Hydrodynamics and Mass Transfer in a Countercurrent Multistage

Article pubs.acs.org/IECR

Hydrodynamics and Mass Transfer in a Countercurrent Multistage Microextraction System Wenjie Lan,† Shan Jing,‡ Shaowei Li,*,‡,§ and Guangsheng Luo§ †

State Key Laboratory of Heavy Oil Processing, China University of Petroleum (Beijing), Beijing 102249, China Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China § State Key Laboratory of Chemical Engineering, Tsinghua University, Beijing 100084, China ‡

ABSTRACT: In our previous study, a bionic system simulating the cardiovascular system was built to realize a countercurrent multistage microextraction. However, further study on the hydrodynamics and mass transfer performances of such a system is still needed. In this study, a theoretical model was first established to describe the relationship between the pressure drop and the flow rate. The flow resistance, including the effect of the two-phase interface, was investigated based on the theoretical model and experimental data. The mass transfer coefficient was then investigated by experiments and computational fluidic dynamics (CFD) simulation. The overall mass transfer coefficient was found positively correlated with the slug velocity. Both the aqueous phase mass transfer coefficient and the organic phase mass transfer coefficient were obtained by CFD simulation. A correlation equation was established to calculate the Sherwood number, and it is proved to be applicable in both the aqueous and the organic phases.

1. INTRODUCTION Liquid−liquid extraction is an important process in chemical engineering. After more than 100 years of development, it has been widely used in the petrochemical industry, nuclear reprocessing, and ore processing.1−5 Various types of extraction equipment such as mixer-settler, pulsed column, and centrifugal extractor have been utilized in the chemical industry. However, these conventional types of equipment cannot satisfy the new requirement of the developing technology. Especially in fine chemical and biochemical engineering, these types of equipment suffer from low efficiency, high energy consumption, and large equipment dimensions. The microextraction system developed in recent years provided a new option to achieve high efficiency extraction. Microextraction systems have the advantages of large specific interface area, large interface-tovolume ratio, and short diffusion distance which results in short diffusion time.6,7 In microextraction systems, high extraction performance can be reached without any mechanical stirring, mixing, or shaking. Moreover, microextraction systems can be integrated with other operation units in a small space. Because of these advantages, microextraction systems experienced a high speed development in recent years and have been used in many areas such as the separation of metal ions,8,9 the detection of pesticide,10 the optical resolution of amino acids,11 the separation of steroids,12 the cleanup of alkaloids,13 and the separation of proteins.14 Nevertheless, the application of microextraction is limited because most of the microextraction systems are cocurrent © XXXX American Chemical Society

operated. It is well-known that the recovery efficiency of cocurrent operation cannot exceed one theoretical separation stage. Countercurrent operation is a common method to increase the recovery efficiency.15−17 Most conventional types of extraction equipment mentioned above are generally counter-current-flow operated. However, it is difficult to realize countercurrent flow in microfluidic devices because the surface wetting and viscosity effects are much larger than gravity and inertial effects.18 Some researchers have solved this problem based on surface modification of the microchannel walls.19 Countercurrent microflow is realized in their microdevices, though the physical properties of the fluid and the operating conditions are limited to a narrow range.20 To achieve more robust countercurrent microextraction that is applicable for a wide range of materials and operation conditions, a bionic system simulating the cardiovascular system was built in our previous study.21 Relatively high throughput and recovery efficiency were achieved. In this system, the aqueous phase and organic phase were alternately introduced under the driving of the asynchronous pulsing pressure of the two phases. The hydrodynamics and mass transfer process of such a system are quite different from the common steady two-phase flow in microchannels. Therefore, further study on the hydrodynamics Received: January 13, 2016 Revised: May 5, 2016 Accepted: May 6, 2016

A

DOI: 10.1021/acs.iecr.6b00162 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

operation is in the organic phase moving stage shown in Figure 2a. In this stage, the solvent in syringe B is pushed into the microextractors. The solvent then moves in the arrow direction and finally into syringe C. Simultaneously, the aqueous phase in syringe A is pushed into the raffinate collection tank. The aqueous feed is drawn out of the feed tank into syringe D. The moving directions of all syringe pistons then are reversed, and the operation is in the aqueous phase moving stage shown in Figure 2b. The aqueous phase is pushed out of syringe D into the microextractors and then moves in the arrow direction finally into syringe A. Simultaneously, the organic phase in syringe C is pushed into the extract collection tank. The solvent is drawn out of the tank into syringe B. The organic moving stage is then repeated to start a new operation cycle. In this operation manner, the organic phase and the aqueous phase alternatively flow in countercurrent directions as shown in Figure 2a,b. But in each microcontactor shown in Figure 1b, the two phases flow concurrently to form slug flow.

and mass transfer performances of such a microfluidic process is needed. Experimental investigation, theoretical model, as well as computational fluid dynamics (CFD) methods will be used to achieve an in-depth research on the issue.

