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Literature Review

  • Dimitrios A. TsaoulidisEmail author
Chapter
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Part of the Springer Theses book series (Springer Theses)

Abstract

Operations in intensified channels have emerged as an important area of research and have found numerous applications in (bio)chemical analysis and synthesis, reactors, micro-power generation, fuel cells and thermal management systems.

Keywords

Ionic Liquid Pressure Drop Particle Image Velocimetry Plug Flow Flow Rate Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

2.1 Multi-phase Flows

Operations in intensified channels have emerged as an important area of research and have found numerous applications in (bio)chemical analysis and synthesis, reactors, micro-power generation, fuel cells and thermal management systems. Because of their large surface to volume ratio, micro-reactors offer enhanced mass transfer rates and, therefore, they are used to carry out fast, mass transfer limited reactions. Unlike the scale-up uncertainties associated with large-scale conventional reactors, micro-reactors are scaled out by simple duplication of individual units. A number of applications in small channels involve two fluid phases, i.e. gas-liquid and liquid-liquid. Understanding of the flow characteristics and flow patterns, pressure drop and mass/heat transfer is essential in the design and the precise control of the multiphase devices. Compared to macro-contactors the flow configurations appearing in liquid-liquid micro-contactors are influenced by a variety of factors, which can be categorized into 3 groups: (a) channel properties (dimensions, orientation, channel material, inlet size, mixing zone, wall roughness and wettability), (b) fluid properties (density, surface tension, viscosity), and (c) operation conditions (fluid flow rates, flow rate ratios temperature, pressure drop). Although there are many studies concerning gas-liquid flows, the number of studies that have been reported on the flow behaviour of two immiscible liquids in micro-channels does not mirror the numerous applications.

2.1.1 Flow Patterns in Micro and Small Channels

In liquid-liquid systems, the flow pattern describes the spatial distributions of the two phases in the microchannels and is strongly related with the performance of the micro-reactors, since it influences the pressure drop, and heat and mass transfer within the reactor. A number of different flow patterns can occur, which mainly depend on flow rates, flow rate ratio, channel size, inlet geometry, etc. Depending on the fluid properties and the channel material, either phase can wet the channel wall and for phases with similar wettabilities both phases can intermittently adhere to the wall, rendering ordered, stable and well-defined patterns more difficult to form than in gas-liquid flows (Wegmann and Rudolf von Rohr 2006). The generation of a unified theory for the prediction of flow patterns for liquid-liquid flows is quite difficult due to the wide variation of physical properties of the two phases, the chemistry, and the hydrodynamics. Controlling the hydrodynamics could decrease pressure drop, improve mass transfer and facilitate product separation from the reaction mixture (Dessimoz et al. 2008).

One of the problems in studying and reporting liquid-liquid flow patterns is the lack of coherence in the terminology used by various investigators for the different flow regimes. The basic flow patterns that someone can identify in microchannels with internal diameter from 0.1 to 10 mm are the following:
  • Drop flow, in which plugs of size smaller than the diameter of the channel are formed (Fig. 2.1a).
    Fig. 2.1

    Flow configurations obtained in microchannels a Drop flow, b Plug (slug) flow, c Plug-drop flow, d Deformed interface flow, e Annular flow, f Parallel flow, g Plug-dispersed flow, h Dispersed flow (Kashid et al. 2011)

  • Plug flow (or slug or segmented flow), where one fluid forms individual plugs cylindrical in shape (Fig. 2.1b).

  • Plug-drop flow, where the dispersed phase flows in the form of irregular plugs and drops (Fig. 2.1c).

  • Intermittent flow (or deformed interface flow), where the dispersed phase flows to a certain distance either in the form of parallel or annular flow and then produces irregular droplets (Fig. 2.1d).

  • Annular flow (wavy, smooth), where one fluid occupies the space adjacent to the tube wall and surrounds the other fluid (with the lower density) that flows in the center of the tube (Fig. 2.1e).

  • Parallel flow (wavy, smooth), where the two liquids are separated with the lighter fluid flowing on the top of the heavier liquid (Fig. 2.1f).

  • Plug-dispersed flow, where part of the continuous phase flows in the form of small droplets in the dispersed phase (Fig. 2.1g).

  • Dispersed flow, where very fine droplets of one phase are formed into the other phase. This flow regime is observed when the total flow rate is increased (Fig. 2.1h).

These patterns can be further sub-divided to other flow regimes. By an order-of-magnitude reduction in the diameter of the flow channel from 10 to 1 mm, significant differences have been reported on the configuration of the flow patterns that are formed for the same flow conditions. Two-phase flows in large channels are mainly dominated by gravitational and inertia forces, whilst in the case of the two-phase flows in microchannels, the interfacial tension and viscous forces are significant because of the small characteristic distances and the low Re numbers (Re < 2000), while gravity and inertia effects become negligible (Kreutzer et al. 2005b). The relative importance of these forces is shown in Fig. 2.2.
Fig. 2.2

Inertial, viscous and gravitational body forces, relative to interfacial forces, as a function of the channel size and characteristic velocity in microfluidic multiphase systems (Günther and Jensen 2006)

The occurrence of different flow patterns in small channels is attributed to the competition between these forces, i.e. interfacial, inertia and viscous forces. The interfacial force tends to minimize the interfacial energy by decreasing the interfacial area, i.e. formation of droplets and plugs (Fig. 2.1b). Inertia force tends to extend the interface in the flow direction and keep the fluids continuous (Fig. 2.1f) (Joanicot and Ajdari 2005). Moreover, if there is a sufficient velocity difference across the interface, the interface could become wavy due to shear instability. The viscous force dissipates the energy of perturbations at the interface and tends to keep the interface smooth (Foroughi and Kawaji 2011; Kashid et al. 2011).

Over the past few years there was an attempt to determine as many as possible impacts that affect the flow configuration in liquid-liquid microchannel flows, as well as the stability of these flow patterns (Burns and Ramshaw 2001; Dessimoz et al. 2008; Kashid and Agar 2007; Ahmed et al. 2006). The different flow patterns that can be obtained in microchannels have been investigated not only for operational conditions, such as flow rates and volumetric flow ratio, and properties of the fluids (Lin and Tavlarides 2009), but also for different geometry of the mixing zone and channel (Kashid et al. 2011), as well as for the channel wall roughness and wettability (Jovanović et al. 2011; Kuhn et al. 2011). Salim et al. (2008) investigated the flow of two immiscible liquids in two types of microchannel, i.e. glass and quartz, and they found that the flow formation was highly affected by the first injected fluid. Furthermore, they demonstrated that drop and plug velocities are proportional to the superficial velocity of the mixture, with a proportionality coefficient depending on the flow pattern.

To define the different parameters responsible for the flow formation, flow pattern maps are used, where the axes represent the superficial velocities or the volumetric flow rates of phases, mixture velocity or total volumetric flow rate against the fraction of one of the phases while dimensionless numbers have also been used (Table 2.1 ). Depending on the dimensionless numbers, different zones where the specific forces are dominant can be defined.
Table 2.1

Dimensionless numbers for the characterisation of the two-phase flow

Dimensionless numbers

Definition

Reynolds number

\({\text{Re}}_{\text{i}} = \frac{{\uprho_{\text{i}} {\text{u}}_{\text{i}} {\text{ID}}}}{{\upmu_{\text{i}} }} = \frac{\text{inertia forces}}{{ {\text{viscous forces}}}}\)

Capillary number

\({\text{Ca}}_{\text{i}} = \frac{{\upmu_{\text{i}} {\text{u}}_{\text{i}} }}{\upgamma} = \frac{\text{viscous forces}}{\text{interfacial forces}}\)

Weber number

\({\text{We}}_{\text{i}} = \frac{{\uprho_{\text{i}} {\text{u}}_{\text{i}}^{2} {\text{ID}}}}{\upgamma} = \frac{\text{inertia forces}}{\text{interfacial forces}}\)

Bond number

\({\rm B}o=\frac{\text{ID}^{2}\Delta \uprho \text{g}} {\gamma}=\frac{\text{buoyancy forces}}{\text{interfacial forces}}\)

It is worth mentioning, that flow pattern mapping is a multi-parametric procedure and it is hard to extrapolate the results found for a specific set of conditions. An example of a flow pattern map based on dimensionless numbers of the two immiscible phases is shown in Fig. 2.3.
Fig. 2.3

Flow patterns map for silicon oil-water flow in a 250 μm microchannel initially saturated with oil. The solid lines indicate the flow pattern transition boundaries, i.e. (I) interfacial forces dominant, (II) interfacial and inertia forces were comparable, (II) viscous forces > inertia > interfacial forces, (IV) inertia and viscous forces were comparable, and (VI) inertia dominant (Foroughi and Kawaji 2011)

In general, the main flow patterns which have been observed and studied extensively are plug (or segmented), drop, annular and parallel flow. Annular and parallel flows are observed when the inertia forces dominate over the interfacial forces at We > 1 which, however, were easily destabilised by changing flow rates and volumetric flow ratios (Zhao et al. 2006). Further increase of the We number (We > 10) will cause turbulence, and chaotic or deformed annular flows are observed. Plug flow has received particular attention from many investigators, due to the promising benefits that offer in numerous applications. In most of the works, Y- and T-junctions or co-flowing configurations (Fig. 2.4) are utilised as mixing zones (Garstecki et al. 2006; Kashid and Agar 2007; Salim et al. 2008; Dessimoz et al. 2008; Foroughi and Kawaji 2011). However, flow patterns do not change significantly among the different channel geometries and mixing zones (Kashid and Kiwi-Minsker 2011).
Fig. 2.4

Mixing zone configurations for plug flow formation

Although the exact position of the transition boundaries between the flow patterns are inherently related to the liquid-liquid system studied, the arrangement of the regions of the different flow patterns are similar to a number of systems. Models based on the Capillary, Reynolds and Weber numbers have been developed in order to allow an a priori prediction of the flow patterns using fluid properties and flow velocities. A general criterion for flow pattern identification in a given microchannel was given in terms of dimensionless ratio of Reynolds to Capillary (Rec/Cac) numbers as a function of the product of Reynolds number and hydraulic diameter (Reddhd) by Kashid and Kiwi-Minsker (2011) and was applied to different literature data which are summarised in Fig. 2.5.
Fig. 2.5

Rec/Cac as a function of Reddhd. (□) surface dominated, (×) transition, (○) inertia dominated (Kashid and Kiwi-Minsker 2011)

It can be concluded that the most significant impact on the formation of the flow patterns originated from the fluid properties, channel size, channel wettability, flow rate ratio and interfacial tension. A comprehensive flow pattern map should be dependent on the fluid and microchannels characteristics, and thus correlate the flow regimes using the relative forces responsible as well as the surface roughness.

