A numerical method for two-phase flow in micro channels and its application to droplet control by electrowetting on dielectric

There is considerable ongoing research on multiphase flows in microfluidic systems. This paper presents a numerical procedure for studying two phase flows in microchannels based on the level set method. Incompressible Navier-Stokes equations are used in both the gas and liquid phases. The interface is computed as the zero level set and the level set function is computed using a level set advection equation. The numerical scheme is based on a standard staggered MAC grid for discretization. The spatial discretization is carried out by using a fifth order WENO scheme for the convective terms and a second order discretization for all other terms. The numerical procedure was validated using comparisons with existing numerical studies and with a grid independence study. The numerical simulations are used to study a cross-shaped gas/liquid mixing section which produces monodisperse gas bubbles coflowing with liquids in a micro-channel. The surface tension, liquid flow rates and gas flow rates are varied and their effects on the bubble sizes and frequencies are studied. The numerical results are compared and found to be in good agreement with existing experimental results.

We present a numerical simulation of two-phase flow in a three-dimensional cross-junction microchannel by using the lattice Boltzmann method (LBM). At first, we validated our LBM code with the velocity profile in a 3-dimensional rectangular channel. Then, we developed a lattice Boltzmann code based on the free energy model to simulate the immiscible binary fluid flow. The parallelization of the developed code is implemented on a PC cluster using the MPI program. The numerical results of two-phase flow in the microchannel reveal droplet formation process, which compares well with corresponding experimental results. The size of droplet decreases with increase of the flow-rate ratio and the capillary number. The movement of a droplet through the microchannel induces three-dimensional circulating flow inside the droplet. This complex flow is thought to enhance the mixing and reaction of reagents.

With increasing computer capabilities, numerical modeling of two-phase flows has developed significantly over the last few years. Although there are two main categories, namely 'one' fluid and 'two' fluid methods, the 'one' fluid methods are more commonly used for tracking or capturing the interface between two fluids. Level set (LS), volume-of-fluid (VOF), front tracking, marker-and-cell (MAC) and lattice Boltzmann (LB) methods are all 'one' fluid methods. It is clear that there is no perfect method; each method has advantages and disadvantages which make it more appropriate for one kind of problem than for others. For instance, a LS method will accurately compute the curvature and the normal to the interface, but tends to loss mass which is physically incorrect. On the other hand, a VOF method will conserve mass up to machine precision, but the computation of the curvature and normal to the interface is not as accurate. In order to minimize the disadvantages of these methods, several authors have used two or more methods together to model two-phase flows. This is the case for the CLSVOF (Couple Level Set Volume Of Fluid) method, where LS and VOF are coupled together in order to better capture the interface. In CLSVOF, the level set function is used to compute the interface curvature and normal to the interface, while the volume of fluid function is used to capture the interface. For two-phase flows in microchannels, surface tension forces play an important role in determining the dynamics of bubbles whereas gravitational forces are generally negligible. Also it is very important to consider the interaction between the boundaries and the fluids by prescribing or computing the correct contact angle between them. The commercial CFD code FLUENT allows the use of static constant angles, or the use of User Defined Functions (UDF) to compute the dynamic contact angles. It is inappropriate to use a static contact angle to model cases involving moving contact lines. For such cases a dynamic contact angle scheme should be implemented. In this study, FLUENT was used to model adiabatic and diabatic, time dependent two-phase flows. Since FLUENT already contains a VOF method, a LS method was implemented and coupled with VOF into FLUENT via UDFs. Furthermore, since the LS function, used to compute the surface tension force, ceases to be a signed distance to the interface even after one time step, a re-initialization equation was solved after each time step. This involved using a fifth order WENO (Weighted Essentially Non Oscillatory) scheme to discretize the space derivatives (otherwise oscillations of the interface occurred), and a first order Euler method for the time integration. In another part of the study, a 3D dynamic contact angle model based on volume fraction, interface reconstruction, and experimentally available advancing and receding static contact angles was also developed and implemented into FLUENT via UDFs. Several validations for the developed CLSVOF method and dynamic contact angle model are presented in this thesis, these includes a static bubble, a bubble rising in a stagnant liquid for Morton numbers ranging from 102 to 10-11, droplet deformation due to a vortex flow field, droplets spreading over a wall under the gravity effect and droplets sliding over a wall due to gravity. These validations demonstrated the high accuracy and the stability of our methods for modeling these phenomena. A heat and mass transfer model was also implemented into the commercial CFD code FLUENT for simulating of boiling (and condensation) heat transfer. Several simulations were presented with water and R134a as working fluids. The influence of the contact angle and the wall superheat was also studied.

