Droplet Coalescence Phenomena during LiquidâLiquid

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Droplet coalescence phenomena during liquidliquid heterogeneous reactions in microreactors Xin Pu, Guangxiao Li, Yang Song, Minjing Shang, and Yuanhai Su Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b03324 • Publication Date (Web): 08 Oct 2017 Downloaded from http://pubs.acs.org on October 8, 2017

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Industrial & Engineering Chemistry Research

Droplet coalescence phenomena during liquid-liquid heterogeneous reactions in microreactors Xin Pu, Guangxiao Li, Yang Song, Minjing Shang and Yuanhai Su∗

Department of Chemical Engineering, School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China

Abstract The sulfonation of naphthalene with sulfuric acid to produce naphthalenesulfonic acid was carried out in capillary microreactors as a model liquid-liquid heterogeneous reaction to study the droplet coalescence phenomena. The effects of various factors associated with the droplet coalescence or the reaction kinetics, such as capillary length (residence time), reaction temperature, molar ratio of reactants, capillary wall wetting properties on the reaction performance were investigated. In particular, the influence of the droplet coalescence on the specific interfacial area, the mass transfer rate and the reaction performance was evaluated in detail. Surprisingly, the specific interfacial area could decrease up to 93% along the flow direction in the capillary microreactor with the droplet coalescence. Interestingly, the microreactor wall surface properties were found to affect the reaction performance significantly. Moreover, the Hatta number was evaluated, which reflected the competition between the mass *

Corresponding author. Tel.: +86 21-54738710, E-mail address: [email protected]. 1

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transfer and the reaction during the sulfonation in the capillary microreactors with the droplet coalescence. Keywords: sulfonation; naphthalene; droplet coalescence; specific interfacial area; mass transfer; Hatta number.

1. Introduction Liquid-liquid heterogeneous reactions such as nitration, sulfonation, amidation, liquid phase oxidation, etc., are widely applied to produce fine chemicals in process industry1-2. In these heterogeneous processes, the mass transfer and the chemical reaction compete between themselves, and thus the overall reaction performance is mainly determined by intrinsic reaction kinetics and transport properties inside reactors3. For fast liquid-liquid heterogeneous reactions, the reaction rate and the yield are significantly influenced by the mass transfer rate, and the key to increase the production rate is to facilitate the mass transfer by increasing the interfacial area between two immiscible liquid phases4. Conventional reactors including tank reactors, thin-film reactors, falling film reactors and jet loop reactors have been employed in liquid-liquid heterogeneous reaction processes

5-6

. However, these reactors have some disadvantages especially

when they are applied for highly exothermic and fast reaction systems. Insufficient heat and mass transfer capabilities of these reactors may give rise to obvious gradients of concentration and temperature inside reactors, which may lead to low reaction rate, local overheating of reactors, formation of many impurities or even runaway of the 2


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reaction7-8. In the past two decades, the application of microreactors in heterogeneous reaction processes for organic synthesis has been rather popular due to its specific properties9-11. Characterization with dimensions in the sub-millimeter range renders microreactors to have much larger surface area-to-volume ratio, higher mixing efficiency, faster heat and mass transfer rates compared with conventional reactors12-14. These properties of microreactors can be used for controlling fast and exothermic reactions such as the process of sulfonation. Compared with traditional batch processing, reactions carried out in microreactors can produce target products in higher yield and purity in shorter reaction time15-16. Müller et al.17 explored the sulfonation of toluene with a gas mixture of SO3 and N2 in a microreactor system. The high selectivity was obtained with precise temperature control and high pressure resistance of the microreactor at a SO3: toluene molar ratio of 0.05-0.15. Chen and his co-workers8 investigated the sulfonation of nitrobenzene using SO3 as the sulfonating agent in a microreactor. Their results indicated that the process safety was improved and the reaction time was obviously reduced with the use of microreactors for the sulfonation of nitrobenzene. As is well known, the mass transfer rate between two immiscible liquid phases strongly depends on flow patterns in microreactors/ microchannels9. Various flow patterns of the liquid-liquid heterogeneous systems in microchannels were observed, including droplet flow, slug flow, slug-drop flow, deformed interface flow, annular flow and parallel flow, etc18-21. As compared with other flow patterns, the slug flow in 3



