Segmented Microflows as a Tool for Optimization of Mass Transfer in

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Kinetics, Catalysis, and Reaction Engineering

Segmented micro-flows as a tool for optimization of mass transfer in liquid-liquid extraction: application at the extraction of europium (III) by a malonamide Axel Vansteene, Jean-Philippe Jasmin, Gérard Cote, and Clarisse Mariet Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b02079 • Publication Date (Web): 07 Aug 2018 Downloaded from http://pubs.acs.org on August 13, 2018

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Industrial & Engineering Chemistry Research

Segmented micro-flows as a tool for optimization of mass transfer in liquidliquid extraction: application at the extraction of europium (III) by a malonamide Axel Vansteene a, Jean-Philippe Jasmin a, Gérard Coteb. Clarisse Mariet*a a)

Den - Service d’Etudes Analytiques et de Réactivité des Surfaces (SEARS), CEA, Université

Paris-Saclay, F-91191, Gif sur Yvette, France. b)

PSL Research University, Chimie ParisTech - CNRS, Institut de Recherche de Chimie Paris,

75005, Paris, France. KEYWORDS: Microfluidics; Liquid-liquid extraction, Microsystem, Reactive transfer, Radiochemistry; Spent nuclear fuel.

ABSTRACT: Segmented flows in T-junction glass microchannels are investigated as a tool for the study of liquid-liquid extraction kinetics of europium (III) by a malonamide. They allow to reach higher extraction yields compared with laminar flows, for a same extraction system. After the

range of volume ratio reached in microsystems and the thickness of the organic film between the

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aqueous plugs and the microchannel walls are determined, the extraction yields in microsystems and at equilibrium are compared. A definition of a pseudo-kinetic coefficient, K, is proposed, as a lower bound limit for the chemical forward coefficient kf. The evolution of this pseudo-kinetic coefficient is investigated as a function of the droplet velocity, and the diffusion-limited regime is identified. A model for the evolution of K is then proposed and the maximum value for K, reached for a velocity of the droplets over 20 cm.s-1, is compared with literature values.

INTRODUCTION Liquid-liquid extraction commonly known as solvent extraction is used for separating the components of a solution by distributing them between two immiscible liquid phases, especially in the nuclear field. The effective Plutonium and Uranium Recovery by EXtraction (PUREX) process demonstrated selectivity and safety for the nuclear industry1. Numerous processes based on liquid-liquid extraction are developed and envisioned like Trivalent Actinide-Lanthanide Separation by Phosphorus reagent Extraction from Aqueous (TALSPEAK)2, and the innovative-Selective ActiNide EXtraction (i-SANEX) process3. However, the sustainable development of nuclear energy may rely on innovative recycling scenarios (e.g. Pu multi-recycling and americium recycling)4-6. Developments of advanced reprocessing technologies are directed towards the reduction of waste volumes and hazardousness, minimizing the proliferation risk and reducing the reprocessing costs. Potential future fuel reprocessing requires the use of new extractant molecules, exhibiting higher efficiency and more specific selectivities and stability under irradiation. Given fast extraction kinetics (maximal extraction duration of a few minutes) are needed to enable the use of the extractant at an industrial scale7, 8, the acquisition of the kinetic data is of great interest. Most often, the determination of the chemical reaction coefficients is performed with macroscopic tools which can be classified into two categories: i) tools characterized by a high dispersion of phases, but for which the interfacial area is unknown; ii) tools with controlled interfacial area for which the turbulence and dispersion are weak. Among them, a distinction can be made between tools in which the two immiscible


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phases are continuous (Lewis cell9, Nitsch cell10, rotating diffusion11 or rotating membrane cells12) and those in which one phase is dispersed and the other continuous (single drop technique)13. These tools have disadvantages. First, they necessitate a significant consumption of reagents that can be costly, the interfacial area is sometimes poorly controlled, and most often cannot be adjusted. In addition, most experimentations are device-dependent, and performed in the diffusion regime. The development of a fast and accurate new kinetic data acquisition methodology is an important issue. In order to be effective, the device used must have three key properties: (1) constant and well known specific interfacial area; (2) fast mixing of the two immiscible liquid phases, in order to operate in the kinetic regime, as opposed to the diffusion regime; (3) rapid and high-purity phase settling and separation14. Hydrodynamics in microsystems offer some benefits for biphasic transfer reactions. In addition to the increase in the specific interfacial area15, the segmentation of flow promotes mixture with advective movements. Indeed, within a drop flowing in a micro-channel, the speed profile is not uniform and contributes to the renewal of compounds at the interface15-22. Mass transfer is therefore a priori favored. Moreover, by controlling the hydrodynamics of the continuous and dispersed phases, it is possible to adjust the size of the drops accurately and so to control and to vary not only the agitation in the drops, but also the specific interfacial area

23-28

. Works have been made on the transfer of mass with segmented

flows in microsystems. The majority of studies covers simple transfer reactions16, 29-31. Reactive transfer of radionuclides has only rarely been implemented up to now. Extraction of U (VI) by TBP in segmented flow nitric acid media has been studied by Tsaoulidis et al.22, 32 and by Darekar et al.33, 34. The kinetics of extraction of 13 lanthanides and americium were determined by controlling the specific interfacial area created by segmented flow35 . In the present work, the extraction properties of the chemical system Eu(III) in HNO3 / dimethyldibutyltetradecylmalonamide (DMDBTDMA) in n-dodecane previously investigated by Hellé et al.36 in parallel flows in a Y-Y junction are revisited with segmented flows in microchannels. Indeed, the best yield obtained for Eu extraction was equal to (26.2 ± 1.0) % due to the necessity to impose