2.1.2 Phase Separation in Micro and Small Channels

Extraction involves three basic steps: (I) mixing of the two liquid phases (II) contacting of the two phases, (III) separating the two phases from each other. As mentioned previously, micro-fluidic devices have been developed for a wide range of applications because of the many advantages, such as short analysis time, reduction of the sample, reagents, and waste volumes, more effective reaction due to large specific area, and smaller space requirement. Phase separation of the multiphase micro-flows is a very important issue for controlling micro-flow networks. The phase separation requires a single phase flow in each output of the micro-device. Separation of the two phases based on density difference is inappropriate for small scale microfluidic devices, where gravitational forces are negligible. Another important issue is to control the pressure difference between the two phases due to pressure loss in each phase and the Laplace pressure generated by the interfacial tension between the separated phases. The microfluidic extraction devices can be categorized based on the way that the immiscible fluids flow within them. Co-current and counter-current parallel flow, and segmented flow are two common flow patterns in extraction processes. The phase separation in these systems is usually achieved by methods that incorporate micro-fabrication of materials with very different surface properties to exploit the different fluid properties of the two phases (i.e. hydrophobicity). In addition, separation by capillary forces and balanced pressure conditions has been widely used (Kralj et al. 2007; Kashid et al. 2007b; Castell et al. 2009; Scheiff et al. 2011; Gaakeer et al. 2012). These methods are effective because they utilize interfacial tension and wetting, which are dominant effects in the microchannels. A general schematic of the phase separation during parallel or segmented flow is shown in Fig. 2.6.
Fig. 2.6

A schematic of separation devices during liquid-liquid plug or parallel flow. a Phase separation using a Y-splitter (Kashid et al. 2007b), b Phase separation by capillary forces (Angelescu et al. 2010), c Phase separation during parallel flow (Aota et al. 2009) and d Phase separation by wettability combined with pressure balance (Scheiff et al. 2011)

2.1.3 Flow Patterns in Pipes

Macro-scale reactors differ substantially from micro-scale ones in terms of flow patterns where gravity and inertia forces are the dominating forces. Studies in pipes have been performed by many investigators in order to enhance the knowledge of the flow patterns and estimate the area of contact. As in the case of microchannels wettability was found to affect the flow configuration. Different parameters, such as pipe orientation, i.e. horizontal, vertical or inclined (Lum et al. 2006), pipe size and the flow orientation of the two immiscible fluids (Rodriguez and Oliemans 2006), fluid properties, i.e. viscosity (Beretta et al. 1997), pipe material (2000) and flow rates (Wegmann and Rudolf von Rohr 2006) influence the flow patterns. An indicative flow pattern map can be seen in Fig. 2.7. Angeli and Hewitt (2000) investigated this effect by using two horizontal pipes made of stainless steel and acrylic, whilst Wegmann and Rudolf von Rohr (2006) used pipes made of glass. They observed a substantial difference in the flow patterns (stratified, stratified/mixed and dispersed flow) between the pipes.
Fig. 2.7

Experimental flow pattern transition lines (Wegmann and Rudolf von Rohr 2006)

2.2 Plug Flow

Liquid-liquid plug flow in small channels plays an important role in many applications such as (bio)chemical and material synthesis, food science, and encapsulation. The development of microfluidic devices and methods to produce monodisperse plugs (or bubbles) by means of controlling and manipulating fluid flows within length scales from micro- to milli-meter, has gained considerable attention in the last decade. Several droplet-based applications have been investigated so far, including mixing enhancement (Song et al. 2003), crystallization of proteins (Zheng et al. 2004), and clinical diagnostics (Srinivasan et al. 2004). Microfluidic devices can facilitate the formation of monodisperse plugs, since the internal dimensions can be fabricated within the micrometer scale. There are several microfluidic designs reported in the literature that can produce plug (segmented) flow. These include cross flowing micro-devices (T-shaped channels) (Kashid et al. 2007b), flow focusing micro-devices (Garstecki et al. 2005), and co-flowing microdevices (Foroughi and Kawaji 2011). Each of these methods utilizes a specific flow configuration to promote the uniform generation of monodisperse droplets. The size and uniformity of the droplets depend on the physical properties of the two fluids, as well as on the dimensions and geometric profile of the microdevice.

2.2.1 Mechanisms of Plug Formation in Cross-Flowing Devices

The T-shaped configuration is one of the most commonly used for the development of plug flow, because of the high level of control and uniformity of the flow patterns, as well as the simplicity of the design. So far, many studies, both experimental (Thorsen et al. 2001; Tice et al. 2004; Garstecki et al. 2006; Christopher et al. 2008) and numerical (Van der Graaf et al. 2006; De Menech et al. 2008; Gupta et al. 2009; Gupta and Kumar 2010) have been performed on the formation of droplets at a T-shaped configuration to provide an understanding on the flow hydrodynamics. Depending on the forces that dominate, the break-up mechanisms can be distinguished into two types, i.e. shear-driven mechanism (Thorsen et al. 2001) and squeezing mechanism (Garstecki et al. 2006). Thorsen et al. (2001) investigated the droplet formation in T-junction and they observed that by increasing the flow rate and the viscosity of the continuous phase, the droplet size decreases and proposed a model to predict the size of the droplet by analysing the balance between the interfacial and the viscous forces of the continuous phase. Garstecki et al. (2006) focused on the scaling law of droplet formation. They found that at low Ca (Ca < 0.01) and We numbers, where interfacial forces dominate over shear stress, the break-up is triggered by the squeezing mechanism. The break-up of the droplet occurs due to the build-up of pressure caused, as a result of the high resistance to the flow of the continuous phase in the thin film that separates the droplet from the channel walls when the droplet occupies almost the entire cross section of the main channel (squeezing mechanism), while the effect of the shear stress can be considered negligible (Fig. 2.8) (Garstecki et al. 2006; van Steijn et al. 2007; Xu et al. 2013).
Fig. 2.8

A schematic illustration of the break-up process of a plug at the T-junction of the microchannels. a the growing stage, b the squeezing stage (Garstecki et al. 2006)

At values above a critical Ca number (Ca ~ 0.015) the shear-driven mechanism also contributes to the droplet formation (De Menech et al. 2008). The shear stress acts to tear off the tip of the dispersed phase, whilst the interfacial tension acts to minimize its surface area. Although a T-shaped configuration favours the formation of plug flow, further increase on the flow rate ratio leads to a change on the flow regime and thus parallel flow will be observed.

2.2.2 Plug Size

The size of the plug is a very important parameter, since it has a direct relation to the performance of the liquid-liquid system. Plug size affects the intensity of the recirculation and subsequently affects heat and mass transfer. For the prediction of the plug size different influencing factors, i.e. total volumetric flow rates, flow rate ratios, channel widths of the main and side channels, and fluid superficial velocities have been investigated and scaling laws and semi-empirical correlations have been suggested (Kreutzer et al. 2005; Hoang et al. 2013; Christopher et al. 2008; van Steijn et al. 2010; Garstecki et al. 2006). In these models the plug size is independent on the Ca number and is affected by the flow rate ratio and the channel geometry (Garstecki et al. 2006; van Steijn et al. 2007).

The model proposed by Garstecki et al. (2006) is based on the squeezing mechanism and is given by Eq. (2.2.1):
$$\frac{{{\text{L}}_{\text{p}} }}{\text{w}} = 1 +\upalpha\frac{{{\text{Q}}_{\text{d}} }}{{{\text{Q}}_{\text{c}} }}$$
(2.2.1)
where Lp is the length of the plug, α is a fitting parameter of order one, and Qd and Qc are the flow rate of the dispersed and the continuous phase, respectively. Similarly to the above law van Steijn et al. (2010) proposed a predictive model for liquid droplets and gas bubbles without any fitting parameters. Their model has been experimentally validated in T-junctions with 0.33 ≤ win/w ≤ 3 and 0.1 ≤ h/w ≤ 0.5 for Ca < 0.01, where win, w and h are the width of the side channel, width of the main channel and height of the main channel, respectively.
Based on the above models, Leclerc et al. (2010) proposed a semi-empirical correlation (Eq. 2.2.2), based on experiments with gas-liquid Taylor flow in T-shaped square microchannels.
$$\frac{{{\text{L}}_{\text{b}} }}{{{\text{w}}_{\text{g}} }} = 1.03(\frac{{{\text{w}}_{\text{g}} {\text{w}}_{\text{l}} }}{{{\text{w}}^{2} }}) + 2.17\frac{{{\text{w}}_{\text{g}} }}{{{\text{w}}_{\text{l}} }}\frac{{{\text{u}}_{\text{g}} }}{{{\text{u}}_{\text{l}} }}$$
(2.2.2)
where Lb, wg, wl, w, ug, ul are the length of the bubble, channel width of the gas phase, channel width of the liquid phase, channel width of the main channel, gas velocity, and liquid velocity, respectively.
In the same way, Xu et al. (2013) proposed a correlation (Eq. 2.2.3) that includes the effects of slug velocity uUC, capillary diameter d, and aqueous to organic phase flow rate ratio q. The capillary diameters for the correlation were 0.6 and 0.8 mm.
$${\text{L}}_{\text{p}} = 0.0116{\text{u}}_{\text{UC}}^{ - 0.32} {\text{ID}}^{1.25} {\text{q}}^{0.89}$$
(2.2.3)

The aforementioned models showed good agreement with one another for low Ca numbers (i.e. squeezing regime) and demonstrated that the size of the plug depends on the microchannel geometry and the flow rates of the two phases, whilst is independent of the fluid properties. However, as mentioned earlier, the shear stresses start to play an important role as the Ca number increases (shear driven regime). This illustrates the fact that the effects of fluid properties should be also considered, when predicting plug size for a large range of operating conditions for process engineering applications. Factors, such as surface wettability, channel depth, and fluid properties also affect the flow and single scaling laws may not always be valid (Abadie et al. 2012; Gupta et al. 2013; Xu et al. 2006). Moreover, it was found that the viscosity ratio (μdc) affected the droplet size when the viscosity values were in the same order of magnitude, whilst when the ratio was considerably low the droplet size was independent (Christopher et al. 2008).

