Liquid-liquid Taylor Flow Research Articles

Liquid-liquid Taylor flow heat transfer: Correlations for predicting Nusselt number and pressure drop based on four independent variables

The numerical simulation of heat transfer in Taylor flows involving water-light mineral oil, water-hexadecane, and water-dodecane configurations was conducted, considering water as the primary phase in three scenarios and oils as the primary phases in three others. Additionally, an investigation into heat transfer in Water-AR20 silicon oil with water as the primary phase was undertaken. In each Taylor flow scenario, two correlations were presented for predicting the thermally developed Nusselt number and pressure drop per unit length, obviating the necessity for experimental observation or numerical simulation. In cases where water served as the secondary phase, fully developed Nusselt number of the two-phase flow increased as the dimensionless effective diameter of the water droplets increased. Anomalously, when water was the primary phase, an optimal dimensionless effective diameter, equivalent to 1 for the secondary phase droplets, resulted in maximum Nusselt. The findings indicated that utilizing water as the primary phase leads to superior heat transfer capacity compared to employing oils as the primary phase. Furthermore, it was deduced that, under the condition where the effective diameter of the secondary oil droplets is set at 1 and three other variables are the same, alterations in oil type yields negligible variations in the Nusselt number. The findings of this paper can be a guide in applying liquid–liquid Taylor flow as a coolant in microchannel heatsinks.

A Comparative Study of Two Numerical Methods Applied for 3D Liquid-Liquid Taylor Flow in a Microchannel

The laminar nature of flow in mini and microchannels has pushed researchers to develop novel solutions to overcome reaction rate reduction and heat/mass transfer issues. In this regard, Taylor flow is one of the possible solutions that could be used to enhance mixing inside mini and microchannels with reasonable pressure drop. The hydrodynamics of Taylor liquid-liquid flow is numerically studied in this work by employing two different droplet generation methods, specifically T-junction and patching methods. To this end, a three-dimensional model of rectangular microchannel flow is considered. The computational domain was designed and meshed by ICEM CFD and then simulated with commercial software ANSYS Fluent. The interface between the two phases was captured using the Volume of Fluid (VOF) method. The generating and development process of water droplets dispersed in an ethylene/propylene glycol carrier phase for both methods is discussed in detail. According to the results, both methods show satisfactory performance regarding liquid film and droplet shape, with only a slight difference. However, the patching method was found to be more economical in terms of computational time. This study would improve the state of knowledge on two-phase flow simulation in microchannels and thus contribute to the understanding of Taylor flow hydrodynamics.

Effects of flow characteristics on the heat transfer mechanism in Taylor flow

The capability of Taylor slugs to enhance heat transfer rate compared to that obtained from single-phase flow is well-documented. This study numerically investigated the hydrodynamics characteristics and heat transfer mechanism in liquid-liquid Taylor flow. A novel analysis method was introduced by comparing fluid flow and heat transfer parameters distributed at the axial and radial planes of the channel. In order to investigate transport phenomena, the unit cell length and frequency of slug generation over a wide range of phase superficial velocity ratio were examined. The simulations showed that the viscosity difference between the phases is a critical parameter of the slug frequency; a higher amount increases the frequency much greater. Conversely, a lower viscosity difference between the phases allows water slugs to expand axially more. The higher temperature gradient and a stronger recirculation in the shorter liquid plug region enhance the heat transfer rate leading to the highest cooling performance over the channel wall within a unit cell. The results also showed the significant importance of establishing shorter slugs, which improves the cooling performance in the slugs and enhances the heat transfer rate in the liquid slug region due to the greater radial flow mixing. The developed numerical model was verified by the results found in the literature showing good agreement.