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Va Q ≈ a ≈16.7 Vo Qo

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to keep a centered interface to achieve easy phase separation at the outlet of the chip. This

experimental tool suffered from both maximum yield limitation due to volume ratio constraints and transfer rate limitations due to the quasi-absence of convection within the two liquid phases, which enhances mass transport. Due to the larger range of phase volume ratios which can be operated in segmented flows compared to parallel flows, first, a special attention is paid to the influence of this parameter on the yield of europium extraction at the equilibrium, i.e., from a thermodynamic point of view. Secondly, the effects of droplet velocity and specific interfacial area on the kinetics of europium (III) extraction in droplet-based microfluidic systems are investigated with the objective to optimize the rate of mass transfer and the efficiency of europium extraction in the chip. Then a pseudo-kinetic coefficient is determined.

EXPERIMENTAL SECTION Experimental set-up. The experimental set-up used for the extraction of Eu(III) from 4 M nitric acid by DMDBDTDMA dissolved in n-dodecane is schematically depicted in Fig. 1. Two Mitos P-Pumps (Dolomite, UK) were used to feed the aqueous and organic phases into two 0.1 mm T-junction hydrophobic glass chips. The ultra-smooth glass channels were hydrophobized using silanization37. A sketch of the two 0.1mm ID T-junction chips (top-view) from Dolomite (Dolomite, UK) is provided in Fig. 1-b. The channel length in which segmented flow occurred comprised two sections: the microchannel itself and the PEEK tubing from the outlet of the chip to the phase separator. Two outlet microchannel lengths were used: 27.8 cm (Fig. 1-b top) and 1.125 cm (Fig. 1-b bottom) in order to reach a large range of droplets velocity. The tubing was chosen to match the internal diameter (0.1 mm ID) and surface properties (hydrophobic) of the microchannel, in order to prevent any disruption in the segmented flow. Its length was chosen to be 10 cm. As a consequence, the total extraction lengths tested were equal to 37.8 cm and 11.1 cm. The aqueous phase was injected perpendicularly to the main channel in order to be dispersed in the organic continuous phase, which preferentially wets the hydrophobic microchannel walls.


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Then, the dispersed phase is the aqueous phase and the organic phase is the continuous one. After the outlet tubing, an Asia FLLEX module (Syrris Ltd., UK), with a separator dead volume of 100 µL, was used as a continuous phase separator, operated via the application of a hydrophilic cross-membrane pressure ranging from 0.3 to 0.9 bar. Therefore, the aqueous segmented flow was forced to cross the membrane, and a pure aqueous phase was collected at the outlet of the module. The aqueous phase was analyzed for Eu(III) concentration using inductively-coupled plasma mass spectrometry (ICP-MS) measurements with a 7700 x Agilent Technologies spectrometer. A high-speed camera (Photron Mini AX-100) was mounted on a digital inverted microscope (DEMIL LED Leica) equipped with an objective lens with a 40 times magnification and used for direct image acquisition of the segmented flow in the microchannel, with adjustable frame rate, from 2,000 to 10,000 fps depending on droplet velocities. The recorded videos were analyzed using a droplet morphometry and velocity software (DMV)38, which provided droplets lengths, spacing, and velocities.

(a)

(b)

Figure 1. (a) Experimental setup for extraction studies, (b) Sketch of the two 0.1mm ID hydrophobic Tjunction glass chips with circular microchannels (top picture – outlet microchannel length L = 27.8 cm without outlet tubing, total extraction length = 37.8 cm with 10 cm long outlet tubing; bottom picture – outlet microchannel length L = 1.125 cm without outlet tubing, total extraction length =11.1 cm with 10 cm long outlet tubing)

Chemicals and Reagents. DMDBTDMA (98.8%) was synthesized by Pharmasynthese SAS, ndodecane, isopropanol and HNO3 65 % (wt) were supplied by Sigma-Aldrich. Organic extractant


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solutions were prepared by dissolving weighted amounts of the desired compound in the diluent. All aqueous solutions were prepared with 18-MΩ deionized water produced by a Milli-Q water purification system (Millipore, Bedford, MA). Europium nitrate solutions used for ICP-MS calibration and for the extraction experiments were prepared from a 1.11.10-2 M SPEX solution (JobinYvon). Europium nitrate solutions were prepared by diluting SPEX solution in 4 M nitric acid solutions previously pre-equilibrated with the organic phase in the absence of the Eu(III). Pre-equilibration of the aqueous and organic phases was performed by contact under shaking overnight. All aqueous and organic solutions were filtered with Millex-HPF nylon filters (0.45 µm) before being injected into the microsystem and all liquid-liquid extraction experiments were performed in the microchip at 293 K. Solution densities were measured using a DMA 4500 density meter (Anton Paar, Austria) at (293.150 ± 0.001) K. The accuracy of the density measurements was about ±3.10-6 kg.dm-3. Viscosity at atmospheric pressure was measured with a rotational automated viscometer Lovis 2000 M/ME (Anton Paar, Austria)39. The accuracy of viscosity measurements was better than 0.5%. Interfacial tensions were measured using the plate method with the tensiometer K100C (Krüss). The physicochemical properties of the aqueous and organic phases are presented Table 1. Table 1. Physicochemical properties of the aqueous and organic phases measured at T=293.15 K Dynamic viscosity η Interfacial tension σ Composition Density ρ (kg.m-3) (mPa.s) (mN.m-1) [HNO3] = 4 M [Eu(III)] = 10-2 M