Qian and Lawal (2006) conducted numerical simulations on the formation and the size of Taylor bubbles in different capillaries for 0.000278 < Ca < 0.01, and 15 < Reub = ρIDub/μ < 1500. They proposed the following correlation for the estimation of the bubble length based on 148 sets of data
$$\frac{{{\text{L}}_{\text{b}} }}{\text{ID}} = 1.637\upvarepsilon_{\text{g}}^{ - 0.107} (1 -\upvarepsilon_{\text{g}} )^{ - 1.05} {\text{Re}}^{ - 0.0075} {\text{Ca}}^{ - 0.0687}$$
(2.2.4)
Laborie et al. (1999) studied experimentally gas-liquid Taylor flow in capillaries of internal diameter varying between 1 and 4 mm, for 55 < Reub = ρIDub/μ < 2000, 0.13 < Bo < 5, and 0.0015 < Ca < 0.1, and proposed Eq. (2.2.5) for the estimation of the plug length
$$\frac{{{\text{L}}_{b} }}{\text{ID}} = 0.0878\frac{{{\text{Re}}_{\text{Ub}}^{0.63} }}{{{\text{Bo}}^{1.26} }}$$
(2.2.5)

2.2.3 Film Thickness

The presence of the film between the dispersed plug and the channel wall offers multiple advantages such as prevention from cross contamination between the segments in biological devices, and enhancement of the heat and mass transfer in chemical engineering processes. Film thickness can be affected by different parameters such as fluid properties, average velocity, flow rate ratio, and channel size.

Many investigations on the deposition of the liquid film on the capillary have been performed, both experimentally (Irandoust and Andersson 1989; Jovanović et al. 2011) and numerically (Heil 2001; Taha and Cui 2004) to estimate the magnitude of the film. While there are many applications that employ liquid-liquid plug flow, limited knowledge about the film thickness is available. In contrast, the film present in gas-liquid flows has been investigated in numerous studies. In most of the works, it was found that the film thickness (normalized by the channel radius) depends on a single parameter, i.e. the capillary number (Ca). As the velocity, and yet the Ca number, was increased the film thickness was also increased. The rate of the film increase follows an asymptotic trend till a threshold Ca number is reached, due to the tube confinement. In Table 2.2 the most referenced models on film thickness regarding gas-liquid systems and the Ca number range that the models are valid, are presented (Angeli and Gavriilidis 2008).
Table 2.2

Correlations for the wall film thickness (δ) for gas-liquid Taylor flow

Dimensionless film thickness

Range of Ca number

Reference

\(\frac{\updelta}{R} = 0.5\sqrt {{\text{C}}\upalpha}\) (2.2.6)

7.5 × 10−5 < Ca < 0.01

Fairbrother and Stubbs (1935)

\(\frac{\updelta}{R} = 1.34{\text{C}}\upalpha^{2/3}\) (2.2.7)

Ca < 0.003

Bretherton (1961)

\(\frac{\updelta}{R} = 0.36(1 - \exp \left( { - 3.1{\text{C}}\upalpha^{0.54} } \right))\) (2.2.8)

9.5 × 10−4 < Ca < 1.9

Irandoust and Andersson (1989)

\(\frac{\updelta}{R} = \frac{{1.34{\text{C}}\upalpha^{2/3} }}{{1 + 2.5(1.34{\text{C}}\upalpha^{2/3} )}}\) (2.2.9)

10−3 < Ca < 1.4

Aussillous and Quéré (2000)

Different methods have been applied to define with accuracy the magnitude of the film thickness for the whole range of Ca numbers. These techniques involved video recording (Aussillous and Quéré 2000), volumetry (Bretherton 1961), conductimetry (Fairbrother and Stubbs 1935), light absorption (Irandoust and Andersson 1989), interferometry (Han and Shikazono 2009), and optical microscopy (Dore et al. 2012; Mac Giolla Eain et al. 2013).

Most investigations on film thickness in segmented flow, originate from the initial attempts by Taylor (1961) to measure it experimentally and the theoretical analysis by Bretherton (1961) of the film thickness across a bubble moving in a horizontal flow at low Ca numbers (<0.003). The bubble was assumed to be inviscid with spherical caps. From their analysis it was found that the dimensionless film thickness was a function of Ca2/3. In the same sense Aussillous and Quere (2000) developed an empirical correlation based on Bretherton’s (1961) solution by measuring the film thickness in vertical gas-liquid flows. In their work they classified two different regimes for the interpretation of the film thickness, i.e. the visco-capillary and the visco-inertia regime. In the visco-capillary regime, the film thickness depends only on Ca number, and the correlation proposed agreed well with Taylor’s (1961) data; for low Ca numbers their model also agreed with Bretherton’s (1961) model. In the visco-inertia regime, where Ca number is higher (Ca > 10−3) they found a deviation from Taylor’s (1961) findings, since inertia becomes important, and the film thickness increases.

The effect of inertia has been investigated by Edvinsson and Irandoust (1996) by using finite element analysis of Taylor flow in a cylindrical capillary. The effects of Ca, Re, and Fr numbers over a wide range were studied, and the simulations revealed that the film thickness was also dependent on Re and Fr numbers. By increasing the Re number the film thickness and the velocity difference between the two phases also increased, while the effect of Fr number (Froude number) was more obvious at higher Ca numbers, with results depending on the flow orientation (downward or upward flow).

The shape of the plug/bubble plays a crucial role on the correct estimation of the film thickness. Depending on the forces that dominate the flow, the profile of the plug will vary. At low Ca numbers, plugs are sufficiently long to maintain hemispherical caps and a uniform flat film along them. By increasing the Ca number the profile of the plug changes, and thus both the rear and the front cap of the plug lose their hemispherical shape. The front cap becomes sharper and the rear cap becomes more flat, hence the area of uniform film thickness diminishes. This makes the choice of the location for the estimation of the film thickness quite difficult. To overcome the problem of the plug profile the film thickness can be defined by using indirect techniques that give film thickness as an average over the whole length of plug (Taylor 1961; Irandoust and Andersson 1989). Han and Shikazono (2009) measured the film thickness in gas-liquid horizontal flows and found that the film thickness changes according to the measuring positions due to gravity. They proposed an empirical correlation based on Ca number, Re number and We number. They found that by increasing the Ca number, an increase in the Re number results to an initial reduction of the film thickness till a threshold before it increases again. Mac Giolla Eain et al. (2013) have also measured the film thickness in horizontal liquid-liquid flows and have reported the effects of the plug length and the fluid properties of the carrier fluid on film thickness.

2.2.4 Plug Velocity

Knowledge of the plug velocity is key parameter in the design of contactors, since it defines the residence time, i.e. the time that the droplet remains in the contactor, while it affects the intensity of the internal circulations within the plug and thus the mixing efficiency. The velocity of the plug within a channel is highly affected by the forces acting on it, i.e. viscous, inertia and interfacial forces.

For a plug that is sufficiently long to maintain a uniform film thickness region (as discussed in Sect. 2.2.3), the velocity profile far away from the rear and front cap is that of an ideal laminar flow, given by Eqs. (2.2.10) and (2.2.11) for the dispersed and the continuous phase, respectively (Lac and Sherwood 2009; Jovanović et al. 2011; Gupta et al. 2013).
$${\text{u}}_{\text{d}} = 2{\text{u}}_{\text{mix}} \frac{{[1 - \frac{{{\text{R}}_{\text{i}}^{2} }}{{{\text{R}}^{2} }}] + \frac{1}{\uplambda}[\left( {\frac{{{\text{R}}_{\text{i}}^{2} }}{{{\text{R}}^{2} }}} \right) - (\frac{{{\text{r}}^{2} }}{{{\text{R}}^{2} }})]}}{{(1 + \frac{{{\text{R}}_{\text{i}}^{4} }}{{{\text{R}}^{4} }})(\frac{1}{\uplambda} - 1)}}\quad {\text{for}}\, \, 0 < {\text{r}} < {\text{R}}_{\text{i}}$$
(2.2.10)
$${\text{u}}_{\text{c}} = 2{\text{u}}_{\text{mix}} \frac{{[1 - \frac{{{\text{R}}_{\text{i}}^{2} }}{{{\text{R}}^{2} }}]}}{{(1 + \frac{{{\text{R}}_{\text{i}}^{4} }}{{{\text{R}}^{4} }})(\frac{1}{\uplambda} - 1)}}\quad {\text{for R}}_{\text{i}} < {\text{r}} < {\text{R}}$$
(2.2.11)
where Ri is the radius of the plug, and R the radius of the channel. The droplet velocity can be calculated by averaging the droplet fluid velocity and is given as
$${\text{u}}_{\text{droplet}} = {\text{u}}_{\text{mix}} \frac{{\left[ {2 + \frac{{{\text{R}}_{\text{i}}^{2} }}{{{\text{R}}^{2} }}} \right][\frac{1}{\uplambda} - 2]}}{{(1 + \frac{{{\text{R}}_{\text{i}}^{4} }}{{{\text{R}}^{4} }})(\frac{1}{\uplambda} - 1)}}$$
(2.2.12)
If there is a large difference between the viscosities of the two phases, then the viscosity ratio (λ = μdc) tends to zero and Eq. (2.2.12) becomes
$${\text{u}}_{\text{droplet}} = {\text{u}}_{\text{mix}} \frac{{{\text{R}}^{2} }}{{{\text{R}}_{\text{i}}^{2} }}$$
(2.2.13)
which however, does not take into account the flow of the continuous phase and is accurate for gas-liquid flows.
Similarly, the film velocity can be obtained by Eq. (2.2.14) as follows
$${\text{u}}_{\text{film}} = {\text{u}}_{\text{mix}} \frac{{[1 - \frac{{{\text{R}}_{\text{i}}^{2} }}{{{\text{R}}^{2} }}]^{2} }}{{(1 + \frac{{{\text{R}}_{\text{i}}^{4} }}{{{\text{R}}^{4} }})(\frac{1}{\uplambda} - 1)}}$$
(2.2.14)
Gupta et al. (2013) found good agreement between the analytical solutions given by Eqs. (2.2.10) and (2.2.11), and the CFD simulations.
To evaluate the bubble velocity in gas-liquid flows, the dimensionless number, m, which gives the relative velocity between the bubble and the continuous phase, is used,
$${\text{m}} = \frac{{{\text{u}}_{\text{b}} - {\text{u}}_{\text{mix}} }}{{{\text{u}}_{\text{b}} }}$$
(2.2.15)
In Table 2.3, empirical correlations for the prediction of the bubble velocity during gas-liquid Taylor flow, as well as the analytical solution of Bretherton (1961) are summarised.
Table 2.3

