響。研究結果表明，忽略現象鏈中任何一個環節的簡化將無法預測這些因素的綜合影響。

論文持續研究該參數鏈的動態及其對流動模式的影響。目標是量化各種幾何因素（如比例、高度和連接配置）以及操作參數（如速度、初始密度和濃度）對側向流動的影響，反之亦然。結果表明在佩克萊特數=1000的條件下，觀察到高達 15 度的旋轉，這遠高於該領域目前的常見做法。 顯示需要考慮這些因素才能準確預測界面處的擴散現象。

最後以實驗結果，我提出了一個經驗數學模型，由 Grashof 和 Reynolds 數組成。 依據作者所知，該模型能夠預測任何牛頓流體的界面旋轉角度和矩形通道中的任何點，以及該流態下的任何操作條件。

令人驚訝的是，儘管水平分層流態在微流體中很普遍，但人們對這種流動模式的傳質和流體動力學缺乏了解。深入了解這些現象，並確定緩解這些現象的方法，對於提高包含混溶液體界面的微流體裝置的性能至關重要。目前的調查將為未來的研究打開大門，以準確估計其微流體設備中的流體行為。

Side-by-side laminar flow (also known as horizontally stratified flows) of two-miscible liquids is one of the most common two-phase flow regimes in microfluidics. While this flow regime presents unique opportunities in a wide range of applications, it also introduces new complexity into these systems which is not well understood. Proper understanding of the mass transfer and hydrodynamics of this flow regime is a prerequisite to designing efficient microfluidic devices.

Herein, lateral flow in horizontally stratified flow regime (HSFR) is thoroughly studied using analytical, numerical and experimental methods. First, the underlying reason for pattern-altering lateral flow is investigated. It is observed that HSFR is much more complicated than previously assumed. A chain of interlinked parameters is found that can explain the observed lateral flow. This chain of parameters arises from the simultaneous effects of diffusivity, mass density and gravitational forces. The findings indicate that simplifications that ignore any one of the links in the phenomena chain will not be able to predict the combined effect of these factors.

The dissertation then proceeds to investigate the dynamics of this chain of parameters and the implications on the flow pattern. The goal is to quantify the effects of various geometrical factors such as scale, height, and junction configuration, as well as operational parameters such as velocity and initial density and concentration on the lateral flow and vice-versa. The results reveal that rotations as high as 15 degrees were observed at Péclet numbers of the order 1000, which is much higher than current common practice in the field. This suggests that these factors need to be considered in order to accurately predict the phenomena of diffusion at the interface.

Finally, based on experimental results, I propose an empirical mathematical model, composed of Grashof and Reynolds numbers. To the best of the author's knowledge, the model is capable of predicting the angle of rotation of the interface and any point in rectangular channels for any Newtonian fluids and any operating conditions in this flow regime.

It is surprising that despite its prevalence in microfluidics, there is a lack of understanding of the mass transfer and hydrodynamics of this flow pattern. Gaining insight into these phenomena, as well as identifying ways to mitigate it, is crucial for enhancing the performance of microfluidic devices that incorporate interfaces of miscible liquids. The current investigation will open the door for future studies to have an accurate estimation of the fluid behavior in their microfluidic devices.

Contents
Abstract (Chinese) I
Abstract II
Contents IV
List of Figures VII
List of Tables X
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Scope of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Literature Review 6
2.1 Two-Phase Liquid-Liquid Flows in Microfluidics . . . . . . . . . . . 6
2.1.1 Annular Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2 Segmented Flow (Also Known as Plug/Slug Flow) . . . . . . 8
2.1.3 Dispersed Flow (Also Known as Droplets) . . . . . . . . . . 9
2.1.4 Stratified Flow (Also Known as Parallel Flow) . . . . . . . . 9
2.2 Examples of Difficulties in Two-Phase Devices . . . . . . . . . . . . 11
2.3 Interface Dynamics in Liquid-Liquid Microfluidics . . . . . . . . . . 14
IV
3 Materials and Methods 19
3.1 Hydrodynamics Principles . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Experimental Setup and Methods . . . . . . . . . . . . . . . . . . . 20
3.2.1 Microfluidic device fabrication . . . . . . . . . . . . . . . . . 20
3.2.2 Fluorescent Confocal Microscopy . . . . . . . . . . . . . . . 21
3.2.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.4 Materials and chemicals . . . . . . . . . . . . . . . . . . . . 25
3.2.5 Experimental Procedure . . . . . . . . . . . . . . . . . . . . 26
3.2.6 Accepted Error Margins . . . . . . . . . . . . . . . . . . . . 29
3.2.7 Post-Processing of the Data . . . . . . . . . . . . . . . . . . 30
3.3 Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . 34
3.3.2 Density, Viscosity and Diffusivity . . . . . . . . . . . . . . . 36
3.3.3 Implementation of the Model . . . . . . . . . . . . . . . . . 38
4 Results 41
4.1 Evidence of Lateral Flow in Equal Density Binary Systems . . . . . 41
4.1.1 Velocity and Evolution of the interface along the Channel . . 41
4.1.2 Effects of Initial Concentration/Density . . . . . . . . . . . . 43
4.1.3 Validation of the Numerical Model . . . . . . . . . . . . . . 45
4.1.4 Underlying Chain of Phenomena . . . . . . . . . . . . . . . 48
4.1.5 The Full Picture of Rotation Angle Profile . . . . . . . . . . 50
4.2 Empirical Model for Orientation of the Interface . . . . . . . . . . . 50
4.2.1 Empirical Model for the Angle of Rotation for Square Cross-
Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2.2 Application to Flows of Unequal Densities . . . . . . . . . . 54
4.2.3 Generalization of the Model to All Aspect Ratios . . . . . . 58
V
4.2.4 Using the Model to Maintain a Vertical Interface . . . . . . 59
4.3 Effects of Inlet Junction . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3.1 Microfluidic Device Inlet Junctions . . . . . . . . . . . . . . 60
4.3.2 Mesh and Geometry of Various Device Types . . . . . . . . 62
4.3.3 Validation for Various Geometries . . . . . . . . . . . . . . . 64
4.3.4 Effects of Geometry on Interface Rotation for Various Inlet
Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.5 Shape of Interface for Various Inlet Geometries . . . . . . . 67
4.3.6 Streamlines at Various Junctions . . . . . . . . . . . . . . . 69
4.3.7 Proposed Lateral Flow Resistant Junction . . . . . . . . . . 70
4.4 Mixing Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.4.1 Increased Mixing Due to Transversal Flow . . . . . . . . . . 71
4.4.2 Interdiffusion zone . . . . . . . . . . . . . . . . . . . . . . . 72
4.4.3 Effect of Aspect Ratio of the Channel . . . . . . . . . . . . . 74
4.4.4 Effects of Initial Concentration . . . . . . . . . . . . . . . . 76
4.4.5 Effects of Velocity . . . . . . . . . . . . . . . . . . . . . . . . 78
5 Discussion and Conclusions 81
5.1 Future Research Directions . . . . . . . . . . . . . . . . . . . . . . . 83
5.1.1 Generalization of the Model to Non-Newtonian Solutions . . 83
5.1.2 Using the Findings to Improve Microfluidics . . . . . . . . . 85
5.1.3 Study the Effects of Asymmetric Channel/inlet Shapes . . . 87
Bibliography 89

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