1116.12 ± 0.01

1.131 ± 0.001 6.1 ± 0.1

[DMDBTDMA] = 1 M in n-dodecane

858.48 ± 0.01

20.27 ± 0.01

Liquid-liquid extraction procedures Batch extraction at the equilibrium. For the equilibrium measurements, a range of volume ratios (Va/Vo) varying from 1 to 50 were tested by shaking 1 mL of 4 M nitric acid solution containing [Eu(III)] = 10-2 M with an appropriate volume of DMDBDTDMA 1 M in n-dodecane (i.e. 20 µL to 1 mL) in a


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thermomixer apparatus under the following conditions: T = 293 K ; 1400 rpm ; agitation time = 15 h. After centrifugation, the concentration of Eu(III) remaining in the aqueous phase was determined by ICPMS. The distribution ratio and the extraction yield of Eu(III) at equilibrium were calculated from the concentrations of Eu(III) in the aqueous phase before and after the extraction. Triplicate experiments showed that the reproducibility of these measurements was within 5% for this chemical system. Extraction in the microchannel. For the continuous extractions in the microfluidic device, the two preequilibrated immiscible liquid phases were introduced as previously mentioned in the T-junction chip at various flow rates to vary both the specific interfacial area, the droplets’ velocity and contact times. After each set of experiments, the microchannel was cleaned with isopropanol to remove any residual liquid and then flushed with compressed air. All experiments were triplicated. In order to determine the domain of use of the microsystem, i.e the flow rates to impose to obtain segmented flows with the experimental set-up displayed in Fig. 1 and for the chemical system described in Table 1, segmented flows were observed for different couples of flow rates imposed on the two phases, ranging from 0.16 to 1.48 mL.h-1 for the aqueous phase and from 0.4 to 2.77 mL.h-1 for the organic phase (Fig. 2). These ranges enabled to achieve the dripping regime, and consequently the production of monodisperse populations of aqueous plugs, separated from each other by a constant spacing. Then, it was found that the available flow-rates ratios

were comprised between 0.35 and 1.18 (Fig. 2). In the

field “no dispersion”, no droplet was formed and back flow was observed in the to-be-dispersed phase. In the “coalescence zone” droplets are formed but eventually coalesce. As the difference in velocity between the aqueous and organic phases stays below 6% during plug flow40, we assumed in the following that the volume ratio is equal to the flow-rate ratio.


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Qa (mL.h-1)


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Limit before the coalescence

Limit before the formation of segmented flow

Qo (mL.h-1) Figure 2. Domain of use (green area) of the two T-junctions chips for the chemical system [Eu(III)] = 102 M/ [HNO3] = 4 M/[DMDBTDMA] = 1 M in n-dodecane. ■ Flow-rate couples reached within the Tjunction chip with an extraction length of 27.8 cm;▲ Flow-rate couples reached within the T-junction chip with an extraction length of 1.125 cm.

RESULTS AND DISCUSSION The extraction equilibrium of Eu(III) from nitric acid by DMDBTDMA can be expressed as follows41, 42:

⇌Eu(NO Eu3+ +3NO3 +2DMDBTDMA 3 )3 (DMDBTDMA)2

(1)

and kf and kb denote the forward and backward limiting reaction kinetics coefficients in the global extraction mechanism (1), respectively. Assuming [NO3-] and [DMDBTDMA] are constant during the reaction, the order of the reaction towards these species is not studied, as a consequence, it must be remembered that kf and kb coefficients integrate concentration terms. Above a nitric acid concentration of 5 M, the extraction efficiency decreases because of the competitive reaction of the extraction of nitric acid in the organic phase and the formation of anionic complexes in the aqueous phase. Following Hellé et al.36 former optimization of the extraction of this ACS Paragon Plus Environment

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chemical system, we decided to use the following conditions: [DMDBTDMA] = 1 M in n-dodecane and [Eu(III)] = 10-2 M and [HNO3] = 4 M in the aqueous phase. Influence of the phase volume ratio on the Eu(III) extraction in batch at equilibrium. A good knowledge of the value of the distribution ratio at a given phase volume ratio can be useful to see whether or not the equilibrium is reached at the outlet of the microchannel. Batch extractions of Eu(III) by DMDBTDMA were performed for 7 different phase volume ratios as reported in Figure 3. The relationship between the distribution ratio DEu(III) and the extraction yield Eeq(%) is recalled in Table 2. The equations (2) and (3) are true at any moment t, out of equilibrium, but also at the equilibrium. Table 2. Characteristic parameters related to the extraction process with Va, Vo the volumes of the aqueous and the organic phases, [Eu(III)]a,t and [Eu(III)]o,t the concentration of europium in the aqueous and organic phases at any moment t, respectively. EuIIIa, ini is the initial concentration of europium in the aqueous phase Expression

Parameters

Distribution ratio Extraction yield

DEu(III) =

[EuIII]o,t Va EuIIIa, ini -EuIIIa, t = ∙ EuIIIa, t [EuIII]a,t Vo 100 E%= 1 Va 1+ D · EuIII Vo

Equation (2) (3)


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DEu(III)

Eeq (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Eeq (%)


Va/Vo

Va/Vo

Figure 3. Extraction yield of europium (III) as a function of the phase volume ratio for the chemical system [Eu(III)] = 10-2 M/[HNO3] = 4 M/[DMDBTDMA] = 1 M in n-dodecane. Black scatter refers to batch experiments (triplicate) at the equilibrium, while red dot refers to the maximal yield reached by Hellé et al.36 in parallel flows. The green region corresponds to the targeted volume ratios in this study. Orange triangles correspond to distribution ratio.