Correlations for the bubble velocity uB for gas-liquid Taylor flow

Correlation

Range of Ca number

Reference

\({\text{m}} = \sqrt {{\text{C}}\upalpha}\) (2.2.16)

7.5 × 10−5 < Ca < 0.01

Fairbrother and Stubbs (1935)

\({\text{m}} = 1.29(3{\text{C}}\upalpha^{{\frac{2}{3}}} )\) (2.2.17)

10−3 < Ca < 10−2

Bretherton (1961)

\({\text{m}} = (\frac{\mu }{\sigma })^{{\frac{1}{2}}} [ - 0.1 + 1.78\sqrt {u_{b} }\) (2.2.18)

7 × 10−6 < Ca < 2 × 10−4

Marchessault and Mason (1960)

\(\frac{{{\text{u}}_{b} }}{{u_{m} }} = \frac{1}{{1 - 0.61{\text{C}}\upalpha^{0.33} )}}\) (2.2.19)

2 × 10−4 < Ca < 0.39

Liu et al. (2005)

2.2.5 Internal Circulation

Taylor (1961) suggested three patterns for slug flow (Fig. 2.9) that depend on Ca number. At high Ca numbers (m > 0.5), a single stagnation point at the front part of the bubble was suggested, which indicates a complete bypass flow (Fig. 2.9a). By decreasing the Ca number (m < 0.5) two possible flow patterns were proposed; in the first case a stagnation ring around the bubble front part was formed (Fig. 2.9b), whilst in the other case two stagnation points were formed, one inside the liquid slug and another one at bubble front part (Fig. 2.9c).
Fig. 2.9

Qualitative schematic of flow streamlines in the liquid slug ahead of elongated bubbles in capillaries. a m > 0.5; b and c m < 0.5, where m = (ub − umix)/ub (Taylor 1961)

The shear between the wall surface and the plug axis produces internal circulations within the plug, which reduce the thickness of the boundary layer at the interface, thereby enhancing the diffusive penetration, heat and radial mass transfer (Kashid et al. 2005; Talimi et al. 2012). The length of the plug and the slug, the velocity of the mixture, and the thickness of the film affect the intensity of the circulations.

Tice et al. (2003) investigated the formation of plugs of multiple reagents and subsequently the mixing within the plug. They concluded that the optimal mixing within the plugs depends on the initial distribution of the reagents, which was established by the eddy flow at the tip of the forming plug. King et al. (2007) investigated the effect of plug length on the formation of internal circulation and they reported the cases where circulation was absent. They found that at short plugs and low flow velocities internal circulation is minimal, since zero velocity gradients exist. Circulation times increased in value as a function of the velocity till a threshold value beyond which the internal circulation no longer increases. For small segments the contribution of the liquid-liquid friction to the phase internal flow is the decisive factor and liquid/wall friction is minimal due to its small contact area (Malsch et al. 2008).

The geometry of the channel has also a decisive impact on the formation of the flow patterns inside a plug (Fig. 2.10). When a plug is flowing in straight channels usually the internal flow patterns observed at the upper and bottom half of the segments are symmetric over the centre of the channel. In bend channels flow circulation is asymmetric as a result of the channel curvature. This leads to more complex flow fields, but also results to higher mass transfer over the whole segment and an improved mixing efficiency.
Fig. 2.10

Flow fields in a droplet when flowing (velocity of 7.6 mm s−1) in straight channels (a) and in bend channels (b) (Malsch et al. 2008)

The mixing inside the segments is quantified by using two dimensionless parameters. The first is the relative vortex length which gives the ratio of the main vortex length over the length of the segment.

Ufer et al. (2011) investigated a two-phase system of water/ethylacetate and found that this ratio varies between 0.3 and 0.75 and increased by increasing the velocity of the plug. Scheiff et al. (2013) investigated the internal circulation in viscous ionic liquid plugs and they found that the vortices in the ionic liquid plugs occupy the entire plug. The other parameter of quantifying the mixing is the dimensional circulation time. This is defined as the ratio of the average time to displace material from the one to the other end of the plug to the time that the plug needs to travel a distance of its own length (Thulasidas et al. 1997; Dore et al. 2012). The structure of the internal circulation, i.e. the location of the stagnation points are essential for quantifying the mixing inside the two phases. Thulasidas et al. (1997) showed that for Poiseuille flow the radial position of the centre of the toroidal vortex, r0 and the radial position of the stagnation streamline, r1 are given by Eqs. (2.2.20) and (2.2.21), respectively.
$${\text{r}}^{ 0} { = }\frac{\text{R}}{\sqrt 2}\sqrt { 2 { - }\uppsi}$$
(2.2.20)
$${\text{r}}^{1} = {\text{R}}\sqrt {2 -\uppsi}$$
(2.2.21)
where ψ = ub/umix. At ψ = 2 the r0 and r1 become 0 which corresponds to the point of complete bypass.

2.2.5.1 Particle Image Velocimetry (PIV)

For understanding the mixing characteristics in two-phase microfluidic systems, details of the velocity profiles within the phases are required. Micro Particle Image Velocimetry (µ-PIV) can be used to extract multipoint information of the velocity inside a single liquid plug or slug with high accuracy and spatial resolution and in a non-intrusive manner (Santiago et al. 1998; Lindken et al. 2009). Important mixing characteristics, such as the recirculation time, can then be derived from the velocity fields and other measured parameters, such as the location of stagnation points, and vortex cores. There have been a number of studies involving the application of µ-PIV on gas-liquid flows (Thulasidas et al. 1997; Günther et al. 2004; Waelchli and Rudolf von Rohr 2006; van Steijn et al. 2007; Malsch et al. 2008), but only limited ones for liquid-liquid systems (Kashid et al. 2005; Sarrazin et al. 2006; Wang et al. 2007; King et al. 2007; Kinoshita et al. 2007). In these studies µ-PIV has been used to visualize the internal recirculation in aqueous slugs or plugs during aqueous/oil two-phase flows. Kinoshita et al. (2007) obtained three-dimensional velocity information and circulation patterns inside a moving aqueous droplet by confocal microscopy, while other investigators (Kashid et al. 2005; Sarrazin et al. 2006) qualitatively compared velocity fields acquired from PIV with CFD simulations, proving the suitability of the experimental technique for these flows. More recently, Fang et al. (2012) proposed a technique to locally enhance DNA concentration by using a plug flow micro-device. PIV velocity data within water plugs were used to locally quantify the shear strain rate, while mixing was investigated by using a continuous dye. Although previous investigations qualitatively related the velocity profiles from PIV to the mixing features, the latter was mainly quantified numerically or experimentally from dye dispersion. Local characterisation of mixing rate via parameters such as circulation time, important for mass transfer operations, is still missing in the literature for liquid-liquid plug flow configurations.

2.2.6 Pressure Drop

Knowledge of pressure drop during two-phase flow in microchannels is essential for the design of energy efficient systems. However, despite its importance only relatively few studies are available in literature concerning pressure drop in liquid-liquid microchannel flows (Chakrabarti et al. 2005; Kashid and Agar 2007; Salim et al. 2008; Jovanović et al. 2011), compared to those available for gas-liquid flows (Triplett et al. 1999; Chen et al. 2002; Kawahara et al. 2002; Kreutzer et al. 2005).

Two-phase pressure drop can typically be correlated with two models, i.e. homogeneous or separated. Homogeneous fluid models are well suited to emulsions and flow with negligible surface forces, where the two-phase mixture can be treated as a single fluid with appropriately averaged physical properties of the individual phases. Separated flow models consider that the two phases flow continuously and separated by an interface across which momentum can be transferred (Angeli and Hewitt 1999). The simplest patterns that can be easily modelled are separated and annular flow (Brauner 1991; Rovinsky et al. 1997; Bannwart 2001). In this case, momentum balances are written for both phases with appropriate interfacial and wall friction factors.