2. EXPERIMENTAL SECTION 2.1. Cheimicals. 30% (volume fraction) tributyl phosphate (TBP)−kerosene/water two-phase flow, which is widely used in nuclear reprocessing and ore processing, was used to study the hydrodynamics of the microextraction system. Nitric acid solution was used to replace water in the above system for the investigation of the extraction process. The kerosene was purchased from Jinzhou Refinery Factory (Liaoning, China). Analytically pure TBP and nitric acid were purchased from Beijing Chemicals Factory (Beijing, China). The nitric acid in the two phases was titrated using a automatic titrator (Metrohm 905 Titrando, Swiss). Density of all solutions was measured by a densitometer (LEMIS Dendi, USA). Viscosity was measured using a viscometer (Brookfield LVDV-II+PRO, USA). The physical properties of the two phases are listed in Table 1.

3. THEORY MODEL AND NUMERICAL METHOD 3.1. Hydrodynamics. We know from Section 2.3 that one operation cycle is composed of two stages. In each stage, only one phase moves into the microextractors. Taking the organic moving stage shown in Figure 2a as an example, the organic phase moves from syringe B to syringe C, passing through N microcontactors, N phase separators, N+1 check valves, and several connecting tubes. The hydrodynamic study should cover the flow in all these components except the phase separators of which the flow resistance can be ignored. We will analyze the flow in these components separately as follows. 3.1.1. Single-Phase Flow in Connecting Tubes. The singlephase flow in the connecting tubes of each phase can be described by the Navier−Stokes equation. For one dimension incompressible flow in tubes, it can be expressed as

Table 1. Physical Properties of the Two Phases (25°C) organic phase organic phase aqueous phase aqueous phase aqueous phase

C (mol/L)

ρ (kg/m3)

μ (Pa·s)

0 0.6 0 2.0 3.0

819 835 997 1063 1095

0.00177 0.00197 0.00089 0.00106 0.00112

2.2. Experimental Setup. The scheme and photo of the experimental setup are shown in Figure 1. The four-stage countercurrent microextraction system is composed of four airtight syringes, 14 check valves, four multichannel microcontactors, four phase separators, four tanks (to store the feed, solvent, extract, and raffinate, respectively), and several contacting tubes. The check valve was fabricated by a stainless steel shell and ruby ball, with an inner structure shown in Figure 1b. When the fluid flows from the bottom into the valve, the inner ball is pushed up and the valve is open. On the contrary, the inner ball falls down and blocks the flow channel. The multichannel contactor was fabricated on a 60 × 80 mm poly(methyl methacrylate) sample plate using an end mill. The channel dimensions were 0.5 × 0.5 × 60 mm (width × height × length). Sixteen parallel channels were placed on the plate with a spacing of 2 mm. The phase separator was fabricated from Teflon tube as the upper part and stainless steel tube as the lower part. Phase separation takes place in the phase separator under the effect of surface wetting and gravity. Online pressure sensors were used to measure the pressure of point P1, P2, P3, and P4 in Figure 1a. Average flow rate of each phase was measured by graduated cylinder at the outlets. The two phases collected in all the four phase separators were titrated to determine their concentration. Reciprocating frequency of the syringes can be controlled on the operation panel. Stroke volume of the reciprocation can be adjusted by changing the syringe diameter. 2.3. Operation Procedure. The operation procedure is illustrated in Figure 2. The four syringes are divided into two pairs: pair AB and pair CD. The pistons of the two pairs always move in opposite directions, as shown in Figure 2. When pair AB moves forward (pair CD moves backward meanwhile), the

ρ

∂p ∂u 1 ∂ ⎛⎜ ∂u ⎞⎟ =− +μ r ∂x ∂t r ∂r ⎝ ∂r ⎠

(1)

The last term of the right side represents the differential frictional pressure drop. If we replace the local velocity u with the cross section average velocity um in eq 1, the last term could be expressed by Hagen−Poiseuille’s law: ρ

∂p du m 32μum =− − dt ∂x d2

(2)

2

Submit um = 4Q/πd into eq 2, then dQ 32μQ πd 2 ∂p + = − dt 4ρ ∂x ρd 2

(3)

The left side of eq 3 is independent of x. Therefore, ∂p/∂x = −Δpt/L, then Δpt =

4ρL dQ 128μLQ + 2 πd 4 π d dt

(4)

Where Δpt is the pressure drop in the connecting tubes. Equation 4 describes the relation between the flow rate and pressure drop of the single phase flow in the tubes. As expressed by eq 4, the pressure drop is composed of two terms, the acceleration term and the friction term. 3.1.2. Single-Phase Flow in Check Valves. As shown in Figure 3, there is a ruby ball in the check valve. The weight of the ruby wall needs to be overcome when the liquid flows through the check valve. Compared to the pressure drop in the B


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Figure 1. Scheme and photo of the experimental setup.

Figure 2. Operation procedure of the countercurrent microextraction system.