The distribution ratio was found to slightly decrease with the volume ratio. It was expected as the extractant can less and less be considered as in excess when the volume ratio is risen. However, the range of targeted volume ratios in microsystems is narrow, from 0.35 to 1.18 as shown in Fig. 2. As a consequence, the extractant can be considered in excess in the scope of our experiments in microsystems and a constant distribution ratio was assumed in the following discussion. A distribution ratio DEu(III) = (12.3 ± 0.4) was determined for a volume ratio of 1 and this optimal value was used as reference value for the extraction experiments in microsystems. Examination of Figure 3 shows that the value of the extraction yield reported by Hellé et al.36 for the same chemical system, at volume ratio of 16.7, but in parallel flows, is significantly lower than the one expected at the equilibrium. This merely means that the equilibrium was not reached in the chip operated in parallel flows.


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In the T-junction, the volume ratio

,

which can be assimilated to the flow-rate ratio, ranged from 0.35 to

1.18 (see section 2.3.2), then extraction yields ranging from about (91.2 ± 0.3) % to (97.2 ± 0.1) % (eqn (3)) can be expected on the condition that the extraction equilibrium can be reached at the outlet of the chip. It highlights the advantage of segmented flows with respect to parallel flows for this chemical system. Indeed, in parallel flows generated in a Y-Y junction36 for the same chemical system, the requirement to position the interface at the center of the microchannel in order to recover the two liquid phases separately and the optimal contact time imposed flow rates equal to 0.50 mL.h-1 and 0.03 mL.h-1 for the aqueous and organic phases, respectively. Then, for the corresponding phase volume ratio equal to 16.7, the maximal achievable extraction yield was about (37.0 ± 1.4) %. Optimization of the extraction in microchannel. Thanks to the segmented flows, the phase volume ratio and the specific interfacial area can be optimized thermodynamically to reach high values of the extraction yields. Such values are upper limits which can be reached only at the condition that the state of the system is close to the equilibrium at the outlet of the chip. Fortunately, compared to parallel flows, in segmented flows the mass transfer benefits from convection created by the movement of the droplets16. For a given microchannel length, the issue is to set the velocity of the droplets in order to combine this enhancement of the mass transfer kinetics and to optimize the shorter contact time that has to be sufficient to reach the equilibrium. The wider the specific interfacial area, the faster the mass transfer kinetics. The faster the droplet velocity, the stronger the convection within the droplets and in the organic slugs between the droplets16 and therefore the thinner the diffusion layers from both sides of the interface, according to the double film theory43. As defined in the double film theory, assuming a first order interfacial reaction but no assumption on the kinetic regime, the extraction rate can be characterized using equation (4)43-46:


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# Kf = 1 1 1 ! + + ! kf ka DEu(III) ·ko

1

ln

Va,droplet Xeq -X A = Kf +Kb t with Xeq -Xini Va,droplet Vo,slug " Kb = ! DEu(III) !

kf

(4)

1 1 DEu(III) + + ko ka

With X the concentration of analyte in the aqueous phase, A the reactive surface area of a droplet, Va,droplet, Vo,slug the respective volumes of an aqueous plug and an organic slug (Fig. 4-a), t the contact time, Kf and Kb the forward and backward global transfer coefficients, kf the reaction kinetic coefficient described in equation (1), and ka, ko, the individual transfer coefficients within the aqueous and organic diffusion layers, respectively. The individual transfer coefficients are generally described as:

ki =

Di δi

(5)

With Di the diffusion coefficient, and δi the thickness of the diffusion layer in the respective phase. The global resistances to mass transfer in the aqueous (Rf) and organic (Rb) phases can then be decomposed into a chemical factor, and two diffusional factors representing the mass transfer resistance inside the diffusion layers on both sides of the interface.

1 1 1 1 (6) = + + =(Rf ) +(Rf ) +(Rf ) chim diff,a diff,o Kf kf ka DEu(III) ·ko 1 DEu(III) 1 DEu(III) (7) Rb = = + + =(Rb ) +(Rb ) +(Rb ) chim diff,o diff,a Kb kf ko ka When the convection is strong enough to make the diffusion layers negligible, the extraction reaction is Rf =

controlled by the chemical kinetics. When increasing the droplet velocity, one can therefore expect the global transfer coefficients Kf and Kb to tend towards the chemical kinetic coefficients kf and kb (eqn (4)).


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Determination of the parameters influencing the mass transfer. The aqueous plugs are separated from the microchannel walls by a thin layer of the organic phase (Fig. 4-a). The existence of this layer was reported by Taylor47 and Bretherton48 in 1961. The impact of this organic film on the plug sides on mass transfer has been described by Ghaini et al.49. The aqueous plug was found to adopt a bullet shape (Fig 4b) when the droplet speed was risen. The volume and surface area of the droplet were calculated accordingly (equations (9) and (10)), considering the front cap as a hemisphere, the back cap as a disk and the body of the droplet as a cylinder (Fig 4-a).

s δ w (a)

VUC Va,droplet

Lfilm

Vo,slug

100 µm

(b)

(c)

Figure 4. (a) Schematic representation of an aqueous droplet (in blue) and an organic slug (in orange) in a microchannel. s is the spacing between two consecutive droplets while Lfilm represents the length of the droplet section in contact with the film, w is the microchannel diameter, δ is the film thickness of organic phase between the cylindrical droplet and the wall of the microchannel, (b) Photograph of the segmented flow within the micro-channel for the chemical system [Eu(III)] = 10-2 M/[HNO3] = 4 M/[DMDBTDMA] = 1 M in n-dodecane, plug velocity ≈ 15 cm.s-1, (c) Illustration of the recirculation circles within the aqueous plugs and organic slugs for the chemical system [Eu(III)] = 10-2 M/[HNO3] = 4 M/[DMDBTDMA] = 1 M in n-dodecane using computational fluid dynamics on COMSOL® Multiphysics. Physicochemical properties of the fluids are given in Table 1, internal channel diameter =


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0.1 mm, plug velocity ≈ 15 cm.s-1, fine meshing, streamlines with uniform density (0.015 separating distance).