Salim et al. (2008) investigated oil-water two-phase flows in quartz and glass microchannels. Their pressure drop measurements were interpreted by using the homogeneous and Lockhart-Martinelli models, where the two-phase pressure drop is correlated to the pressure drop of each single phase:
$$\left( {\frac{{\Delta {\text{P}}}}{\text{L}}} \right)_{\text{TP}} = \left( {\frac{{\Delta {\text{P}}}}{\text{L}}} \right)_{\text{c}} + \,\upeta \upvarepsilon _{\text{d}} \left( {\frac{{\Delta {\text{P}}}}{\text{L}}} \right)_{\text{c}}$$
(2.2.22)
where (ΔP/L)TP is the two-phase pressure drop per unit capillary length, (ΔP/L)c and (ΔP/L)d are the continuous and dispersed single-phase pressure drops per unit capillary length, respectively. εd is the dispersed phase volume fraction and η is a fitting factor which depends on the wettability of the wall. In the case of quartz microchannel, according to their experimental results η was equal to 0.67, while in the case of glass microchannel it was equal to 0.8.
The homogeneous model is not suitable for plug flow because of the use of dynamic viscosity of the two-phase mixture, the fact that it does not take into account the influence of plug length on the pressure drop, and the absence of surface tension. Salim et al. (2008) also found out that the pressure drop depends on the first injected fluid, and the type of the microchannel material. Although the separated model considers the contributions of each phase separately, it is not suited to plug flow. In the plug flow, pressure drop is usually modelled as a series of unit cells, composed of a dispersed plug and a continuous slug as it can be seen in Fig. 2.11. Frictional pressure drop (ΔPFr) of the individual phases and the pressure drop due to the interfacial effects (ΔPI) need to be taken into account in the calculation of the two-phase pressure drop.
Fig. 2.11

a Unit cell without film, b Unit cell with thin film, c plug flow in the case of a dry wall, and d plug flow in the case of a wetted wall (Jovanović et al. 2011)

The overall pressure drop can be written as:
$$\Delta {\text{P}}_{\text{plug flow}} =\Delta {\text{P}}_{\text{Fr}} +\Delta {\text{P}}_{\text{I}} = (\Delta {\text{P}}_{{{\text{Fr}}, {\text{c}}}} +\Delta {\text{P}}_{{{\text{Fr}}, {\text{d}}}} ) +\Delta {\text{P}}_{\text{I}}$$
(2.2.23)
The frictional pressure drop, ΔPFr is calculated from the Hagen-Poiseuille equation for a cylindrical tube and is expressed as a function of the unit length (LUC = Ld + Lc, where Ld and Lc are the lengths of the dispersed plug and the slug, respectively) and the dispersed phase length fraction (k = Ld/LUC):
$$\Delta {\text{P}}_{{{\text{Fr}},{\text{d}}}} = \frac{{8\upmu_{\text{d}} {\text{u}}_{\text{mix}} {\text{kL}}_{\text{UC}} }}{{{\text{R}}^{2} }}$$
(2.2.24)
$$\Delta {\text{P}}_{{{\text{Fr}},{\text{c}}}} = \frac{{8\upmu_{\text{c}} {\text{u}}_{\text{mix}} (1 - {\text{k}}){\text{L}}_{\text{UC}} }}{{{\text{R}}^{2} }}$$
(2.2.25)
$${\text{u}}_{\text{mix}} = \frac{{{\text{Q}}_{\text{c}} + {\text{Q}}_{\text{d}} }}{\text{A}}$$
(2.2.26)
where μd and μc are the viscosity of the dispersed and continuous phase, respectively, and umix is the superficial velocity which is determined from the total flow rate.
The interface pressure drop, ΔPI is obtained from the Young-Laplace equation:
$$\Delta {\text{P}}_{\text{I}} = \frac{{2\upgamma}}{\text{R}}{ \cos }\uptheta$$
(2.2.27)
Kashid and Agar (2007) investigated the effects of various operating conditions on pressure drop in a PTFE microchannel reactor with a Y-junction as mixing zone. They developed a theoretical prediction for pressure drop based on the capillary pressure and the hydrodynamic pressure drop without the presence of a continuous film and for a constant contact angle between the dispersed plug and the channel wall (Fig. 2.11a).

Their proposed model overestimated the experimental pressure drop, because when a liquid film is present (Fig. 2.11b) there is no direct contact between the dispersed phase plugs and the channel wall, so the contact angle values become different from the dry channel wall case. Moreover as it can be seen in Fig. 2.11c, d the interfacial pressure drop should be different depending on the presence of film or not. More specific, in the case of dry wall, the interfaces of the plug are deformed in the direction of the flow, thus the interfacial pressure drop over the plug is acquired by adding the interfacial pressure drops at the front and back of the plug. In contrast, in the case of wetted wall the interfaces of the plug are deformed in opposite directions, and the interface pressure drop over the plug is acquired by subtracting the interfacial pressure drops at front and back. The front meniscus has a positive contribution to the pressure drop and the rear meniscus has a negative contribution. The frictional pressure drop was calculated by taking into account the superficial velocity of the mixture. However, if a thin film is present then the plug travels at a higher velocity than the continuous phase (Warnier et al. 2008).

Jovanović et al. (2011) tried to overcome these drawbacks by developing a pressure drop model which incorporates the effect of film thickness, surface shape, slug size, and capillary diameter. Furthermore, they determined the parameters with the highest impact on the pressure drop. They investigated two liquid-liquid systems (i.e. water-toluene and ethylene glycol/water-toluene) in fused silica capillaries. They presented two models, i.e. the stagnant film and the moving film. It was found that the film velocity has negligible effect on the pressure drop; therefore the stagnant model was chosen to predict the experimental pressure drops. In their model they also assumed a fully developed Hagen-Poiseuille flow, which is disturbed by the caps of the dispersed phase plug, causing an excess pressure drop. The frictional pressure drop is described by Eqs. (2.2.24) and (2.2.25) for the dispersed and continuous phase, respectively and the interface pressure was described by Bretherton’s solution for the pressure drop over a single bubble in a capillary (Bretherton 1961). The plug flow was modelled as a series of unit cells (Fig. 2.11b).The film at the wall is reducing the radius of the channel through which the dispersed plug is travelling.
$${\text{R}}_{\text{ch}} = {\text{R}} -\updelta$$
(2.2.28)
where δ is the liquid film thickness and is calculated as a function of the Ca number,
$$\updelta = 1.34{\text{RCa}}^{2/3}$$
(2.2.29)
which is valid for δ below 0.01R. In the systems where the continuous phase has a considerably higher viscosity than the dispersed phase the Bretherton’s equation should be corrected by a factor of 22/3 as explained by Schwartz et al. (Schwartz et al. 1986; Bico and Quere 2000). The interface pressure is then calculated by taking into account the Laplace pressure and the change in curvature due to the presence of the liquid film surrounding the plug
$$\Delta {\text{P}}_{\text{I}} = {\text{C}}\left( {3{\text{Ca}}^{{\frac{2}{3}}} } \right)\frac{\upgamma}{\text{ID}}$$
(2.2.30)
Assuming ideally semispherical caps, the constant C, which accounts for the influence of the interface curvature, was found to be 7.16 (Bretherton 1961) for Ca < 5 × 10−3 and We << 1 and for conditions where inertia is absent. Inserting Eqs. (2.2.24), (2.2.25), (2.2.29) and (2.2.30) in Eq. (2.2.23) results in the plug flow pressure drop equation for the stagnant film (ΔPSF) case:
$$\Delta {\text{P}}_{\text{SF}} = \frac{{8{\text{u}}_{\text{p}}\upmu_{\text{d}} {\text{kL}}}}{{({\text{R}} -\updelta)^{2} }} + \frac{{8{\text{u}}_{\text{mix}}\upmu_{\text{c}} \left( {1 - {\text{k}}} \right){\text{L}}}}{{{\text{R}}^{2} }} + \frac{\text{L}}{{{\text{L}}_{\text{UC}} }}{\text{C}}\left( {3{\text{Ca}}} \right)^{{\frac{2}{3}}} \frac{\upgamma}{\text{d}}$$
(2.2.31)
The pressure drop was found to be highly affected by the unit cell size. By changing the flow ratios, the sizes of the continuous and dispersed phases changed, thus varying the total number of interfaces in the system, and consequently the frictional and interface pressure drop terms.

2.2.7 Mass Transfer

The characterisation of mass transfer is essential for the design of the micro-reactor. In liquid-liquid flows most studies have focused on the estimation of overall mass transfer coefficients, while no model based on theory has been developed so far. The overall volumetric mass transfer coefficient (kLα) is a characteristic parameter of a system used to evaluate the performance of the contactors, and is a combination of the mass transfer coefficient (kL), which depends mainly on the diffusivity of solute, characteristic diffusion length and interfacial hydrodynamics, and of the specific interfacial area (α), which depends on the flow pattern. The prediction of the overall volumetric mass transfer coefficient remains difficult due to secondary phenomena, like interfacial instabilities.

Mass transfer coefficients in micro-reactors are much higher than those obtained in conventional macro-contactors as it can be seen in Table 2.4. One common drawback of conventional contactors is the inability to predict precisely flow characteristics and interfacial area, because of the complexities of the governing hydrodynamics. This often leads to uncertainties in the design and causes limitations on the performance than can be achieved. Mass transfer rates in micro-reactors can be up to 2 orders of magnitude higher. In addition, consecutive reactions can be efficiently suppressed by strict control of residence time and its distribution (Kashid et al. 2011).
Table 2.4

kLα of different types of contactors

References

Contactor

α (m2/m3)

kLα (s−1)

Fernandes and Sharma (1967)

Agitated contactor

32–311

(48–83) × 10−3

Verma and Sharma (1975)

Packed bed column

80–450

(3.4–5) × 10−3

Charpentier (1981)

Bubble column

50–600

(5–240) × 10−3

Kies et al. (2004)

• Spray column

• Stirred tank

75–170

100–2000

(15–2.2) × 10−3

(30–400) × 10−3

Dehkordi (2001, 2002)

• Two impinging jets reactor

• Air operated two impinging reactors

1000–3400

350–900

0.28

0.075

Kashid et al. (2007b)

Capillary microchannel, ID = 0.5–1 mm

830–3200

0.88–1.67

There are two transport mechanisms that promote mass transfer in liquid-liquid plug flow, i.e. convection and diffusion (Fig. 2.12). The convection is achieved through the internal circulations within each phase, while the diffusion is due to concentration gradients between a plug and a slug. The diffusive penetration is enhanced more by the internal circulations that renew the interface (Burns and Ramshaw 2001; Dummann et al. 2003; Kashid et al. 2005; Ghaini et al. 2010).
Fig. 2.12

Schematic representation of the transport mechanisms within a plug. (Ghaini et al. 2011)

In liquid-liquid systems several parameters that affect the performance of the extractor, such as channel size, flow patterns, fluid properties, mixing zone, and flow orientation, have been investigated (Burns and Ramshaw 2001; Zhao et al. 2007; Kashid et al. 2007b; Dessimoz et al. 2008; Su et al. 2010; Ghaini et al. 2010; Tsaoulidis et al. 2013a; Tsaoulidis et al. 2013b; Sarrazin et al. 2008). A number of investigations have focused on the development of numerical and empirical models to describe the mass transfer for fixed interface location (Kashid et al. 2007a; Raimondi and Prat 2011; Skelland and Wellek 1964). Harries et al. (2003) developed a numerical model during liquid-liquid plug flow to investigate the hydrodynamics within both segments and the mass transfer of dissolved chemical species within and across the segments interface.