Experimentally investigating the pressure drop of liquid-liquid Taylor flows over varying viscosity ratios

Micro-capillary liquid-liquid Taylor flows have emerged as a promising new platform for achieving higher heat and mass transfer compared to single-phase flows. In any application benefiting from such flows, pressure drop is a fundamental characteristic in evaluating the required input power in order to achieve an optimum configuration. Despite several attempts to develop an all-encompassing model to estimate pressure drop in immiscible liquid-liquid flows, existing models are still limited to narrow ranges of Reynolds, Capillary and Weber numbers and are insufficiently accurate over a wide range of viscosity ratios. To push the limits, the present study proposes a new expression for interfacial pressure drop based on experimental investigations over a wide range of Capillary (3×10−4≤CaC≤7.6×10−2), Reynolds (0.1≤ReC≤49) and Weber (7×10−4≤We≤1.5) numbers while continuous to dispersed viscosity ratio (μC/μD) spanned from 0.058 to23.2. To obtain these ranges, five distinct liquid-liquid fluid combinations were examined within a capillary of diameter 800 µm. A novel experimental setup is employed in this study to ensure high accuracy and repeatability of the measurements. The strengths and weaknesses of existing models are identified and a more fundamental understanding of predicting pressure drop in Taylor flow regimes is developed. The new model uses standard Hagen–Poiseuille flow theory in combination with an empirical optimized term for predicting the effect of differential Laplace pressure between leading/trailing caps of dispersed phase droplets. This correlation fits the experimental data within ±20% and can provide a prediction certainty for estimating pressure drop in applications that deal with such flows.

An experimental study on the mobility of droplets in liquid-liquid Taylor flows within circular capillaries

Further development of microfluidics devices that reply on liquid-liquid droplet flows, requires a thorough understanding of the parameters influencing droplet velocity. This study provides greater insights into this subject through an analysis of parameters effecting droplet mobility in such flows. A novel, fully automated experimental setup was designed to accurately measure droplet velocity and length. Measurements were performed over a wide range of Capillary number (2×10−4 to 3.7×10−2), Bond number (0.05 to 3.2) and carrier to dispersed viscosity ratio (0.059 to 23.2) while also varying droplet length. Five different fluid combinations were examined within circular capillaries with inlet diameters ranging from 555μm to 1.70mm. Results reveal a complex relationship between droplet velocity and droplet length, viscosity ratio and Bond number. In all cases, as droplet length exceeds a threshold value, droplet velocity becomes independent of length and is shown to scale with ∼ Ca0.5. As the droplet length falls below the threshold, the droplet velocity faces a changeover zone in which the velocity initially declines and then rises by further increase in the length. For shorter droplets, higher Bond numbers cause the droplet phase to travel asymmetrically with respect to the channel centre line which substantially impacts the mobility of these droplets. Finally, a new expression has been developed to estimate the velocity of elongated droplets.

Velocity measurements of individual droplets in liquid-liquid Taylor flows in circular capillaries

This study is focused on the effect of droplet length on droplet velocity in liquid-liquid Taylor flows for microfluidic applications. An experimental set up was designed to measure droplet velocity over a wide range of droplet lengths and flow velocities while also varying viscosity ratio. Five different fluid combinations were examined by employing AR20, FC40, HFE7500 and water. Results indicate the complexity of predicting droplet velocity in such flow regimes and also show a strong influence of viscosity ratio and Bond number.

Boundary Condition Effect on Two-Phase Fluid Flow ‎and Heat Transfer inside 3-D Microchannels