In eqn (4), there are four tunable parameters: the contact time t, the volume of the aqueous droplet Va,droplet, the area of the droplet A and the volume of the organic phase of the slug Vo,slug (Fig.4-a). The contact time was assumed to be the total length of the extraction channel (including both the microchip itself and the tubing) divided by the velocity of the droplets vdroplet (eqn (8)). t=

L+Ltubing

(8)

vdroplet

During the experiments in microsystems, the contact time varied from 0.55 to 1.37 s in the short Tjunction chip and from 4.25 to 16.73 s in the long T-junction chip. The reactive interfacial area can be defined in two different ways. A first way consists in considering the total area of the droplet, Adroplet (Fig. 4-a). In this case, the volume and the area of the droplet are defined by eqn (9) and eqn (10).

Va,droplet =

3 π 2 π ·.w-2δ/ + ·L ·.w-2δ/ film 12 4

(9)

2

Adroplet =Acaps +Abody= π·.w-2δ/ +π·Lfilm ·.w-2δ/ 0

(10)

with the film thickness of the organic phase 1 between the cylindrical body of the plug and the wall of the microchannel, and Lfilm, defined as the length of the droplet section in contact with the film (Fig. 4-a). Experimentally, the length of the film is derived from the droplet/plug length and the film thickness, as: Lfilm = Ldroplet −

456 5

(11)

An alternative way to estimate the reactive interfacial area is to consider only the area of the front and back caps of the droplet, Acaps (Fig. 4-a). For a microchannel with an internal diameter of 500 µm and a droplet velocity inferior to 8 cm/s, Ghaini et al.49 showed the specific interfacial area acquired with a


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chemical method using instantaneous reactions was identical to those obtained by a physical method, not considering the film between the droplet and the microchannel walls. Assuming a saturation in complex of the film between the droplet and the microchannel walls, only the caps of the droplets were considered in the calculation of the interfacial area 789:; (eqn (12)). Acaps = π·.w-2δ/ 4 3

2

(12)

As far as the film thickness is concerned, various correlations have been reported in the literature between the film thickness and the capillary number of the segmented flow Ca as defined by eqn (13)48, 51-55. These empirical models are presented in Table 3.

Ca =

ηo vdroplet σ

(13)

With ηo the dynamic viscosity of the organic phase, σ the interfacial tension between the two immiscible liquid phases. Table 3. Empirical models for the determination of the film thickness issued from the literature Film thickness between droplets and microchannel walls δ

0.18∙w∙1-exp-3.08∙Ca0.54 ) 0.67∙w∙

Ca2⁄3 1+3.35∙Ca2⁄3

0.67∙w∙Ca2⁄3

0.67∙w∙

Ca2⁄3 1+2.14∙Ca2⁄3

0.5∙w∙N

ηo

∙ −0.05

σ + 0.89Ovdroplet

0.25∙w∙√IJ

Conditions

References

9,5. 100 < IJ < 1,9

Irandoust and Anderson51

1. 10 < IJ < 1,4 IJ < 0,003

2. 10 < IJ < 0,011 5. 10P < IJ < 2,7. 100 7,5. 10R < IJ < 0,01

Aussillous and Quere52 Bretherton48 Mac Giolla Eain et al.53

Marchessault and Mason54

Fairbrother and Stubbs55

In order to select the model simulating the best our results, the film thicknesses were measured using high-resolution photographs acquired from droplet populations, for various velocities, and compared with


15


the correlations issued from the literature (Fig. 5). Marchessault54 and Bretherton et al.48 correlations were not plotted because overestimating the experimental film thickness (approximately two times and four times respectively at the maximum tested plug velocity ≈ 20 cm.s-1).

Irandoust and Anderson Aussillous and Quere Mac Giolla Eain et al. Fairbrother and Stubbs

2.4E-05 2.0E-05 Film thickness (m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.6E-05 1.2E-05 8.0E-06 4.0E-06 0.02

0.04

0.06

0.08 0.10 0.12 0.14 0.16 Droplet velocity (m.s-1)

0.18

0.20

Figure 5. Experimental film thickness obtained with the long (■) or short (∆) T-junction chips, and calculated film thickness (lines) as a function of the droplet velocity with correlations from Mac Giolla Eain et al. (blue), Fairbrother and Stubbs (green), Irandoust and Anderson (black), and Aussillous and Quere (red), respectively. Values obtained for the chemical system [Eu(III)] = 10-2 M/[HNO3] = 4 M/[DMDBTDMA] = 1 M in n-dodecane in the T-junction (triplicate).

The film thickness was found to be in good agreement with correlations from Fairbrother and Stubbs and Aussilious and Quere at relatively low droplet velocity, and with correlations from Irandoust and Anderson and Aussilious and Quere at high droplet velocity. The range of capillary numbers tested in our

experiments is 0.075 < IJ < 0.67. Given the range of previous studies (Table 3), these agreements are coherent. Hence, Aussillous and Quere’s52 correlation was selected as a way to evaluate the film thickness.