3.1.3. Two-Phase Flow in Microcontactors. The pressure drop in the multichannel contactor is rather complex because of the two-phase slug flow in the microchannels. Considering one microchannel, the pressure drop is also composed of three terms, the acceleration term, the friction term, and the interfacial force term. According to the study of Kashid et al.22 on the friction and interfacial pressure drop of the slug flow in microchannels, the pressure drop in the multichannel contactor could be expressed by eq 7.

tube, an additional buoyancy term should be considered, as expressed in eq 5. Δpc =

4ρLc dQ 128μξcLcQ + + Δpb 2 πdc 4 πdc dt

(5)

Where ξc is a factor characterizing the divergence of the friction pressure drop in the valve channel from that in a cylindrical tube. Δpb is the buoyancy term caused by the weight of the inner ball, expressed as Δpb =

(ρb − ρ)gVb Sb

2Δρgdb = 3

Δpm = (6)

4ρm Lm dQ 2

nπdm dt

+

128μm LmQ nπdm 4

+ ΔpI

(7)

Where C


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Industrial & Engineering Chemistry Research ⎛ 4ρL Nρm Lm ⎞ dQ 4(N + 1)ρLc ⎟ Δp = ⎜ 2 + + 2 4πdm 2 ⎠ dt πdc ⎝ πd ⎛ 128μL 8Nμm Lm 128(N + 1)μξcLc +⎜ + + 4 4 πdc πd m 4 ⎝ πd +

NNsRI ⎞ ⎟Q + (N + 1)Δpb 16 ⎠

(13)

In our experiments, four stages countercurrent microextraction was performed, thus N = 4. Because Lc ≪ L and Lm ≪ L, eq 13 can be approximate to the following equation: ⎛ 32μ πd 2NsRI ⎞ dQ πd 2 Δp − Δps ⎟Q = +⎜ 2 + dt 16ρL ⎠ 4ρ L ⎝ ρd

Figure 3. Inner structure of the check valve.

ρm =

μm =

αρA + ρO α+1

Where Δps = 5Δpc is the static pressure drop. Only when the total pressure drop is greater than the static pressure drop, it can provide a driving force to the flow. The static pressure drop could be determined by the inflection point of the pressure drop curve measured by the online pressure sensor in our experiments, which will be explained as follows. Figure 4 shows a typical pressure drop curve measured in our experiments. The pressure drop equals to the difference

(8)

αμA + μO α+1

(9)

are the average density and viscosity of the two phases with flow ratio α (the aqueous versus the organic phase). n is the channel number of the multichannel contactor, which is 16 in our experiment. ΔpI is the pressure drop caused by the liquid− liquid interfacial force. Kashid et al.22 expressed it simply as the sum of Young−Laplace pressure of all the slug interfaces with a constant contact angle. However, the bend directions of the interfaces on the two end of a slug are opposite and the Young−Laplace pressures of the two interfaces are counteracted. One must consider the difference between the advancing and receding contact angles to express the interfacial pressure drop when the slugs move in the microchannel. We expressed ΔpI in a new form based on the above analysis: ΔpI =

Lm 4γ(cos θR − cos θA) lA + lO dm

(10)

where lA and lO are the lengths of the aqueous and organic slugs. θA and θR are the advancing and receding contact angle, respectively. Both of them are related to the flow velocity of the slugs. On the basis of Schwartz and Tejada’s report,23 cos θR − cos θA is proportional to the moving velocity of the slug in our experimental condition range. Thus ΔpI =

N Lm Q RI = s RIQ lA + lO n n

Figure 4. A representative pressure drop curve of the organic phase in a period. The reciprocation frequency of the syringes was 0.043 s−1, and the stroke was 80 μL.

between the pressure measured at points P2 and P3 in Figure 2. Corresponding to the pressure drop curve, the status of syringe B is illustrated below the time axis. The syringe experiences a “moving forward−stop−moving backward− stop−moving forward” cycle in a period. There is some gas in the syringes (blank area in the syringe of Figure 4) as buffer to avoid syringe destroying. Five important time points, t0−t4, are marked in Figure 4. At time t0, syringe B begins to move forward and the pressure drop increased rapidly. But the liquid does not move until the pressure drop reaches Δps at time t1. Only the gas in the syringe is compressed during time t0 to t1. The liquid begins to move at time t1 and the flow rate increased gradually because of the driving of the pressure drop until it achieves a maximum value at time t2. dQ/dt is larger than 0 in this duration based on eq 14. From time t2 to t3, it is almost a

(11)

Here RI can be named as the interfacial flow resistance. NS is the number of slug units in a microchannel. 3.1.4. Comprehensive Analysis of Flow in the System. The total pressure drop for each phase is the sum of the pressure drop in the tubes, the check valves and the multichannel contactors. Then, the total pressure drop is Δp = Δpt + (N + 1)Δpc + N Δpm

(14)

(12)

Combing eqs 4, 5, 7, and 12 gives the relationship between the total pressure drop and the flow rate. D


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Figure 5. Mass transfer of the slug flow in microchannels.