Even though numerical simulation of two-phase flows in microchannels has been attempted by many investigators, most efforts seem to have failed in correctly capturing the flow physics, especially the slug-flow regime characteristics. The presence of a thin liquid film in the order of 10 μm around the bubble (sometimes called gas pocket or gas slug) may be a contributing factor to the above difficulty. Typically, liquid films have a significant effect on the flow field. Thus, there is a strong motivation to employ numerical simulation methods to avoid some of the experimental difficulties. In this paper, the characteristics of two-phase slug flows in microchannels are calculated with the help of the volume-of-fluid (VOF) method. Formation of the slugs for different superficial velocities, capillary numbers, and gas volume fractions are investigated. The minimum mesh resolution required to capture the liquid film surrounding the gas bubble is reported employing a dynamic mesh adaptation methodology with interface tracking. Results are shown to be in good agreement with experimental data and empirical correlations.

A numerical investigation is carried out to study hydrodynamic behavior and thermal performance of slug flow in serpentine microchannel with different curvature ratio and wall properties. By using coupled Level Set and Volume of Fluid (CLSVOF) method implemented in Fluent, gas-liquid interface shows good consistency with experimental results especially for slug flow. Distribution of sectional velocity profile in curved microchannel with various curvature ratios was investigated. On the basis of fluid flow in microchannel with non-slip boundary condition, by means of user defined function (UDF), influence of slip velocity on hydrodynamic characteristics was performed numerically. For a better prediction on thermal performance, further analysis of combined effect of wall properties and curvature ratio on fluid flow characteristics was also conducted. As a consequence, the increasing slip velocity on channel wall can reduce hydraulic resistance. Both the contact angle and the curvature ratio have an appreciable influence on thermal performance of gas-liquid two-phase flow in serpentine microchannel.

This paper details the first reported integration of two advanced digital microfluidic technologies where 100 µm silicon cubes are transported with ElectroWetting On Dielectric (EWOD) and the droplet then held with EWOD while the silicon cubes are mixed with another liquid using a Surface Acoustic Wave (SAW). Together these two technologies provide a comprehensive lab-on-a-chip combination with well developed functionalities. These include droplet generation, splitting and transportation offered by EWOD with transportation, mixing and biosensing being potentially available with SAW. The fabrication of both EWOD and SAW structures on LiNbO 3 substrates used low temperature Ta/Ta 2 O 5 /CYTOP layer deposition and patterning technologies, which enabled efficient transportation and mixing functions to be demonstrated.

In this paper, we propose a microscale liquid oscillator using electrowetting-on-dielectric (EWOD). Specifically, a mesoscale liquid bridge (LB) between two horizontal surfaces with EWOD is considered. When EWOD is applied, the solid surface becomes more hydrophilic, and hence the contact angle (CA) is reduced. Following the activation of EWOD, the LB can remain connected or it can break into either symmetric or asymmetric shapes depending on the initial liquid volume and wettability of the two surfaces. The LB dynamics activated by EWOD is studied using the multibody dissipative particle dynamics (MDPD) method. Our numerical results show that the behavior of an LB under EWOD can be interpreted via three modes. In the first mode, the LB does not break after applying EWOD. In the second mode, the LB breaks and does not reform. The third mode happens when, depending on the interplay of the volume of the liquid and CA manipulation, the LB continuously breaks, recoils, and reforms. For asymmetric cases, it was observed that the LB may completely detach from one surface and may not reform. It was also observed that decreasing the wettability of a surface, for cases with a continuous breaking and reformation behavior, increases the connecting time interval and decreases the breaking time interval in one break-reform cycle. The results provided in this investigation facilitate fundamental understanding of LB dynamics and their application for the design of microscale liquid oscillators using EWOD.

In recent years, micro-technologies have become very important to cutting edge industries such as aerospace and biotechnology. In the fluidic research area, two-phase flow study in microchannels has been an emerging topic in the past few years. Characteristics of two-phase flow in microchannels such as flow regimes, pressure drop, void fraction, and heat transfer are now being extensively studied by numerous groups. The ultimate goal of this research ranges from compact heat exchangers to small-sized refrigeration systems. One of the major drawbacks in this area to date is the lack of a universal flow regime map enabling the prediction of flow regimes in microchannels. In the present study, a new test rig was designed and constructed to extend the range of the existing data on flow regimes. Several flow regime maps, for a hydraulic diameter of less than 1.0 mm obtained from a comprehensive literature review, are tested and compared. A total of approximately 1475 experimental data points from present and previous studies performed in channels with Dh ≤ 1.0 mm were used for comparison. Two universal flow regime maps were created, one each for horizontal and vertical channels with a hydraulic diameter ranging between 0.1 mm and 1.0 mm. The resulting universal maps presented here are based on flow regimes observed in all the studies on two-phase flow in microchannels. We suggest that the use of these flow regimes could help diminish the amount of discord present among research groups pertaining to the definition of flow regimes. Based on the comparisons between the universal maps and different experimental flow regime maps, appropriate conclusions on the effects of channel orientation and geometry are suggested.