16

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Below, mass transfer coefficients calculations were performed considering either that the reactive area of the droplet is the whole area of the latter (eqn (10)), or that the reactive area is limited to the front and back caps of the droplet (eqn (12)). Determination of the reactive regime. In order to determine the reactive regime, a pseudo-kinetic coefficient K was introduced, derived from eqn(4) :

K =

1+

1

Va,droplet DEuIII Vo,slug 1

Kf +Kb

Va,droplet Vo,slug

(14)

Following this definition, K can be calculated from experiments using:

K =

A

Va,droplet

∙1+

1

Va,droplet DEuIII Vo,slug 1

X eq -X 1 ∙ ∙ ln t X eq -Xini

(15)

The definition of K is valid in all the kinetic regimes and can vary or not with droplet velocity depending on the kinetic regime. Our goal is to study this coefficient. In the diffusion or mixed regime, this pseudokinetic coefficient represents a lower bound limit for the forward chemical coefficient kf. When increasing the velocity of the droplets (analog to the stirring rate in classical contactors), the global transfer coefficients Kf and Kb should tend towards the chemical coefficients kf and kb, as described in Section 3.2. As a consequence, K should tend to be equal to kf, according to eqn (14) (see supplementary material), which is a chemical coefficient and does not depend on the droplet velocity or stirring rate. In eqn (15), no assumption on the effective reactive area of the droplet A was made. Hence, Fig. 6 depicts the evolution of the pseudo-kinetic coefficient K as a function of the droplet velocity, for both definitions of the reactive surface, either through the whole droplet surface or through the caps only. Whatever the definition of the reactive surface, the pseudo-kinetic coefficient K of the reaction was found to be dependent of the droplet velocity. As a consequence, the corresponding regime was diffusion-limited or at least a mixed diffusion and chemically limited regime. In addition, the experiments in the two chips could


17


be correlated when considering only the caps of the plugs as the reactive surface area for a velocity below 8 cm.s-1 and the whole plug for a higher velocity (Fig. 6). Interestingly, the organic film between the droplet body and the microchannel walls was also found to contribute to mass transfer by Ghaini et al.49 at high droplet velocities (>8 cm.s-1 for a capillary with an internal diameter of 500 µm). By increasing the velocity of the plugs, the thickness of the diffusion layers diminishes, while the thickness of the organic film between the aqueous plugs and the microchannel walls increases. As a consequence, one may assume that for a value of the plug velocity of 8 cm.s-1, the thickness of the organic diffusion layer becomes inferior to the organic film between the aqueous plugs and the microchannel walls, thus enhancing mass transfer within the organic slugs.

K (m.s-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 31

Droplet velocity (m.s-1) Figure 6. Pseudo-kinetic coefficient K of the reaction of extraction of europium(III) with DMDBTDMA as a function of the droplet velocity (triplicate), assuming a contribution of the whole droplet surface to mass transfer in the long (■) and short (▲) T-junction chips or a contribution of the caps only in the long (□) and short (∆) T-junction chips. While being unable to conclude on the real value of the forward and backward chemical coefficients of the Eu(III)/DMDBTDMA system, as only the diffusion-limited regime could be reached, one can however estimate a lower bound limit for the forward chemical coefficient.


18

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Indeed, the pseudo-kinetic coefficient, K is expected to be dependent on both the phase volume ratio, and the velocity of the droplets. Experimental data was fitted using a power surface, with the caps only defined as the reactive surface area for the long T-junction chip and the whole droplet area for the short T-junction chip (eqns (10) and (12)) in order to determine an empirical model linking the droplet velocity, the phase volume ratio and K. K expressed by eqn (16) is renamed Kmodel: β

K model =α∙.vdroplet / ∙ ^

Va,droplet Vo,slug

γ

_

With 0.023 ≤ bcde:fgh ≤ 0.202 i. j k and 0.35 ≤

(16) ,lm nopq ,rost

≈

≤ 1.18, respectively.

From the values of K reported in Figure 6, the values of α, β, and γ reported in Table 4 were calculated. Table 4. Fitting parameters associated with eqn (16) - values and standard error – R² = 0.962 Parameter

α β γ

Parameter values Value 2.46.10-4 0.829 -0.02

Standard error 2.4.10-5 0.035 0.05

The pseudo-kinetic coefficient K was finally found to be dependent only on the velocity of the droplets. For the range of volume ratios that was tested, no influence of this parameter on the value of K was found. Finally, the following expression of K was chosen: Kmodel =α·.vdroplet /

β

(17)

Given the internal diameter of the microchannels was chosen constant (0.1 mm ID) during our experiments, and given only a single chemical system was tested, the universality of eqn (17) should be assessed in further works. However, if we expect only a slight deviation towards the formulation that was proposed, the value of the coefficients (Table 4) is thought to be dependent on the used chemical system and microsystem.


19


Deviation between experimental and estimated values of K was investigated by plotting the experimental error as a function of the droplet velocity (Fig. 7) and phase volume ratio using the relation (18). Deviation %=100·

K-Kmodel Kmodel

(18)

Deviation (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 31

Droplet velocity (m.s-1) Figure 7. Deviation between the experimental value of the pseudo-kinetic mass transfer coefficients (triplicate) and its estimated value derived from eqn(17), as a function of the slug-flow velocity, assuming a contribution of the whole droplet surface to mass transfer in the short (▲) T-junction chip and a contribution of the caps only in the long (□) T-junction chip.