steady flow in the system. dQ/dt approximately equals to 0 in this duration and the total pressure drop equals to the total resistance pressure drop. Only in this duration, the flow rate of the liquid equals to the volume changing rate of the syringe. The syringe stops at time t3. After this time point, the liquid moves under the driving of the compressed gas in the syringe. The pressure of the gas is released in this process and the flow rate of the liquid decreased gradually. In theory, the liquid flow rate as well as its derivative will reach zero after infinite time. The total pressure drop equals to the static pressure drop Δps in this situation according to eq 14. The theoretical infinite time cannot be reached in practice. Actually, the syringe begins to move backward at time t4. However, during the time point t3 to t4, It is long enough to approximately reach the value of the static pressure drop because the changing rate of the total pressure drop gets sufficiently small just before time t4. Therefore, Δps can be determined by the inflection point of the pressure drop curve at time t4. The liquid flow rate will be zero after time t4 because the driving force becomes minus. On the basis of the above analysis and eq 14, the relationship between the pressure drop and the fluid flow rate in the microextraction system should be expressed by the following equation:

Here R = Rμ + Ns/4RI is the total flow resistance with the 128μL viscous resistance Rμ = πd 4 and the total interfacial resistance on the flow path Ns/4RI. Thus, Δpave can be separated into average viscous pressure drop and average interfacial pressure drop: Δpave = Δpμ ,ave + 4ΔpI,ave

with Δpμ,ave = RμQave and ΔpI,ave = NsRIQave/16. Δpave can be calculated from the area of the shaded part in Figure 4. Rμ can be calculated from the liquid viscosity and the size of the tube. Then, once we measured the average flow rate Qave, the interfacial resistance could be determined. 3.2. Mass Transfer. The mass transfer of nitic acid from the aqueous phase to the organic phase takes place in the multichannel contactor. As shown in Figure 5, there is innerrecirculation in both the aqueous and organic slugs, which greatly enhances the mass transfer in both phases. If we denote the average concentration of nitric acid in the aqueous and organic phases as CA and CO respectively, the mass transfer flux of nitric acid can be expressed by eq 20. N = K OA ΔCA = K OA(CA − CA*)

CA* = mCO + Cvt

Q ave

∫

(15)

0

1 T

1 128μL πd 4

+

s

(16)

To define the driving force of the flow as 1 T

∫Δp>Δp (Δp − Δps )dt s

(17)

(23)

2Sc (1 + sin θ)

is the area of the aqueous−organic

(24)

Integrating eq 24, we have

Δpave R

dC O 2NSI = dt VO

⎛1 dΔCA m⎞ 4 = −⎜ + ⎟ K OA ΔCA dt lO ⎠ 1 + sin θ ⎝ lA

eq 16 can be rewritten as a simple formula: Q ave =

(22)

interface. Sc is the cross-sectional area of the channel. The difference between the advancing and receding contact angles is ignored since the error is very small. VA = lASc and VO = lOSc are the volumes of the aqueous and organic slugs respectively, ignoring the bending of the interface. Combing eqs 20−23 gives

NsRI 4

∫Δp>Δp (Δp − Δps )dt

Δpave =

dCA 2NSI =− dt VA

Here SI =

T

Q dT =

(21)

The values of m and Cvt can be found in our previous study.24 The changing rate of concentration in the two phases can be expressed as

Given a measured total pressure drop curve, Δps could be determined by the method described above. Then the transient flow rate could be calculated based on eq 15 using a numerical method. To calculate the integral of eq 15 in a period T, considering Q(0) = Q(T) = 0, we can calculate the average flow rate by eq 16. 1 = T

(20)

Here KOA is the overall mass transfer coefficient with ΔCA as the mass transfer driving force. C*A is the aqueous contraction in equilibrium with the organic concentration of CO. Thus,

⎛ 32μ πd 2NsRI ⎞ dQ ⎟Q +⎜ 2 + dt 16ρL ⎠ ⎝ ρd ⎧ πd 2 Δp − Δp s ⎪ , when Q > 0 or Δp > Δps L = ⎨ 4ρ ⎪ ⎩ 0, when Q = 0 and Δp < Δps

(19)

ln (18) E

⎛1 ΔCA 4 m⎞ = −⎜ + ⎟ K OAt ΔCA,0 lO ⎠ 1 + sin θ ⎝ lA

(25)


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Industrial & Engineering Chemistry Research Here ΔCA,0 is the initial mass transfer driving force, which can be obtained by measuring the two-phase concentration of the inlet of the multichannel contactor. After the two phases pass through the multichannel contactor, the concentration are measured to obtain an ending driving force ΔCA,e. Knowing the residence time te of the multichannel contactor, the overall mass transfer coefficient KOA can be calculated based on eq 25. 3.3. Numerical Method for Mass Transfer. The overall mass transfer coefficient KOA depends on three factors, i.e., the aqueous phase mass transfer coefficient kA, the interphase reaction rate coefficient kE, and the organic phase mass transfer coefficient kO: 1 K OA = 1 1 m + k + k k (26) A

E

The transport equation for nitric acid in both phases can be expressed as eq 30, assuming the diffusion coefficient of nitric acid a constant in each phase. ρ

rs = kECAI − k SCOI

kE

(27)