Their model showed good agreement with experimental results. Raimondi et al. (2008) carried out numerical simulations of the mass transfer during liquid-liquid plug flow in square microchannels, where it was assumed that mass transfer did not deform the interface, since the hydrodynamics were decoupled from the mass transfer. Kashid et al. (2010) performed dimensional analysis to obtain a relationship (Eq. 2.2.32) between the mass transfer coefficient and various independent variables. In their studies however, they did not take into account the effect of contacting geometry and microchannel shape.
$${\text{k}}_{\text{L}}\upalpha\frac{\text{L}}{{{\text{u}}_{\text{mix}} }} = {\text{aCa}}^{\text{b}} {\text{Re}}^{\text{c}} (\frac{\text{ID}}{\text{L}})^{\text{d}}$$
(2.2.32)
As far as the gas-liquid systems are concerned, a number of models for the prediction of the kLα have been developed based on both empirical correlations, and on film and penetration theory. These models provide estimates of the mass transfer coefficient in the continuous liquid phase, while the mass transfer resistance in the gas phase is considered negligible. In these models the individual contributions of the caps of the plugs, and of the fully developed film separating the plugs from the channel wall are estimated. Berčič and Pintar (1997) proposed a model for the calculation of the mass transfer coefficient in small channels (Eq. 2.2.33), that includes only the contribution of the caps because of the rapid saturation of the film, which is given by
$${\text{k}}_{\text{L}}\upalpha = \frac{{0.111{\text{u}}_{\text{p}}^{1.19} }}{{((1 -\upvarepsilon_{\text{d}} ){\text{L}}_{\text{UC}} )^{0.57} }}$$
(2.2.33)
However, the absence of any parameter related to the channel size limits the application of the model to different two-phase systems. Van Baten and Krishna (2004) and Irandoust and Andersson (1989) included in their models the contributions of both bubble caps and film (Eq. 2.2.34). Van Baten and Krishna (2004) evaluated the contribution of the caps according to the Higbie penetration theory (Eq. 2.2.35), whilst the transfer through the film was obtained based on mass transfer in a falling film in laminar flow (Eqs. 2.2.36 and 2.2.37).
$${\text{k}}_{\text{L}}\upalpha = {\text{k}}_{{{\text{L}},{\text{cap}}}}\upalpha_{\text{cap}} + {\text{k}}_{{{\text{L}},{\text{film}}}}\upalpha_{\text{film}}$$
(2.2.34)
$${\text{k}}_{{{\text{L}},{\text{cap}}}}\upalpha_{\text{cap}} = 2\frac{\sqrt 2 }{\uppi}\sqrt {\left( {\frac{{{\text{D}}_{\text{c}} {\text{u}}_{\text{p}} }}{\text{ID}}} \right)} \frac{4}{{{\text{L}}_{\text{UC}} }}$$
(2.2.35)
$${\text{k}}_{{{\text{L}},{\text{film}}}}\upalpha_{\text{film}} = \frac{2}{{\sqrt\uppi }}\sqrt {\frac{{{\text{D}}_{\text{c}} {\text{u}}_{\text{p}} }}{{{\text{L}}_{\text{film}} }}} \frac{{4{\text{L}}_{\text{film}} }}{{{\text{ID L}}_{\text{UC}} }},\quad {\text{Fo}}\,{ < }\, 0. 1$$
(2.2.36)
$${\text{k}}_{{{\text{L}},{\text{film}}}}\upalpha_{\text{film}} = 3.41\frac{{{\text{D}}_{\text{c}} }}{\updelta}\frac{{4{\text{L}}_{\text{film}} }}{{{\text{ID L}}_{\text{UC}} }},\quad {\text{ Fo}}\, > \,1$$
(2.2.37)
$${\text{Fo}}_{\text{film}} = \frac{{{\text{D}}_{\text{c}} {\text{L}}_{\text{film}} }}{{{\text{u}}_{\text{p}}\updelta^{2} }}$$
(2.2.38)
Similarly, Vandu et al. (2005) suggested a model based only on the contribution of the film in circular and square capillaries.
$${\text{k}}_{\text{L}}\upalpha = {\text{C}}\sqrt {\frac{{{\text{D}}_{\text{c}} {\text{u}}_{\text{g}} }}{{{\text{L}}_{\text{UC}} }}} \frac{1}{\text{ID}}$$
(2.2.39)
Apart from the overall volumetric mass transfer coefficient (kLα) the mass transfer performance of a system can also be characterised by the extraction efficiency (%Eeff). The extraction efficiency is the ratio of the amount transferred to the maximum amount transferable.
$$ {\text{\% E}}_{\text{eff}} = \frac{{[{\text{C}}]_{{{\text{aq}},{\text{fin}}}} - [{\text{C}}]_{{{\text{aq}},{\text{init}}}} }}{{[{\text{C}}]_{{{\text{aq}},{\text{eq}}}} - [{\text{C}}]_{{{\text{aq}}.{\text{init}}}} }} $$
(2.2.40)
Moreover, the mixing in the liquid-liquid system can be characterised by dimensionless numbers, such as, Sherwood number (Sh), which is the ratio of convective mass transfer to the molecular diffusion, and Schmidt number (Sc), which is the ratio of the viscous diffusion rate to the molecular diffusion. In addition to these, the Fourier number (Fo) can also give an idea about the dynamics of diffusive transport process.
$${\text{Sh}} = \frac{{{\text{k}}_{\text{L}} {\text{L}}^{ *} }}{\text{D}} = \frac{\text{convective mass transfer}}{\text{molecular diffusion}}$$
(2.2.41)
$${\text{Sc}} = \frac{\upmu}{{\uprho{\text{D}}}} = \frac{\text{viscous diffusion}}{\text{molecular diffussion}}$$
(2.2.42)
$${\text{Fo}} = \frac{{\uptau{\text{D}}}}{{{\text{R}}^{2} }} = \frac{\text{species diffusion rate}}{\text{species storage rate}}$$
(2.2.43)
In Table 2.5 the mass transfer coefficients during liquid-liquid plug and parallel flow are presented. The mass transfer performance of different types of micro-reactors was investigated for reacting and non-reacting systems.
Table 2.5

Mass transfer coefficients during liquid-liquid plug and parallel flow

References

Multi-phase system

Conditions

Equation

kLα (s−1)

Burns and Ramshaw (2001)

• Kerosene/acetic acid/water + NaOH

• Glass chip reactor, dH = 380 μm

• U < 35 mm/s

• Plug flow

\({\text{k}}_{\text{L}} \alpha = \frac{1}{{\uptau_{re} }}{ \ln }(\frac{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}}}} - \,\,[{\text{C}}]_{{{\text{aq}},{\text{init}}}} }}{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}}}} - \,\left[ {\text{C}} \right]_{{{\text{aq}},{\text{fin}}}} }})\)

Order of magnitude of 0.5

Kashid et al. (2007b)

• Kerosene/acetic acid/water

• Water/iodine/kerosene

• Water/succinic acid/n-butanol

• Y-junction and capillary tubing (Teflon), dc = 0.5–1 mm,

L = 100–300 mm

• U = 10–70 mm/s

• Plug flow

\({\text{k}}_{\text{L}} \alpha = \frac{1}{{\uptau_{re} }}{ \ln }(\frac{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}}}} - [{\text{C}}]_{{{\text{aq}},{\text{init}}}} }}{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}}}} - \left[ {\text{C}} \right]_{{{\text{aq}},{\text{fin}}}} }})\)

0.02–1.4

Zhao et al. (2007)

• Water/succinic acid/n-butanol

• Stainless steel microchannel,

T-junction, dc = 0.4–0.6 mm

• U = 0.005–2.5 m/s

• Parallel flow

\({\text{k}}_{\text{L}} \alpha = \frac{1}{{\uptau_{re} [1 + \frac{{Q_{\text{aq}} }}{{{\text{mQ}}_{\text{or}} }}]}}{ \ln }(\frac{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}},{\text{inlet}}}} - \,[{\text{C}}]_{{{\text{aq}},{\text{inlet}}}} }}{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}},{\text{outlet}}}} - \,\left[ {\text{C}} \right]_{{{\text{aq}},{\text{outlet}}}} }})\)

0.067–17.35

Dessimoz et al. (2008)

• Hexane/trichloroacetic acid/water + NaOH

• Glass chip reactor, T-,Y-junction, dc = 269–400 μm

• U < 50 mm/s

• Plug flow

\({\text{k}}_{\text{L}} \alpha = \frac{1}{{\uptau_{re} }}{ \ln }(\frac{{\left[ {\text{C}} \right]_{\text{or}} }}{{\left[ {\text{C}} \right]_{{{\text{or}},0}} }})\)

0.2–0.5

Ghaini et al. (2010)