Most experimental data points were found to fall within 10% deviation from the empirical curve defined by equation (17). Thus, for a given droplet velocity, the pseudo-kinetic coefficient K for the Eu/DMDBTDMA chemical system can be predicted accurately by using eqn (17). The dependence of the pseudo-kinetic coefficient K towards the slug-flow velocity was quite expected. An increased velocity of the droplets brings in an improved recirculation of the compound in both the continuous and dispersed phases, while potentially acting on the thickness of the two stagnant films at both sides of the interface15. As a consequence, when trying to improve the kinetics of liquid-liquid


20

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extraction in microchannels, trying to implement high plug velocities should be a priority. However, one should also bear in mind that for a given extraction length, the contact time varies as

1 . vdroplet

As a

consequence, increasing the droplet velocity may well be counter-productive if the extraction yield is number one priority. Indeed, the higher the velocity, the higher the mass transfer global coefficients, but the smaller the contact time. In our study, using segmented flow in microsystems, the highest pseudo-kinetic coefficient K that was reached is equal to 6.6.10-5 m.s-1, considering the whole droplet for the reactive surface area. It was obtained in the short T-junction chip with the fastest droplets created when setting Qo = (2.77 ± 0.1) mL.h-1 (Table 5). As an illustration, two other examples are presented: the smallest droplets created for Qo = (2.03 ± 0.01) mL.h-1 and the the slowest droplets obtained for Qo = (0.47 ± 0.04) mL.h-1. Table 5. Operating conditions used for the optimal segmented flow, resulting flow and pseudokinetic coefficient K Qo (mL.h-1)

Qa (mL.h-1)

vdroplet (cm.s-1)

t (s)

Specific interfacial area (m-1)

K (m s-1) x 105

Acaps

Adroplet

With Acaps

With Adroplet

Microscopic Photography

100 µm

2.03 ±0.01

0.71 ±0.01

13.8

0.8

40900

80700

10.70 ±0.03

5.42±0.15

2.77 ± 0.01

1.48± 0.01

20.2

0.55

25700

71500

18.20 ±0.08

6.56±0.10

0.39 ±0.01

0.18 ±0.01

2.3

16.7

23400

59800

1.08±0.03

0.42±0.01

100 µm

100 µm

The determined maximum value of the pseudo-kinetic coefficient K has been compared with the value of the global forward coefficient 2.6.10-5 m.s-1 estimated by Weigl et al.42 using a Nitsch cell, with very similar concentrations for the relevant compounds, [DMDBTDMA] = 0.5 M and [HNO3] = 3.5 M. However, given the kinetic regime was not reached, the coefficient which was found is expected to be a


21


Page 22 of 31

lower bound limit for the kinetic coefficient kf. Additional experiments at higher droplet velocity (which were not feasible using our microchips) would be necessary to conclude on the value of kf. Comparison of the highest pseudo-kinetic coefficient K measured in the present study with literature results. The pseudo-kinetic coefficient K is a lower bound limit for the forward kinetic coefficient kf. As a consequence, it is possible to compare the maximum pseudo-kinetic coefficient K that was reached in the present study with the kinetic coefficients that were previously reported in the literature. The kinetics of Eu(III) extraction using DMDBTDMA as an extractant were investigated by Toulemonde56, Daldon57, Charbonnel et al.58, Weigl et al.42 and more recently by Simonin et al.59, and the various operating conditions and the obtained results are summarized in Table 6. The work of Toulemonde highlights the impact of the concentration of nitric acid on the resulting kinetic coefficient. Below, our study should mostly be compared to works in which the nitric acid concentration is similar to ours, such as Toulemonde56 with 4 M nitric acid, and Weigl42. Table 6. Operating conditions and mass transfer coefficients for Eu(III) extraction by DMDBDTMA, assuming the reactive area of the droplet in the scope of our study is assimilated to the whole droplet surface. *Calculation detailed in the supplementary material kf (m.s-1) K (m.s-1) x 105 Operating x 105 References Devices Regime Diffusional or conditions Kinetic combined regime Toulemonde – Thought as 7.10-2 Lewis cell 2;4;6M HNO3 56 1995 1M DMDBTDMA kinetic 1.4.10-1 in 2.10-1 n-dodecane Daldon – 199757 Lewis cell 2M HNO3 Thought as 6.7.10-2 0.5M kinetic DMDBTDMA in TPH Charbonnel – 199958 Lewis cell 2M HNO3 Thought as 7.10-2 0.5M kinetic DMDBTDMA in TPH


22

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Weigl – 200142

Nitsch cell

Simonin – 201459

Rotative membrane cell (RMC)

This work - 2018

Segmented flow in microsystem

3.5M HNO3 0.5M DMDBTDMA in TPH 2M HNO3 0.5M DMDBTDMA in TPH 4M HNO3 1M DMDBTDMA in n-dodecane

Combined

Kf =2.6

Combined

Kf = 8.8.10-2

Combined

6.56 ± 0.01

One of the main issues in the extraction field is the minimization of the diffusive contribution to the overall mass transfer process59. Using a Lewis cell, workers56-58 concluded that the mass transfer was ruled by a slow interfacial reaction. However, when using a Lewis cell, the plateau generally observed for the extraction flux as a function of the rotation speed of the propellers, which is generally attributed to a kinetic regime, can result as a “slip effect”. In Lewis cells, Danesi60 describe this effect as the possibility that, in spite of an increased stirring rate, the thickness of the diffusion layer never decreases below a sufficiently low value, so that despite creating a plateau for the extraction flux, the diffusion cannot be totally neglected compared to the rate of the chemical reaction. This “slip effect” is thought to be responsible for the very low value of the chemical forward coefficient (≈ 1.10-6 m.s-1) obtained by Toulemonde, Daldon, and Charbonnel for the Eu(III) extraction kinetics with DMDBTDMA56-58. Using a Nitsch cell, which was designed to overcome the weaknesses/drawbacks of Lewis cells, with a more effective stirring, Weigl et al.42 identified a diffusion-controlled regime, with a maximum global forward coefficient Kf = 2.6.10-5 m.s-1. More recently, Simonin et al.59 used the rotating membrane cell (RMC) technique, at 600 rpm and 22°C to study the extraction kinetics of Eu(III) from a 2 M HNO3 aqueous solution into an organic solution of 0.5 M DMDBTDMA in HTP. Simonin identified a global forward coefficient Kf with approximately the same value as Toulemonde et al.56, i.e., Kf = 8.8.10-7 m.s-1.