Where kS = mkE is the reverse reaction rate coefficient. Though KOA can be obtained from the experimental data, the three partial coefficients kA, kE, and kO cannot be measured directly. The CFD simulation provides a powerful tool to obtain these parameters based on the experimental data. The CFD simulation in this study was carried out in a flow domain as shown in Figure 6, by using the commercial software CFX

4. RESULTS AND DISCUSSION 4.1. Relationship between Pressure Drop and Flow Rate. As described by eq 18, the flow resistance can be obtained by linear fitting the measured Δpave with Qave. The measured Δpave and Qave of both the aqueous and organic phases in different experimental conditions are plotted in Figure 7, where SA and SO were the strokes of the aqueous and organic phases separately. The flow rate was adjusted by changing the reciprocation frequency of the syringes in fixed strokes. We can see from Figure 7 that the relationship between Δpave and Qave is linear for both the two phases, even in

Figure 6. CFD simulation domain and meshes.

5.6. The mass transfer in one slug unit (containing one aqueous slug and one organic slug) was simulated. The organic slug (continuous phase) was set as two half-slugs on both side of the aqueous slug (dispersed phase). The mesh for the geometry was created by CFX Build. As shown in Figure 6, the mesh was consisted of 2.18 M unstructured, tetrahedral cells. The maximum mesh sizing was 25 μm. Laminar flow model was used as the Reynolds number was very small in the microchannel. The liquid−liquid interface was equivalently defined as a thin wall with conservative mass and momentum flux. The governing equations for conservation laws of mass and momentum on both sides of the interface can be written as the following form with the assumption that the fluid is incompressible. (28) ∇·⇀ u =0 ρ

u ∂⇀ u ·∇⇀ u = ρ⇀ FM − ∇p + μ∇2 ⇀ u +⇀ ∂t

(31)

A first-order reaction rate equation was used because the TBP concentration was much higher than the nitric acid. CAI and COI denoted the nitric acid concentration on the aqueous side and the organic side of the interface, respectively. Different from kA and kO, kE was independent of the flowing condition of the two phases. Therefore, kE could be determined by simulating several cases with different flow rates and comparing the simulated KOA with the experimental KOA. By using this method, kE was determined as 4 × 10−4 m/s. The channel walls were set as nonslip and smooth walls and a wall velocity was set to equivalently simulate the slugs flowing in an opposite direction with the same velocity. A periodic boundary condition was set for the two plane ends of the organic slug. A transient-state simulation was performed. The time step was set as 10−5 s. The maximum number of coefficient loops for each time step was set as 10. The convergence criterion was set as that the normalized rootmean-square of the equation residuals reaches 0.000 01.

The interphase reaction equation can be denoted as kS

(30)

The diffusion coefficient used in the simulation was 1.60 × 10−9 m2/s and 5.82 × 10−10 m2/s in the aqueous and organic phase, respectively. CFX’s high resolution discretization for the advection term was used for the calculation of the equations. Second order backward Euler discretization was used for the transient term. A reaction rate according to eq 27 was defined on the interface:

O

(H+ + NO3−)(A) + TBP(O) ⇄ TBP ·HNO3(O)

∂C +⇀ u ·∇C = D∇2 C ∂t

Figure 7. Determination of the resistance. The slope is the resistance RA and RO.

(29) F


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Figure 8. Measured pressure drop curves and calculated transient flow rate in one period at conditions of (a) f = 0.13 Hz, SA = SO = 80 μL, (b) f = 0.77 Hz, SA = SO = 80 μL, (c) f = 0.13 Hz, SA = 80 μL, SO = 160 μL, and (d) f = 0.13 Hz, SA = 80 μL, SO = 400 μL.

steady state is then established with a nearly constant flow rate. The steady segment ends once the syringe piston stops moving. Then the liquid flows under the driving of the compressed gas in the syringe and the flow rate decreases slowly to zero. The pressure drop of the organic phase is larger than the aqueous phase at almost the same flow rate as shown in Figure 8a,b. The reason is that the larger viscosity of the organic phase caused larger viscous resistance as calculated above. Comparing Figure 8a,b, we can see that the pressure drop and the flow rate increase when the reciprocation frequency of the syringes increases. Meanwhile, the proportion of the steady segment in the whole period decreases because the compression ratio of the gas in the syringes increases with the increase of the frequency. When the syringe stroke is enlarged, the pressure drop and the flow rate are also increased as shown in Figure 8c,d. Moreover, the enlarged strokes of the organic phase affect little on the flow of the aqueous phase. This feature allows us to alter easily the flow ratio in a large range by changing the strokes of the two phases. 4.2. Interfacial Pressure Drop. To investigate the variation of the interfacial resistance when changing the syringe strokes, the average interfacial pressure drop is calculated from the measured total pressure drop based on eq 19. The results are shown in Figure 9. Linear fitting ΔpI,ave and Qave, the slope is the value of NsRI/16. According to the above analysis, we know that RI is a constant whereas Ns depends on the strokes. The increase of the stroke leads to the increase of the slug length. Therefore, when the organic stroke increases, Ns decreases and causes the decreasing of the slope. We can also see that the data points of the aqueous phase and organic phase in Figure 9 are almost on the same line when fixing the stroke pair. The reason is that the number of slug units in the microchannel is the same for the two phases. Considering ±1% error of the total average pressure drop, the maximum errors of ΔpI,ave for the four stroke pairs are ±20%, ±30%, ±40%, and ±50%, respectively. It is then obtained that the values of NsRI for the four stroke pairs are (1.9 ± 0.4) × 1010Pa·s/m3, (1.4 ±

