3.4. ICEK for two-phase liquid flow systems
Two-phase flow microfluidic devices have been widely used for chemical filtration, pharmacology and drug delivery (Azizian et al., 2019; Bazazi, Sanati-Nezhad, & Hejazi, 2018). When a leaky dielectric droplet immersed in another immiscible leaky dielectric liquid, four symmetric MVs are induced inside and outside the droplet (Lin, Skjetne, & Carlson, 2012). This phenomenon was first observed by Taylor (Taylor, 1966) in his experimental work. Small deformation of the droplet was predicted theoretically by calculating the exerted electrical stress on droplet-medium interface (Taylor, 1966). This deformation is generated due to the distribution of the interfacial polarization charge on the interface (Lin et al., 2012). The induced charge on the interface of the liquid and the generated MVs around the droplet have a resemblance to the generated MVs around polarizable solid cylinder immersed in the electrolyte under an external electric field (Bazant, 2015). Squires and Bazant (Todd M Squires & Bazant, 2004) utilized this analogy to determine radial and azimuthal fluid velocities of the ICEO flow around a conducting cylinder. Jung et al. (Jung, Oh, & Kang, 2008) calculated the amount of induced charge in a leaky dielectric water droplet oscillated between two fixed electrodes. Flittner and Přiby (Flittner & Přibyl, 2017) proposed a mathematical model for such oscillatory behavior of water droplets. Wuzhang et al. (Wuzhang, Song, Sun, Pan, & Li, 2015) investigated oil droplet motion in different ionic surfactant solutions and observed that an increase in surfactant concentration led to a higher droplet velocity due to the enhancement in surface charge density. It was also found that two MVs are generated around the oil droplet as a consequence of the redistribution of the mobile surface charges on the droplet surface (Daghighi, Gao, & Li, 2011). Li et al. (Li & Li, 2016a) studied this phenomenon more precisely and proposed an analytical presentation for the local zeta potential distribution on the oil droplet. Furthermore, they experimentally observed the accumulation of passivated aluminum nanoparticles on one side of the droplet, which confirmed the charge redistribution on the droplet (Li & Li, 2016b). Mori and Young (Mori & Young, 2018) further improved the Taylor model (Taylor, 1966) and simulated the droplet deformation using electro-diffusion theory, as an essential tool for describing electrokinetic phenomena by considering the charge diffusion model.
Besides the above studies for describing ICEK occurrence in two-phase flows, this phenomenon has also been employed in various microfluidic applications, such as electric separation of droplets (Guo et al., 2010), droplet coalescence (Xiaodong Chen, Song, Li, & Hu, 2015; Y. Jia et al., 2018), emulsion micro-pumping (Bhaumik, Roy, Chakraborty, & DasGupta, 2014), controlling microdroplet generation (Azizian et al., 2019; Kamali & Manshadi, 2016), regulating the micro reactions (Y. Jia et al., 2017), droplet separation (Li & Li, 2017; K. Zhao & Li, 2018), controlling multiphase flow systems (W. Liu et al., 2017), particle flow-focusing (Ren, Liu, Liu, et al., 2018), droplet motion in water-air and water-oil interfaces (C. Wang, Li, Song, Pan, & Li, 2018; C. Wang, Song, Pan, & Li, 2018a, 2018b), and microvalves (Li & Li, 2018).