Two-phase Taylor flows play a vital role in dissipating heat effectively for the proper functioning of electronic systems. In the present study, the thermal performance of liquid-liquid Taylor flow was carried out in a 3D microchannel with uniform wall heat flux boundary for five different cases: uniform heat flux on the four walls, three walls, two opposite walls, single wall, and two adjacent walls, and the aspect ratio of microchannel was varied in the range of 0.2-5. The length of the microchannel was 4 mm, height and width were 0.1 mm each for a square microchannel. For varying aspect ratios of the microchannel, the height and width of the microchannel were taken in the range of 0.06-0.3 mm to keep the hydraulic diameter constant. Dodecane and water were the working fluids in the study and assumed to be Newtonian, incompressible, immiscible, and the properties of fluids were assumed to be independent of temperature. The pressure distribution in the microchannel was investigated under five thermal boundary cases and the aspect ratio effect on pressure drop was also discussed. Results showed Nusselt number of two-phase flow with four-wall heat flux increases up to 280% compared to liquid-only flow and it has been validated with standard heat transfer correlation available in the literature. A higher heat transfer rate (Nu=10.41) was recorded in the opposite walls boundary condition and the heat transfer rate (Nu=7.81) was minimum when the adjacent walls were subjected to uniform heat flux. The effect of microchannel aspect ratio on Taylor flow heat transfer under thermal boundary conditions was also analyzed‎.

On the performance of liquid-liquid Taylor flow electrochemistry in a microreactor – A CFD study

A comprehensive understanding of the underlying phenomena (coupled fluid flow, charge transfer, mass transfer and chemical reaction) is fundamental for a proper design, analysis and scale-out of chemical reactors when carrying out multiphase electro-organic transformations. In this study, we have explored the novel combination of organic electrochemical synthesis and computational fluid dynamics (CFD) to perform a systematic theoretical investigation concerning the effect of different operational parameters on the performance of organic-aqueous Taylor flow in electrochemical microreactors. The results indicate that operating at high concentrations of the rate-limiting species (>5 mol⋅m−3 for Di≥10-9 m2⋅s−1; 500 mol⋅m−3 for Di~10-10 m2⋅s−1) is beneficial for the reactor performance. However, excessively high concentrations (>500 mol⋅m−3) do not result in a further improvement in mass transfer and current/voltage relation. Higher diffusivities are also beneficial, but even in this scenario limiting current densities can be found when working at low concentrations. Overall, keeping an internal:external phase electrical conductivity ratio > 1 improves the reactor performance. Working at lower velocities can be beneficial in some scenarios, since higher limiting current densities can be obtained. However, the velocity impact on the reactor performance is not significant in some operating conditions (e.g., at higher concentrations and diffusivities). Finally, working with higher cell potentials is beneficial, but limiting current densities can be encountered at lower concentrations and diffusivities. Variables such as internal phase volume fraction, droplet length and interelectrode distance also have relevant impact on the reactor performance, but are subjected to the same conditioning factors previously mentioned. A comprehensive potential balance was also conducted, showing the relative importance of the activation, Ohmic and concentration overpotentials under different operating conditions. We believe the insights gained herein will be of interest to researchers in both academia and industry to develop more efficient electrochemical flow reactors for liquid–liquid transformations.

Mathematical model of gas-liquid or liquid-liquid Taylor flow with non-Newtonian continuous liquid in microchannels

Mathematical model of gas-liquid or liquid-liquid Taylor flow with non-Newtonian continuous liquid in microchannels

Pressure Drop and Film Thickness of Liquid-Liquid Taylor Flow in Square Microchannels

The fluid flow and pressure drop of liquid-liquid Taylor flow in a square microchannel are studied, both experimentally, and numerically using a three-dimensional numerical simulation. The experiments were carried out with a square channel having a hydraulic diameter of 2 mm, and the numerical simulations were performed for square channels with hydraulic diameters of 1 and 2 mm. The working fluids were water droplets in a hexadecane or kerosene carrier fluid. The droplet shape, droplet velocity, film thickness and pressure drop of the liquid-liquid Taylor flows were studied over Reynolds number and Capillary number ranges of 6 ≤ Re ≤ 100 and 0.0005 ≤ Ca ≤ 0.02 respectively. It was found that the droplet velocity and the geometry of the front and rear of the droplet are independent of the droplet volume. The droplet velocity was found to be approximately 10% higher than the mixture velocity for 0.0005 < Ca < 0.02. Correlations have been developed to predict the film thickness and pressure drop of liquid-liquid Taylor flow in square microchannels.