different strokes. The slope is the resistance. The resistances of the aqueous phase and organic phase are separately RA = 1.77 × 1010Pa·s/m3 and RO = 2.74 × 1010Pa·s/m3. Because the nominal measuring error of our pressure sensor is below ±0.1%, the error of the calculated resistance should be no more than ±1% when considering the integral of the pressure drop curve. On the other hand, the viscous resistance can be 128μL calculated from Rμ = πd 4 . The results are RμA = 1.27 × 1010Pa·s/m3 and RμO = 2.43 × 1010Pa·s/m3, respectively. Because R = Rμ + 4NsRI, we can know from the results that the interfacial resistance occupies no more than 30% of the total resistance. This is the reason why the strokes affect little on the total resistance. As the strokes mainly affect Ns, the number of slug units in a microchannel, the total interfacial resistance changes with the strokes. The proportion of the viscous resistance in the total resistance is much higher than the interfacial resistance. Therefore, the total resistance almost remains constant when the interfacial resistance changes with the strokes. With the above determined resistance, we can calculate the transient flow rate by numerically integrating eq 15 when the pressure drop curve is measured. The calculated flow rate curves and the corresponding pressure drop curves are shown in Figure 8. The results of four different experimental conditions are presented here. The flow rate is mainly determined by the pressure drop higher than the static pressure drop (which was described in detail in Figure 4). The minus pressure drop has no effect on the flow because of the blocking of the check valves on the reverse direction. The flow rate curve can be departed into three segments: the fast increasing segment, the steady segment, and the slowly decreasing segment. In the fast increasing segment, the syringe piston moves forward and the driving pressure drop is higher than the viscous and interfacial resistant pressure drop. The resistant pressure drop increases with the flow rate, increasing until it reaches a balance value with the driving pressure drop. A G


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extend the application scope of the formula, more fluid pairs and channel materials need to be tested and the influences of interfacial tension, viscosity and static contact angle need to be considered. 4.3. Overall Mass Transfer Coefficient. The overall mass transfer coefficient could be calculated based on eq 25 with the measured concentration of the two phases in each phase separator. In theory, the mass transfer coefficients in all of the four stages of contactors can be calculated. But we only calculated that of the first two stages because the amount of the mass transfer in the last two stages was small, which would lead to large calculation errors of the mass transfer coefficient. The calculated overall mass transfer coefficients and the volumetric overall mass transfer coefficients in different experimental conditions are shown in Figure 11. It can be observed that the initial concentration has little effect on the mass transfer coefficient. Furthermore, the mass transfer coefficients of the first stage and second stage are nearly the same under the same experimental condition. The reason is that the difference between the two stages is only the different initial concentrations. The overall mass transfer coefficient increases with increasing of the frequency and stroke of the two phases. The volumetric mass transfer coefficients of the present work are compared with the experimental data of the slug flows in the literature25−28 as shown in Figure 12. Generally speaking,

Figure 9. Linear fitting of the average interfacial pressure drop and the average flow rate. The slope is NsRI/16.

0.4) × 1010Pa·s/m3, (1.0 ± 0.4) × 1010Pa·s/m3, and (0.8 ± 0.4) × 1010Pa·s/m3 separately. Ns is determined by measuring the average slug length in the microchannels and the values for the four stroke pairs are separately 11.8, 6.3, 4.7, and 4.1. As shown in Figure 10, linear fitting NsRI versus Ns, the slope is the

Figure 10. Determination of the interfacial flow resistance. The slope is RI.

interfacial flow resistance. Considering the maximum ±50% error of NsRI, the interfacial flow resistance is RI = (1.8 ± 0.9) × 109Pa·s/m3. On the basis of eqs 10 and 11, we can then obtain the relationship between the advancing/receding contact angles and the slug moving velocity: cos θR − cos θA =

πd m 3 RIu = 4.5 s/mm·u 16γ

(32)

Figure 12. Comparison of volumetric mass transfer coefficients with data in literature.

This formula can be used to predict the interfacial flow resistance of the same fluids in different channel sizes. To

Figure 11. (a) Overall mass transfer coefficients and (b) volumetric overall mass transfer coefficients in different experimental conditions. H


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layer thickness decreases and causes the increasing of the mass transfer coefficient. The boundary layer can also be seen from the simulation result shown in Figure 15.

the volumetric mass transfer coefficient increases with the increasing of the slug velocity though there are some other effective factors including the physical properties of the system, the size of the microchannel, and the existence of the interface reaction. The volumetric mass transfer coefficient of the present work is relatively lower than the literature data as shown in the figure. It is because the slug velocity of our experiments is smaller. Nevertheless, the changing trend of our data is consistent with the literature data. On the other hand, comparing to the conventional extraction columns29,30 in which the volumetric overall mass transfer coefficient is in the range of 10−4 to 10−3 s−1, the data of the present work is in the range of 0.01 to 0.1 s−1, which indicates that the microextractor is much more efficient. 4.4. Effect of Slug Velocity on Mass Transfer Coefficient. The data of Figure 11a was reprocessed with the average slug moving velocity as the abscissa. The results are shown in Figure 13. We can see that the mass transfer

Figure 15. Velocity field in slugs.

