Microfluidic devices are increasingly finding application in mechanical and chemical engineering due to their increased heat and mass transfer rates, and their enabling of better flow control [1]. Applications include electronic cooling, microscale heat exchangers, and microreactors.
Taylor flow of a droplet in a carrier liquid is of increasing interest due to its applications in microreactor technology, cooling of electronic devices, and heat exchangers [2], [3], [4]. In this two phase fluid flow there is no phase change, and a train of droplets of one liquid phase (the secondary phase), with each droplet having a length greater than the channel diameter, are periodically aligned in the flow of a carrier liquid (the primary fluid). The droplet is surrounded by a thin layer of the liquid carrier fluid that forms a thin film of thickness δ between the droplet and the channel walls; the body of carrier fluid between successive droplets forms the slug region. Each periodic section comprising one droplet, and two half slugs, as shown in Fig. 1, is called a unit cell that has a length LUC. A two phase flow formed in this manner is more stable, predictable, and does not suffer the problems of backflow and instability typical of two phase flow formed by the evaporation of the carrier fluid.
A number of experimental and numerical studies of gas-liquid Taylor flow in microchannels have been published, but few studies have been made of liquid-liquid Taylor flows in microchannels [4]. The hydrodynamics and pressure drop of liquid-liquid flow in circular microchannels have been numerically and experimentally studied by Jovanovic et al. [5], Kashid et al. [6], [7], Salim et al. [8], Foroughi and Kawaji [9] and Eain et al. [10], and correlations have been developed to predict the pressure drop of Taylor flow in microtubes.Bandara et al. [11] numerically studied the pressure drop of liquid-liquid Taylor flow in an 800 µm diameter microchannel using four different correlations for gas-liquid Taylor flow from the literature. Significant differences were found in the predicted pressure drop, which demonstrated the incomplete understanding of the fundamental physics of liquid-liquid two phase flow. In contrast, Gupta et al. [12] experimentally and numerically studied the pressure drop of liquid-liquid flow in a circular microchannel and a good agreement was reported between their results and predictions of the correlation of Jovanovic et al. [5].
Numerical models of Taylor flow in microchannels have used either a fixed frame of reference (FFR), where the droplet moves through a stationary domain, or a moving frame of reference (MFR) where the frame of reference moves with the droplet. Santos and Kawaji [13], Qian and Lawal [14], Rocha et al. [15] and Shao et al. [16] used FFR methods in their studies, while Araújo et al. [17], Asadolahi et al. [18], [19], Dai et al. [3] and Zhang et al. [20] used MFR methods. For a 3D simulation a MFR method is preferable to reduce computational time [21].
A survey of the literature suggests that most simulations of Taylor flow have been limited to two dimensional axisymmetric simulations of microchannels with a circular cross section, but there is limited numerical and experimental data for square microchannels [4], and none of the numerical studies of Taylor flow in square microchannels that have been validated against experimental data [4]. However, in reality microchannels are commonly square or rectangular in cross section due to the ease of manufacturing. Therefore a two-dimensional model does not realistically simulate the fluid flow and thermal characteristics of Taylor flow in a microchannel with a rectangular cross-section. This issue is addressed in the current work.
This paper reports on a study of the three-dimensional liquid-liquid Taylor flow comprising water droplets in an oil carrier fluid that flows in a square microchannel, using experimental and numerical methods. The pressure drop, friction factor, film thickness, and droplet velocity of liquid-liquid Taylor droplet flow are reported. The experiments and numerical / CFD simulations were carried out for kerosene (carrier fluid) – water (droplet) in a 2 mm square channel. Then a series of parametric numerical (CFD) studies were done for hexadecane-water in a 1 mm square channel. Two correlations were developed to predict the pressure drop of liquid-liquid Taylor flow in a square microchannel.