Mass transfer in liquid-liquid Taylor flow in a microchannel: Local concentration distribution, mass transfer regime and the effect of fluid viscosity

Mass transfer characteristics of liquid-liquid Taylor flow with various fluid pairs are investigated, in order to reveal the viscous effects of the fluids. The concentration pattern in continuous slugs, mass transfer time and mass transfer coefficient are discussed and analyzed. Several different concentration patterns originated from recirculation are observed at both straight channels and curved bends, respectively. It is shown that the mass transfer coefficient (Ka and K) can increase with the increase in the viscosity of the continuous phase at large flow rates, which is explained by the increased contribution of the film at the lateral droplet side and its exchange with the bulk slug. Based on the dominance of different parts (i.e., film, cap), three mass transfer regimes are distinguished. Correlations for each regime, which covers a wide range of fluid viscosity of 0.89–45.6 mPa·s, are developed to predict the mass transfer coefficient.

Fluid flow and heat transfer of liquid-liquid Taylor flow in square microchannels

The fluid flow and heat transfer of liquid-liquid Taylor flow in a square microchannel are studied both experimentally and numerically using a three-dimensional numerical simulation. The experiment was carried out with a square channel with a hydraulic diameter of 2 mm, and the CFD simulations were performed for square channels with hydraulic diameters of 1 and 2 mm. Constant heat flux boundary conditions were applied in both the experiment and the simulations. Hexadecane, kerosene and water were used as working fluids. The friction factor and the heat transfer rate of the liquid-liquid Taylor flows have been determined. The results indicate that liquid-liquid Taylor flow can increase the rate of heat transfer by up to 700 percent over that single phase flow. It was found that shorter slugs with longer droplets significantly increased the heat transfer performance. Correlations have been developed to predict the friction factor and Nusselt number of liquid-liquid Taylor flow in square microchannels.

Influence of Capillary Number on the droplet Shape, Film Thickness, and Pressure Drop in a Liquid-Liquid Taylor Flow inside a Microcapillary

Numerical analysis of a two-dimensional, axisymmetric, incompressible, laminar liquid-liquid Taylor flow inside a vertical circular microchannel is carried out in the present study. The focus is laid on fluid flow characteristics in the slug flow regime. Although many researchers have performed numerical and experimental studies of two-phase flows in narrow channels, their efforts seem to have been fairly successful in explaining the underlying mechanisms of fluid flow phenomena, especially for slug flow regime. Here, an attempt has been made to explore the hydrodynamics of such flows. In the present study, dodecane and Pd5 have been used as the carrier phases and water is used as the discontinuous phase. The internal diameter of the circular microchannel is 1.5 mm with its wall being insulated. The flow and volume fraction equations are solved by the finite volume approach (FVM). The volume of fluid (VOF) method has been adopted for capturing the interface. The effect of Capillary number on film thickness and interfacial pressure drop is explained. The film thickness is found to increase with Capillary number and is also found to be in a close match with the models available in the literature. The pressure drop per unit length obtained from the CFD study is compared with a standard model available in the literature. The pressure drop across the unit cell is found to be following the phenomenological model. It is observed that the pressure drop at the interface has the highest contribution to the total pressure drop in contrast to the other pressure drops in the channel, with ~50-55% in dodecane-water and ~55-62% in Pd5-water systems. Besides, the distribution of the velocity, axial, and wall pressure fields inside the microcapillary are also discussed.