4.5. Effect of Slug Length on Mass Transfer Coefficient. The slug length in our experiments is proportional to the stroke volume but independent of the frequency, which is a specific feature of our operation manner and different from the mostly reported operation manner in which the slug length is a strong function of the flow rate. As shown in Figure 11a, with the same frequency, the overall mass transfer coefficient is slightly increased when the slug length of the aqueous phase or the organic phase is doubled. However, if we consider the problem at the same slug velocity, the slug length will have little effect on the mass transfer coefficient, as shown in Figure 13. This can also be explained by the two-film model shown in Figure 14. In this model, the thickness of the boundary layer is mainly determined by the slug velocity but independent of the slug length. Though the slug length affects the circulation time, which is defined as the time for the liquid to move from one end of the slug to the other end,31 it has little effect on the mass transfer coefficient because the effect of convection is negligible. One should notice that the above conclusion is quite different from the literature report. The mostly reported results show that the mass transfer rate is decreased when the slug length is increased. For example, Harries et al.32 and Kashid et al.33 have proved this law by simulating an interface neutralization reaction in the slug flow. However, they have also mentioned that the slug length in their work is a function of slug velocity. The relationship between the slug length and the slug velocity can be found in Burns’ experimental data34 which was used to verify the simulation results in the literature.32,33 Because the slug length is not independent of the slug velocity, the effect of the slug velocity is included when considering the slug length effect. Though the mass transfer rate increases when the slug length is decreased, the reason for the mass transfer enhancing is probably the increasing of the slug velocity. Therefore, the results of the present work are not contradictory with the literature report. The special operation manner of the present work provides a method to relieve the relationship between the slug length and the flow velocity so

Figure 13. Variation of the overall mass transfer coefficient as a function of the average slug velocity.

coefficient is nearly proportional to the slug moving velocity. Though the slug length changes with the variation of the strokes, the experimental data still falls on the same line. This can be explained by the simple model illustrated in Figure 14,

Figure 14. Two-film model for the mass transfer in the slug flow.

which is known as the two-film model. In this model, the mass transfer process is dominated by diffusion and the effect of convection is negligible. The partial mass transfer coefficient in each phase can be simply expressed by D ki = i , (i = A or O) δi (33) where Di is the diffusion coefficient and δi is the thickness of the boundary layer. On the basis of this model, the overall mass transfer coefficient mainly depends upon the boundary layer thickness. With the increasing of the slug velocity, boundary I


Article


Figure 16. Concentration distribution in mass transfer process u = 4.17 mm/s, CA,0 = 3.0 mol/L, t = 1.0 s.

that one can investigate the effect of the slug length independent of the flow velocity. 4.6. Simulated Mass Transfer Coefficient. CFD simulation was carried out to investigate the partial mass transfer coefficients in both the aqueous and organic phases. The simulated velocity distribution and concentration distribution in the slugs are shown in Figures 15 and 16. The innerrecirculation can be clearly observed in Figure 15. In fact, the inner-recirculation can be observed only when the slug interfaces are selected as the reference. If the channel wall is set as the reference (which is the most commonly used static reference frame), the inner-recirculation cannot be observed. In the static reference system, the interface moving velocity is equal to the slug moving velocity. The fluid on the axis of a slug flows with a velocity about 2 times that of the slug velocity. When flowing close to the interface, the fluid suddenly slow down and flows toward the channel wall. Meanwhile, the fluid near the wall flows to the axis at the tail of the slug. The fluid exchange between the near wall area and the axis area enhances the mass transfer in the slug, which is commonly known as the inner-recirculation. The mass transfer enhancement can be observed from Figure 16. The concentration change at the interface is fast spread to the center of the slug by the recirculation. One can also see from Figure 15 that the velocity around the interface is very low and form boundary layers where the mass transfer is mainly in form of molecular diffusion. The mass transfer coefficient is mainly determined by the thickness of the boundary layer based on the two-film theory. Correspondingly, the concentration gradient around the interface is much bigger than at other places, as shown in Figure 16. To verify the simulation results, the overall mass transfer coefficient was first calculated from the simulated average concentration based on eq 25. The comparison of the simulation results and the experimental results is shown in Figure 13. We can see that the simulation results agree well with the experiment results. This proves that the numeric method used in this study is applicable to simulate the mass transfer in slug flow. The partial mass transfer coefficients at the front and the tail of a slug should be different as can be seen from Figure 16. Separately considering them is not necessary because it is not convenient to use such mass transfer coefficients for calculation. The average mass transfer coefficients in both the aqueous and organic phases are calculated based on the simulated concentration distribution. The results are shown in Figure 17. We can see from Figure 17 that the mass transfer coefficients of both the phases increase with the slug velocity increasing. The mass transfer coefficient in the organic phase is larger than that in the aqueous phase. The reason is that the aqueous boundary layer around the liquid−liquid interface is much thicker than the organic boundary layer, which can be seen from Figure 15. The difference of the boundary layer thickness is due to the shape of the interface.