• Saturated n-butyl formate-water

• Y-junction and capillary tubing, dc = 1 mm

• U = 10–70 mm/s

• Plug flow

\({\text{k}}_{\text{L}} \alpha = \frac{1}{{\uptau_{re} }}{ \ln }(\frac{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}}}} - [{\text{C}}]_{{{\text{aq}},{\text{init}}}} }}{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}}}} - \left[ {\text{C}} \right]_{{{\text{aq}},{\text{fin}}}} }})\)

0.7–1.57

Kashid et al. (2011)

• Water-acetone-toluene

• T-square (TS): dH = 400 μm, L = 56 mm, U = 0.1–0.42 m/s

• T-trapezoidal (TT): dH = 400, L = 75 mm, U = 0.1–0.42 m/s

• Y-rectangular (YR): dH = 269 μm, L = 40 mm, U = 0.228–0.9 m/s

• Concentric (CC): dc = 1600 μm, L = 200 mm, U0.008–0.083 m/s

• Caterpillar (CT): dH = 150 μm, L = 5 mm, U = 0.74–4.44 m/s

• Plug flow

\({\text{k}}_{\text{L}} \alpha = \frac{1}{{\uptau_{re} [\frac{1}{{{\text{K}}_{{\upvarepsilon_{1} }} }} + \frac{1}{{1 - \varepsilon_{1} }}]}}{ \ln }(\frac{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}}}} - [{\text{C}}]_{{{\text{aq}},{\text{init}}}} }}{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}}}} - \left[ {\text{C}} \right]_{{{\text{aq}},{\text{fin}}}} }})\)

0.01–0.74

Assmann and von Rohr (2011)

• Water-vanillin-toluene

• PDMS capillary reactor: dc = 300 μm, L = 13.5 mm

• U > 0.08 m/s

\({\text{k}}_{\text{L}} \alpha = \frac{1}{{\uptau_{re} }}{ \ln }(\frac{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}}}} - [{\text{C}}]_{{{\text{aq}},{\text{init}}}} }}{{\left[ {\text{C}} \right]_{{{\text{aq}},{\text{eq}}}} - \left[ {\text{C}} \right]_{{{\text{aq}},{\text{fin}}}} }})\)

5.5–11

2.3 Ionic Liquid-Based Extractions: Reprocessing of Spent Nuclear Fuel

Nuclear energy from fission can provide substantial amounts of carbon free electricity and process heat. However, one of the main concerns in the use of the nuclear power generation is the management of the irradiated nuclear fuel from the reactor (spent fuel) which can remain toxic for thousands of years. Efficient spent fuel reprocessing through a series of operations can separate uranium to be reused as reactor fuel and reduce the volume and toxicity of the rest of the spent fuel that needs to be stored or disposed. One of the common operations in reprocessing is extraction that involves the flow of two immiscible liquids. Commercially the PUREX process is commonly used where uranium(VI) is extracted from nitric acid solutions of the spent fuel using extractants such as tributylphosphate (TBP) in diluents of large aliphatic chain hydrocarbons (i.e. kerosene, dodecane) (Giridhar et al. 2008). The need to use volatile organic compounds (VOCs) as solvents or the subsequent generation of VOCs, introduce safety risks (Visser and Rogers 2003). Recently ionic liquids (ILs) have been suggested as alternatives to organic solvents because of their negligible volatility and flammability at common industrial conditions (Rogers and Seddon 2002; Plechkova and Seddon 2008), which reduce solvent loss and make them inherently safe and environmentally friendly.

Ionic liquids (ILs) are salts with low melting points (below 100 °C) composed exclusively of ions (Wasserscheid and Welton 2008; Chiappe and Pieraccini 2005). The ability to tune the properties of ionic liquids by the choice of the anion and the cation (Fig. 2.13) and optimise them for a particular application (Seddon et al. 2000) has expanded significantly their use in synthesis, catalysis and separations in recent years (Binnemans 2007; Murali et al. 2010). Their high resistance to radiation (much higher than the commonly used TBP/kerosene mixtures) makes ionic liquids particularly suitable for extractions in spent fuel reprocessing.
Fig. 2.13

Typical cations and anions for the composition of ionic liquids

For use in extraction applications with aqueous solutions, hydrophobic ionic liquids are required. The hydrophobicity of the ionic liquids depends on the alkyl chain length of the associated cation and on the anion. Recently, the bis(trifluoromethylsulfonyl)imide anion, [(CF3SO2)2N] (abbreviated to [Tf2N]), has become a popular anion choice for synthesizing hydrophobic ionic liquids that are chemically and thermally more robust and of lower viscosity compared to the majority of ILs (Binnemans 2007).

2.3.1 Studies on the Extraction Mechanisms

Studies of uranium(VI) extraction from nitric acid solutions to ionic liquids suggest different mechanisms of the extraction, i.e. cation exchange, anion exchange and solvation, depending on the nature of extractant, concentration of counteranion, structure of the ionic liquid and the aqueous phase composition (Dietz and Dzielawa 2001; Wei et al. 2003) which are different to those occurring in traditional solvents. Given the substantial differences between ILs and conventional molecular solvents, it is conceivable that the complexes found in ILs are different from the complexes known in molecular solvents. The dioxouranium(VI) extraction proceeds via a double cationic exchange at low acidity and via an anionic exchange at high acidity. Many equilibrium studies have been performed so far to identify the extraction mechanisms (Dietz and Stepinski 2008; Giridhar et al. 2008; Billard et al. 2011b; Wang et al. 2009; Murali et al. 2010). According to the mechanisms, ionic liquid is released to the aqueous phase and metal ions are extracted. The ion exchange processes results in the loss of the ionic liquid phase and contaminate the aqueous phase.
$$ {\begin{aligned} & {\text{UO}}_{2}^{ 2+} + {\text{C}}_{4} - {\text{mim}}^{+} + {\text{H}}^{+} + {\text{2TBP}} \leftrightarrow \, \left[ {{\text{UO}}_{2} \left( {\text{TBP}} \right)_{2} } \right]^{2+} + {\text{H}}^{+} + {\text{C}}_{4} - {\text{mim}}^{+} \left( {{\text{cation}}\,\,{\text{exchange}}} \right) \\ & {\text{UO}}_{2}^{ 2+} + {\text{3NO}}_{3}^{-} + {\text{2TBP}} + {\text{Tf}}_{2} {\text{N}}^{-} \leftrightarrow \, \left[ {{\text{UO}}_{2} \left( {{\text{NO}}_{3} } \right)_{3} \left( {\text{TBP}} \right)_{2} } \right]^{-} + {\text{Tf}}_{2} {\text{N}}^{-} \left( {{\text{anion}}\,\,{\text{exchange}}} \right) \\ & {\text{UO}}_{2}^{2+} + {\text{2NO}}_{3}^{-} + {\text{2TBP}} \leftrightarrow {\text{UO}}_{2} \left( {{\text{NO}}_{3} } \right)_{2} \left( {\text{TBP}} \right)_{2} \left( {{\text{neutral}}\,\,{\text{exchange}}} \right) \end{aligned}} $$
The equilibrium distribution coefficients DU for IL with the same anionic part (NTf 2 ) but different cationic parts can be seen in Fig. 2.14. As it can be seen at low initial nitric acid concentration,[HNO3]aq,init, values of the distribution coefficients strongly depend on the cationic part of the IL. By contrast at high [HNO3]aq,init the values of KU follow a similar curve for the different ILs, suggesting that the extraction mechanism is independent of the cationic part of the IL. The [HNO3]aq,init value at which the mechanism is changing from cation-dependent to cation independent is varying from 0.02 M for [C10mim][NTf2] to ca. 1.5 M for [C4mim][NTf2].
Fig. 2.14

Variation of the dioxouranium(VI) extraction coefficient as a function [HNO3]aq,init, at [TBP]IL,init. = 1.1 M. (Dietz and Stepinski 2008): ∆—[C10mim][NTf2], ■—[C8mim][NTf2], ◊—[C5mim][NTf2]. (Giridhar et al. 2008): ♦—[C4mim][NTf2]. (Billard et al. 2011b): o—[C4mim][NTf2]. [U] = 10−2 M or 10−3 M. (Billard et al. 2011b)

Regarding the ionic liquid [C10mim][NTf2], the shape of the distribution curve indicates that the uranium(VI) extraction involves partitioning of the neutral dioxouranium(VI)-TBP-nitrato complex as observed in alkanes. This is illustrated in Fig. 2.15, where one can notice the dependence of KU on TBP concentration which resembles that obtained for dodecane. This observation suggests that the hydrophobicity of the IL cation affects the extraction of neutral compounds (Cocalia et al. 2005).
Fig. 2.15

Dependency of the uranium distribution ratio, KU, on TBP concentration in [C10mim][NTf2] at constant (3 M) nitric acid concentration (Dietz and Stepinski 2008)

Ionic liquids are in general non-coordinating and in the absence of an extractant, do not extract metal ions from the aqueous phase (Fig. 2.16). To enable extractions in spent fuel reprocessing many investigators have dissolved in the ionic liquids known extracting moieties (other than TBP) such as CMPO (octyl(phenyl)-N,N-diisobutylcarbamoylmethylphosphine oxide) (Visser and Rogers 2003; Nakasima et al. 2003), TTA (2-thenolyltrifluoroacetone) (Jensen et al. 2003), HDEHP (bis(2-ethylhexyl)phosphoric acid) or Cyanex-272 (Cocalia et al. 2005).
Fig. 2.16

Comparison of distribution ratios for the extraction of U(VI) by [bmim][PF6], [bmim][NTf2] and 1.1 M TBP/diluent as a function of the initial nitric acid concentration. The diluents are n-dodecane (DD), [bmim][NTf2] and [bmim][PF6] (Vasudeva Rao et al. 2008)

In traditional solvents such as dodecane, the apparent stoichiometry of dioxouranium(VI) extraction by TBP is UO2 2+ + 2NO3  + 2TBP ↔ UO2(NO3)2(TBP)2, which suggest that the extracted dioxouranium(VI) forms a complex with two nitrates and TBP (Cocalia et al. 2005; Vasudeva Rao et al. 2008). Comparisons of TBP/ionic liquid mixtures with the TBP/dodecane system showed different trends as a function of the nitric acid concentration (Fig. 2.16). At low nitric acid concentrations, [C4mim][NTf2] exhibits a high extraction of dioxouranium(VI) from low nitric acid concentrations in contrast to TBP/dodecane. TPB/dodecane system increases till [HNO3]aq,init = 3 M and then decreases, which is attributed to the non-availability of free TBP, due to significant extraction of nitric acid and also to the conversion of dioxouranium(VI) ion to the less extractable anionic dioxouranium(VI) nitrate species at high [HNO3]aq,init. The significant extraction of dioxouranium(VI) by the ILs at high nitric acid concentrations can be attributed to an ion exchange mechanism in which the UO2(NO3) 3 anions are exchanged with the anion of the ionic liquids.