Numerical study of the hydrodynamics and heat transfer characteristics of liquid–liquid Taylor flow in microchannel

AbstractA numerical study of an oil–water Taylor flow is presented in this paper to explore its flow and heat transfer characteristics. Due to the large surface area to volume ratio in narrow channels, using slug flows, high heat and mass transfer rates could be achieved. Sound knowledge of the underlying physics of slug flow is required for the practical design of microfluidic devices. In this study, hydrodynamics and heat transfer characteristics of dispersed oil droplets flowing inside a vertically upward circular microchannel (D = 0.1 mm) with water being the carrier phase have been explored numerically. ANSYS Fluent was employed to capture the liquid–liquid interface using volume of fluid method. Two different boundary conditions were considered in the present study. First, an isothermal wall of 373 K and later a constant wall heat flux (420 kW/m2) were, respectively, prescribed over the wall of the microchannel. The numerical code was validated against the results available in the literature, and the significant results in the form of pressure drop and heat transfer rates have been discussed. A considerable increase in Nusselt number, up to 180% and 210%, was observed with the oil–water slug flow in contrast to the liquid‐only single‐phase flow inside the microchannel for isothermal and constant wall heat flux conditions, respectively.

Numerical study of liquid-gas and liquid-liquid Taylor flows using a two-phase flow model based on Arbitrary-Lagrangian–Eulerian (ALE) formulation

The liquid-gas and liquid-liquid Taylor flows in circular capillary tubes are numerically studied using a mathematical model developed in the frame of Arbitrary-Lagrangian–Eulerian (ALE), where the interface is tracked so that the important interfacial curvature and forces for Taylor flow can be accurately estimated. It is found that for liquid-gas Taylor flow, thin film thickness predicted by the present numerical model agrees very well with the benchmark experimental data both in visco-capillary and visco-inertia flow regimes. Thin film thicknesses decreases first and then increases as Reynolds number (Re) increases at relatively large capillary numbers (Ca). With the increase of Ca, classical pressure drop correlations become inaccurate, because of strong internal circulation inside liquid slug, the appearance of waves at rear meniscus, as well as the deviation from semi-spherical shape of head meniscus. For liquid-liquid flow, when Ca is small, thin film thickness correlations for liquid-gas flow can be used since the disperse phase has negligible effects, while when Ca is relatively large, the viscosity ratio and density ratio of continuous phase to disperse phase become two additional influencing factors. The larger are the viscosity ratio and the density ratio, the thicker is the film thickness. Different from stagnant thin film in liquid-gas flow, the flow in thin film of liquid-liquid flow is not stagnant and has a large contribution to pressure drop. The numerical model developed in this study is shown to be a powerful and accurate tool to study both the liquid-gas and liquid-liquid Taylor flows.

Experimental study of the contribution of liquid film for liquid-liquid Taylor flow mass transfer in a microchannel

Liquid-liquid two-phase Taylor flow mass transfer in microchannels, which has many advantages for heat and mass transfer operations, should be studied to develop practical applications in various chemical processes. To understand the effects of various parameters on mass transfer and develop an estimation method of mass transfer performance, mass transfer in microchannels was examined by an evaluation of phenol extraction from dodecane to water. Under stable Taylor flow conditions in a 1mm inner diameter glass channel, the organic phase (dodecane) formed liquid droplets and the aqueous phase (water) formed liquid slugs with a liquid film enclosing the organic phase droplets. The effect of the droplet length on mass transfer was investigated with a microchannel device that consists of a circular channel with a 1mm inner diameter and union tees with inner diameters of 2.0mm and 2.4mm. Although the droplets lengths were varied in the range of 7.4mm to 30.5mm, approximately the same volumetric mass transfer coefficients (Ka) were obtained. This result suggested that the side interface of the droplets that contact the thin liquid film becomes a mass transfer interface as well as an end interface. This occurs because the side interface area increases with increasing droplet length and droplet volume while the specific interfacial area remains approximately constant. The volumetric mass transfer coefficients were obtained for various cross-sectional shapes and hydraulic equivalent channel diameters at various flow velocities. The mass transfer coefficients were derived by dividing the volumetric mass transfer coefficients by the specific interfacial area. It was found that the Sherwood number (Sh), which is a dimensionless expression of the mass transfer coefficient, has excellent correlation with the Reynolds number (Re); thus, the estimation of the mass transfer performance for a given channel and given operational conditions can be determined using the correlation between Sh and Re.