Figure 17. Partial mass transfer coefficients based on simulation results.

The partial mass transfer coefficient is commonly expressed by the Sherwood number, which is defined as kdm (34) D The Sherwood number is usually correlated to the Reynolds number and the Schmidt number, which represent the effect of operation conditions and physical properties, respectively. We perform such a correlation using the simulated data. The correlation equation as expressed by eq 35 is applicable for both the aqueous and organic phases. Sh =

Sh = 0.0015Re1.37Sc1.51

(35)

Equation 35 can also be used to predict the mass transfer coefficient in similar systems.

5. CONCLUSIONS The hydrodynamics and mass transfer study were performed in a newly developed countercurrent multistage microextraction system. A theoretical model was derived to describe the relationship between the pressure drop and the transient flow rate in such a pulsation system. The total flow resistance of the two phases was investigated based on the theoretical model and was found independent of the flow rate. The interfacial flow resistance was further studied and was found a constant, which indicated that the relationship between the slug velocity and the difference of the cosine value of dynamic contact angles was linear. The overall mass transfer coefficient was determined based on the extraction experimental data and was found positively correlated with the slug velocity. CFD simulation was carried out to investigate further the partial mass transfer coefficient in both the two phases. The Sherwood number in both phases was correlated to the Reynolds number and the Schmidt number. A correlation equation applicable in both phases was established. The correlation could further be used to predict the mass transfer coefficient in similar systems.

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AUTHOR INFORMATION

Corresponding Author

*S. Li. E-mail: [email protected]. J


Article

Industrial & Engineering Chemistry Research Notes

T = Period (s) u = Velocity of flow (m/s) um = Cross section average velocity (m/s)

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (21106077, 21376132, 21576147), and the Science Foundation of China University of Petroleum, Beijing (2462013YJRC025).

Greek Letters

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NOMENCLATURE C = Concentration of nitric acid (mol/L) CA = Concentration of nitric acid in the aqueous phase (mol/L) ΔCA = Mass transfer driving force (mol/L) CO = Concentration of nitric acid in the organic phase (mol/ L) d = Diameter of the connecting tubes (m) dc = Diameter of the check valve (m) dm = Diameter of a microchannel in the multichannel contactor (m) D = Diffusion coefficient (m2/s) f = Reciprocation frequency of the syringes (s−1) k = Partial mass transfer coefficient (m/s) kA = Partial mass transfer coefficient in the aqueous phase (m/s) kE = Interphase reaction rate coefficient (m/s) kO = Partial mass transfer coefficient in the organic phase (m/s) KOA = Overall mass transfer coefficient (m/s) lA = Length of an aqueous slug (m) lO = Length of an organic slug (m) L = Length of the connecting tubes (m) Lc = Length of the check valve (m) Lm = Length of a microchannel in the multichannel contactor (m) n = Channel number of the multichannel contactor Ns = Number of slug units in a microchannel p = Pressure (Pa) Δp = Total pressure drop (Pa) Δpave = Average pressure drop (Pa) Δpb = Pressure drop caused by the weight of the ball in a check valve (Pa) Δpc = Pressure drop in the check valve (Pa) ΔpI = Pressure drop caused by the interfacial force (Pa) ΔpI,ave = Average interfacial pressure drop (Pa) Δpm = Pressure drop in a microchannel of the multichannel (Pa) Δps = Static pressure drop (Pa) Δpt = Pressure drop in the connecting tubes (Pa) Δpμ,ave = Average viscous pressure drop (Pa) Q = Flow rate (μL/min) Qave = Average flow rate (μL/min) r = Variable radius in the connecting tubes (m) rs = Interface reaction rate, mol/(m2·s) R = Total flow resistance (Pa·s/m3) RI = Interfacial flow resistance (Pa·s/m3) Rμ = Viscous flow resistance (Pa·s/m3) Re = Reynolds number Sc = Schmidt number SA = Stroke volume of the aqueous phase syringe (μL) SO = Stroke volume of the organic phase syringe (μL) Sh = Sherwood number t = Time (s)

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α = Flow ratio between the aqueous phase and the organic phase γ = Interfacial tension between two phases (N/m) θ = Contact angle θA = Advancing contact angle θR = Receding contact angle μ = Viscosity of the fluid (Pa·s) μA = Viscosity of the aqueous phase (Pa·s) μO = Viscosity of the organic phase (Pa·s) ξc = A factor to correct the resistance in a check valve ρ = Density of the fluid (kg/m3) ρA = Density of the aqueous phase (kg/m3) ρO = Density of the organic phase (kg/m3)

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Hydrodynamics and Mass Transfer in a Countercurrent Multistage

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