The effects of gas-liquid inlet geometry and mixing method on adiabatic gas-liquid two-phase flow in a microchannel of 100 μm diameter have been investigated using a T-junction inlet with the same internal diameter as the microchannel. Two-phase flow patterns, void fraction, and friction pressure drop data obtained with the T-junction inlet were found to be significantly different from those obtained previously with a reducer inlet. For the T-junction inlet, the two-phase flow patterns in the microchannel were predominantly intermittent flows with short gas and liquid plugs/slugs flowing with nearly equal velocities. The void fraction data then conformed nearly to that of a homogeneous flow model, and the two-phase friction multiplier data could be described by the Lockhart–Martinelli correlation applicable to larger channels. However, when a reducer inlet was used previously and the diameter of the inlet section was much larger than that of the microchannel, an intermittent flow of long gas slugs separated by long liquid slugs became prevalent and the void fraction decreased to values far below the homogeneous void fraction. The differences in the two-phase flow characteristics between a T-junction inlet and reducer inlet were attributed to the differences in the gas bubble/slug generation mechanisms.

The present lecture summarizes some of the most recent joint research results from the cooperation between the Federal University of Rio de Janeiro, Brasil, and the University of Miami, USA, on the transient analysis of both fluid flow and heat transfer within microchannels. This collaborative link is a natural extension of a long term cooperation between the two groups, in the context of fundamental work on transient forced convection, aimed at the development of hybrid numerical-analytical techniques and the experimental validation of proposed models and methodologies [19]. The motivation of this new phase of the cooperation was thus to extend the previously developed hybrid tools to handle both transient flow and transient convection problems in microchannels within the slip flow regime. The analysis of internal flows in the slip-flow regime recently gained an important role in association with the fluid mechanics of various microelectromechanical systems (MEMS) applications, as well as in the thermal control of microelectronics, as reviewed in different sources [10-16]. For steady-state incompressible fully developed flow situations and laminar regime within simple geometries such as circular microtubes and parallel-plate microchannels, explicit expressions for the velocity field in terms of the Knudsen number are readily obtainable, and have been widely employed in the heat transfer analysis of microsystems, such as in [17-23]. Only quite recently, attention has been directed to the analysis of transient flow in microchannels [24-33]. Unsteady one-dimensional models have been extended from classical works, and analytical solutions have been sought for fully developed flows in simple geometries. These recent works are also concerned with situations in which a simple and well-defined functional form for the pressure gradient time variation is prescribed or for the time dependence of the wall imposed velocity, in the case of a Couette flow application. Research findings are yet to be further pursued in the analytical and robust solution of more generalized models, which will accommodate more general conditions and parameter specifications, and thus offer a wider validation range for the automatic general purpose numerical codes. Mikhailov and Ozisik [34] presented a unified solution for transient one-dimensional laminar flow models, with the usual no-slip boundary condition, based on the classical integral transform method. Their solution was then specialized to two situations: step change and periodically varying pressure gradient. The knowledge in regular size channels is therefore fairly well consolidated for models that use simple functional forms for the pressure gradient variation such as for the two cases cited above. One of the objectives of this paper is to illustrate the solution of a onedimensional mathematical model for transient laminar incompressible flow in microchannels such as circular tubes and parallel-plate channels, that accounts for a source term time variation in any functional form, including electrokinetic effects for liquid flows, by making use of the Generalized Integral Transform Technique (GITT) [35-40], and thus yielding analytical expressions for the time and space dependence of the velocity fields in the fully developed region. We then demonstrate this hybrid numerical-analytical solution for transient internal slip flow, obtained employing mixed symbolic-numerical computations with the Mathematica platform [41]. The goal here is to improve and complement existing analytical solution implementations to study laminar fully developed flows in micro-ducts subjected to arbitrary source term disturbances in space and time. On the other hand, the heat transfer literature of the last decade has demonstrated a vivid and growing interest in thermal analysis of flows in micro-channels, both through experimental and analytical approaches, in connection with cooling techniques of micro-electronics and with the development of micro-electromechanical sensors and actuators (MEMS), as also pointed out in recent reviews [12-16]. Since the available analytical information on heat transfer in ducts could not be directly extended to flows within microchannels with wall slip, a number of contributions have been recently directed towards the analysis of internal forced convection in the micro-scale. In the paper by Barron et al.