CONCLUSION


23


Page 24 of 31

In this study, segmented flows in microsystems were created as a tool for the investigation of liquid-liquid extraction kinetics of europium (III) by a malonamide, the DMDBTDMA. For droplet velocities ranging from 2.3 to 20.2 cm.s-1, the thickness of the organic phase film separating plugs from the microchannel walls was measured, and the model of Aussilous and Quere52 was found to fit precisely the experimental data. Consequently, the volume and surface of the aqueous plugs were calculated, and for each microsystem experiment, the extraction yield was compared to the extraction yield at the equilibrium. A pseudo-kinetic coefficient was defined as a lower bound limit for the kinetic forward coefficient, and a model was proposed for the evolution of this pseudo-kinetic coefficient with the velocity of the droplets, analog to the stirring rate. Interestingly, the organic phase film was found to contribute to mass transfer only for droplet velocities higher than 8 cm.s-1, as mentioned in a previous publication by Ghaini et al.49. Then the maximum value for the pseudo-kinetic coefficient K, (6.56 ± 0.01) m.s-1 was compared to other results from the literature. It was found that in segmented flows in microsystems, the mass transfer is very effective not only compared with traditional contactors, i.e. Lewis, Nitsch cells and the Rotating Membrane Cell technique, but also compared with laminar flows in microchannels. Several assumptions were made however, and should be mentioned as a perspective for model improvement. First, the contact time is thought to be exactly the same for the organic and aqueous phases (velocity difference below 6%40, 50). However, it was shown that the velocity difference between the

dispersed and continuous phases was proportional to IJk⁄ in square section microchannels61 and to

IJ5⁄ in circular section microchannels48. Given 0.075 < IJ < 0.67 in our circular microchannels, the velocity difference may have an impact on mass transfer. Indeed, the aqueous plugs are faster than the

continuous organic phase, and as a consequence, the organic phase is apparently enriching more in complex than the dispersed phase is depleted in analyte.

ASSOCIATED CONTENT


24

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Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI: xxx. The double film theory and the evaluation of the pseudo-kinetic coefficient in a rotating membrane cell were described (PDF).

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes: The authors declare no competing financial interest. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Axel Vansteene, Jean-Philippe Jasmin, Clarisse Mariet, Gérard Cote contributed equally.

Funding Sources This work was supported by the French Alternative Energies and Atomic Energy Commission.

ACKNOWLEDGMENT We would like to thank Amar Basu (Electrical and Computer Engineering, Wayne State University, Michigan) for providing us the DMV software we used to acquire droplets shapes and velocities.

ABBREVIATIONS


25


(X, Y)

Analyte and complex concentration in double film theory (mol m-3)

(α,β,γ)

Parameters associated with eqn (16)

[Eu(III)]

Europium concentration (mol m-3)

A

Reactive surface area of a droplet (m²)

Ca

Capillary number

CFD

Computational fluid dynamics

D

Diffusion coefficient (m² s-1)

DEu(III)

Distribution ratio

Page 26 of 31

DMDBDTMA N,N’-dimethyl N,N’-dibutyl tetradecylmalonamide DMV

Droplet morphometry and velocity software

E(%)

Extraction yield

Eeff

Extraction efficiency

eqn

Equation

Fps

Frame per second (s-1)

ICP-MS

Inductively-coupled plasma mass spectrometry

ID

Internal diameter (m)

i-SANEX

Innovative-Selective ActiNide EXtraction

J

Mass transfer flux (mol m-2 s-1)

k

Transfer coefficient (m s-1)

K

Pseudo-kinetic coefficient (m s-1)

K’obs

Volumetric mass transfer coefficient (s-1)

L

Length of the microchannel (m)

L tubing

Length of the tubing at the outlet of the microchannel

PUREX

Plutonium Uranium Refining by EXtraction

PIV

Particle image velocimetry (PIV)

Q

Flow-rate (m3 s-1)

Rpm

Round per minute (min-1)

t

Contact time (s)


26

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TALSPEAK

Trivalent Actinide-Lanthanide Separation by Phosphorus reagent Extraction from Aqueous

V

Volume (m3)

v

Velocity (m s-1)

w

Channel diameter (m)

δ

Film thickness (m)

η

Dynamic viscosity (Pa s)

ρ

Density (kg m-3)

σ

Interfacial tension (N m-1)

Subscripts a

Aqueous phase, referring droplets

eq

At equilibrium

exp

Experimental

f

Forward kinetic

i

At the interface

ini

Initial

model Empirical model (eqn(16)) M

Metal ion studied

o

Organic phase, referring to slugs

t

At contact time t

th

Theoretical

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Segmented micro-flows benefits for the acceleration and control of mass transfer

100 μm

Low polydispercity Controlled and accurate specific interfacial area Very short diffusion length


1

Segmented Microflows as a Tool for Optimization of Mass Transfer in

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