2.3.2 Task Specific Ionic Liquids

Another promising approach for metal extraction lies in the concept of task-specific ionic liquids (TSILs). These compounds, consisting of extracting entities grafted onto the cation of the ionic liquid combine the properties of ionic liquids with those of extracting compounds, and thus behave both as the organic phase and the extracting agent, suppressing the problems encountered through extractant/solvent miscibility and facilitating species extraction and solvent recovery. One case of TSILs is the inclusion of quaternary ammonium cations in [Tf2N] based ionic liquids which gave in some cases very high partition coefficients for uranium(VI). Studies on the extraction of uranium(VI) using ionic liquids based on quaternary ammonium cation and bearing phosphoryl groups resulted in distribution coefficients DU of 170 (Ouadi et al. 2007).

Bell and Ikeda (Bell and Ikeda 2011) investigated the key factors for optimising the separation of uranium(VI) from nitric acid solutions using novel hydrophobic ammonium based ionic liquids (Fig. 2.17). It was found that the extraction of uranium(VI) from the aqueous phase to ionic liquid phase could proceed through either a cationic exchange at low nitric acid concentrations, and neutral partitioning or anionic exchange mechanism at higher nitric acid concentration. The findings seem to be in agreement with those of the previous investigators.
Fig. 2.17

Generic structure of the ionic liquids synthesized by Bell and Ikeda (2011)

2.3.3 Physicochemical Properties of Ionic Liquids

The physical properties of ionic liquids play an important role on the efficiency of phase separations. In ionic liquid-based extractions, the viscosity of an ionic liquid affects the mass transfer efficiency. For imidazolium-based ionic liquids (Cnmim), the viscosity increases by increasing the alkyl chain length due to the increased van der Waals interactions, while the choice of the anion also affects the viscosity as it participates in hydrogen bonding (Kagimoto et al. 2010). For [Cnmim][NTf2] ionic liquids an almost linear increase of the viscosity to the length of the alkyl group has been observed (Dzyuba and Bartsch 2002). It is known that water has a strong impact on the viscosity of ILs. Even when ionic liquids are immiscible with water they absorb some water. The amount of water present in the ionic liquid at equilibrium depends also on the initial HNO3 concentration of the aqueous phase. TBP was also found to affect the amount of water absorbed at low nitric acid concentrations (see Fig. 2.18) (Billard et al. 2011b; Giridhar et al. 2008).
Fig. 2.18

Variation of the water in the [C4mim][NTf2] phase as a function of [HNO3]aq,init, for various values of TBP loading. •—[TBP]IL,init = 0 M; □—[TBP]IL,init = 0.18 M; o—[TBP]IL,init = 0.55 M; ▲—[TBP]IL,init = 1.1 M (Billard et al. 2011b)

Decreasing the solubility of ionic liquids in water plays an important role in ionic liquid-based extraction. The anion has the primary effect on water miscibility, whilst the cation seems not to affect miscibility much (Seddon et al. 2000). The order of increasing hydrophobicity for the anions is Br, Cl < [BF4] < [PF6] < [NTf2] (Toh et al. 2006). Metal ions are poorly soluble in ILs except when coordinated with, or solvated by, hydrophobic molecules added to the IL phase, or with hydrophilic complexing anions that can facilitate metal ion transport into the IL phase.

The densities of ionic liquids are also affected by the choice of the cation and anion. For imidazolium ionic liquids the density decreases slightly as the alkyl chain of the cation increases in length. In addition, the absoption of water by ionic liquids by increasing nitric acid concentration can also cause a decrease in the density (Giridhar et al. 2004). Regarding imidazolium-based ionic liquids, by increasing the alkyl chain it was found that the surface tension decreased due to the orientation of hydrocarbon tails on the surface (Kilaru et al. 2007). The vapour pressure of an ionic liquid is usually unmeasurable at room temperature. Studies on the thermal stability of ionic liquids showed that the type of the associated anion has the primary effect on the thermal stability of the ionic liquids (Holbrey and Seddon 1999). Although ionic liquids are not flammable, studies showed that they are not safe to use near fire, since the products that formed during thermal decomposition for some ionic liquids are sensitive to combustion (Smiglak et al. 2006). Another outstanding property of the ionic liquids is the wide electrochemical window that they exhibit, which enables them to be unaffected from oxidation or reduction for a wide range of voltage. However, an increase in the water content of ionic liquids would narrow their electrochemical window. Determination of the toxicity of the ionic liquid is also important, since extractions may result in the release of ionic liquid, which if hazardous will cause further contamination. It should be noted that there are cases, where ionic liquids exhibit even more toxicity to microorganisms than VOCs. The toxicity of imidazolium based ionic liquids depends mainly on the length of the alkyl chain; the shorter the chain length the lower the toxicity (Romero et al. 2008). Moreover, studies on the radiolysis of ionic liquids, when subjected to doses of gamma radiation, showed better stability compared to TBP/kerosene mixtures (Allen et al. 2002).

2.3.4 UV-Vis Spectroscopy

Differences between ionic liquids and traditional solvents would give rise to differences in the stoichiometry of the extracted species. Although slope analysis may be sufficient to determine such stoichiometries, the exact amount of nitrate ions in the aqueous phase and of the free ligand in the ionic liquid phase are largely unknown and this hampers the use of this graphical method. Different inner-coordination environments are observed for the dioxouranium(VI)-nitrate complexes formed in the different ionic liquids and other organic solvents (dodecane). Qualitative differences in the coordination environment of the extracted dioxouranium(VI) species are implied by changes in peak intensity patterns and locations for UV-Vis spectral bands when the solvent is changed (Bell and Ikeda 2011). Optical absorption spectra have proven useful in distinguishing differences in the coordination environment in organic solvents. Given the complexity of the ionic liquid medium, speciation of dioxouranium(VI) complexes is not an easy task. UV-Vis spectroscopy is useful technique for the specification of uranium(VI) complexes, because each oxidation state of uranium(VI) gives a typical spectrum. Although the dioxouranium(VI) ion has no f-electrons, electronic transitions are possible between the molecular orbitals formed by interaction between ligand and dioxouranium(VI) atomic orbitals. The absorption spectra are in the 350--525 nm range. The differences in the coordination environment between ILs and conventional solvents have been under investigation in the last few years. Studies of the spectra of uranium(VI) containing solutions in ionic liquids ([C10mim][NTf2]) and in dodecane after contacting with the appropriate uranium(VI)/HNO3 solutions showed that there are equivalent dioxouranium(VI) inner sphere coordination environments in both solvents (Cocalia et al. 2005). The typical spectra of the ligands have a minor influence on the spectral fine structure, while water has a pronounced effect on the spectroscopic behaviour of dioxouranium(VI) in ionic liquids with weakly coordinating anions (Nockemann et al. 2007). The UV-Vis spectra of the ionic liquid phase ([C4mimNTf2]) after the extraction of uranium(VI) from nitric acid solutions are shown in Fig. 2.19. Because of the low molar absorption coefficient of uranium(VI) in ILs the concentration of dioxouranium(VI) should be sufficiently high (ca. 10−2 M). It can be seen that the excitation peaks of dioxouranium(VI) in the ionic liquid have been slightly shifted compared to that of dioxouranium(VI) in the aqueous phase, because the chemical environment in the IL is probably more favourable for the formation of a dioxouranium(VI)-nitrate acid complex (Wang et al. 2009). The absorption shape is changing as the nitric acid concentration is increasing, which implies a change in the stoichiometry of the extracted species from low to high acidities of the aqueous phase.
Fig. 2.19

a Aqueous phase spectra of uranium(VI) before extraction; b IL-phase spectra after extraction of uranium(VI) from the aqueous phase into [bmim][NTf2]. Extraction of uranium(VI) in 3 M HNO3 reaches 95 % with 30 %v/v TBP in the IL phase (Wang et al. 2009)

2.4 Overview

The hydrodynamic behaviour of two-phase flows and particularly of plug flow has been extensively studied by many investigators. However, most of the studies involved conventional fluids and little is known concerning the hydrodynamics when ionic liquids are involved. In addition, studies of liquid-liquid flows are usually limited to either sub-millimetre channels or to much larger ones, but not for channels with few millimetres in diameter. Moreover, the reprocessing of spent nuclear fuel by using ionic liquids seems a promising and interesting method. A number of investigations have been conducted on the extraction of uranium(VI) from nitric acid solutions by TBP/ionic liquid mixtures. However, all the extractions with ionic liquids have been carried out in equilibrium, while no reported cases of continuous extraction during plug flow are available.

In the following studies, the hydrodynamics and mass transfer during liquid-liquid flow with ionic liquids in channels with a range of diameters are presented. Flow patterns, as well as several hydrodynamic characteristics, such as plug length, plug velocity, film thickness, and pressure drop have been investigated, whilst predictive correlations have been proposed. In addition, continuous extractions of uranium(VI) with ionic liquids were studied during plug flow. Finally a numerical finite element model for the hydrodynamics and mass transfer was developed.

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Chemical Engineering DepartmentUniversity College LondonLondonUK

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