With respect to the importance of a multiphase flow behaviour in a microchannel, this study is focused on developing a numerical modelling of two-phase flows using lattice Boltzmann method (LBM). This method utilizes a different vision for surveying the behaviour of fluids. The LBM be able to capture fluid motion via a microscopic vision in contrary to classical CFD methods (Navier–Stokes approach). Based on this capability, the LBM is a powerful method for solving complex problems in multiphase and multicomponent fluid dynamics problems. This research attempts to employ the chromo-dynamic model, which is compatible for high-density ratio flow in a microchannel and introduces different approaches to achieve this objective. This study examined both Huang and Lishchuk methods and the obtained results show a sharp interface between two phases by using Haung model. However, utilization of this method can impose some difficulties on stability of calculation. The research tries to eliminate or at least weaken numerical errors caused by density contrast in the interface of different phases from the exertion of an artificial force. A numerical modelling approach comprises an accurate treatment of the surface tension between phases and a passive-scalar heat transfer method. This research used a high-performance simulation to obtain real-time flow visualizations. The proposed method is applied to a new geometry with variable cross section. A correlation introduced between this geometry and dimensionless numbers (Bejan number, Laplace number, Reynolds number). This new correlation defines an operational criterion for a step-contracted microchannel and enables us to capture the delay time between fluctuations. The results are compared to available exact solutions for high-density ratio flow in a microchannel.

Active surface tension driven micropump using droplet/meniscus pressure gradient

Motivated by systematic CO2 evaporation experiments which recently became available (J. Pettersen, “Flow vaporization of CO2 in microchannel tubes,” Doctor technicae thesis, Norwegian University of Science and Technology, 2002), the present work constitutes an exploratory investigation of isothermal flow of CO2 near its liquid–vapor critical point through a long 5 μm diameter microchannel. A modified van der Waals constitutive model—with properties closely approximating those of “real” near-critical CO2—is incorporated in a two-dimensional lattice Boltzmann hydrodynamics model by embedding a dimensionless parameter X, with X→1 denoting the “real” fluid. The hydrodynamic phenomena resulting by imposing a constant pressure gradient along a periodic channel are investigated by considering two regimes in tandem: (1) transition from bubbly to annular flow with a liquid film formed at the channel walls and (2) destabilization of the liquid film by the Kelvin–Helmholtz instability. Due to numerical constraints, intrinsic modeling errors are introduced and are shown to be associated with discrepancies in the relative vapor–liquid interfacial thickness, which is expressed by X. The effects of these errors are investigated both theoretically and numerically in the physical limit X→1. Numerically determined flow patterns compare qualitatively well with direct visualization results obtained by Pettersen. Overall, the characteristics of isothermal near-critical two-phase flow in microchannels can be reproduced by the appropriate modification of the thermophysical properties of CO2.

Numerical Investigation of Heat Transfer Enhancement due to Two-Phase Flow in Microchannel

Slug flow is the representative flow regime of two-phase flow in micro channels. It is well known that the thin liquid film formed around the confined vapor bubble plays an important role in micro channel heat transfer. In the present study, experiments are carried out to clarify the effects of parameters that affect the formation of the thin liquid film in micro channel slug flow. Laser focus displacement meter is used to measure the thickness of the thin liquid film. Air, ethanol, water and FC-40 are used as working fluids. Circular tubes with five different diameters, D = 0.3, 0.5, 0.7, 1.0, 1.3 mm, and square channels with two different sizes, 0.3 × 0.3 and 0.5 × 0.5 mm, are used. It is confirmed that the liquid film thickness is determined only by capillary number at small capillary numbers. However, the effect of inertial force and flow acceleration cannot be neglected as capillary number increases. The effect of cross sectional shape is also investigated. Experimental correlation for the adiabatic liquid film thickness in circular tubes based on capillary number, Reynolds number and Weber number is proposed. When viscous boundary layer is thin, liquid film thickness is limited by the viscous boundary layer thickness. Thus, in order to develop precise flow boiling models in micro tubes, it is important to consider the effects of inertial force and boundary layer thickness on the liquid film thickness.