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microchannels is frequently applied for various reaction processes due to enhanced mixing, increased mass transfer and less axial dispersion resulting from higher specific interfacial area and the internal circulations inside the slugs22-25. Nevertheless, only few reports focused on the flow pattern transformation during the liquid-liquid heterogeneous reaction processes in microreactors. Guan et al.26 studied the flow patterns during the transesterification of waste cooking oil in microreactors, using sunflower oil with water or oleic acid as a model reaction. It was found that the flow pattern in the microreactor changed from the slug flow at the inlet region to the parallel flow at the middle region, and then to a homogeneous liquid flow at the outlet region as the reaction proceeded. In microreactors, droplet flow plays an important role in realizing reactions or operations. It offers a unique platform for the miniaturization of chemical and biological research due to its high monodispersity, extremely small volumes and virtually unlimited numbers27. The dispersed phase typically used as the bearer of reactions can be wrapped by the continuous phase and the molecular diffusion between the dispersed phase droplets is avoided. Droplet coalescence is one of important droplet control technologies, which can be used to realize hydrate crystallization28, protein analysis29, etc. However, the effect of droplet coalescence on the liquid-liquid heterogeneous reactions in microreactors has not been thoroughly studied. Sulfonation of aromatics with sulfuric acid is a typical heterogeneous process, in which the aromatics transfer into the aqueous phase through the interface of two 4


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immiscible liquid phases and then react with active sulfonating components to produce the sulfonated products (Scheme 1)30. This kind of liquid-liquid heterogenous reactions is of importance in the synthesis of intermediates for the preparation of numerous useful dyes and dispersants30-31. In this work, the sulfonation of naphthalene with sulfuric acid to produce naphthalenesulfonic acid as a model reaction was carried out in capillary microreactors to study the droplet coalescence phenomena and its effects on the reaction performance of the liquid-liquid heterogeneous processes. Various factors influencing the droplet coalescence and the reaction performance, such as capillary length (residence time), reaction temperature and molar ratio of reactants were investigated. The influence of the droplet coalescence during the sulfonation on the specific interfacial area, the mass transfer and the reaction performance was evaluated. Moreover, the effect of the surface wettability of microreactor wall on the reaction performance was investigated. A film model was applied to calculated the variation of Hatta number due to the droplet coalescence during the sulfonation in the capillary microreactors.

Scheme 1. Proposed mechanism on the sulfonation of aromatic compounds with 5



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sulfuric acid.

2. Experimental 2.1. Material and apparatus Sulfuric acid (AR, 98%), tetrachloroethane (AR, 99%) and naphthalene (AR, 99%) were purchased from Sinopharm Chemical Reagent Company, China. All chemicals were purchased from commercial companies and used without further purification. The schematic diagram of experimental setup is shown in Figure 1. The polyetheretherketone (PEEK) T-micromixer and perfluoroalkoxy (PFA) capillary were purchased from IDEX Health & Science LLC, USA. The stainless steel capillary and T-micromixer were purchased from Valco Instruments Co. Inc., USA. All the capillaries applied had the same inner diameter (1 mm) and the same outer diameter (1.6 mm). The organic phase with naphthalene dissolved in tetrachloroethane (continuous phase) and the aqueous solution with 98 wt % sulfuric acid (dispersed phase) were separately delivered into the capillary microreactor system by two syringe pumps (NE-1800, New Era Pump System, Inc., USA). In all experiments, the initial concentration of naphthalene in the organic phase was 1 mol/l. These two immiscible reactive solutions were firstly mixed in a PEEK T-micromixer with an inner diameter of 1.0 mm, and then reacted in a PFA capillary or a stainless steel capillary with the same inner diameter. Naphthalene transferred from the organic phase to the aqueous phase, in which the sulfonation occurred. The residence time was regulated by changing the capillary length. The feeding tubing, the T-micromixer 6


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and the capillary were all immersed in an oil bath to ensure a constant reaction temperature. The reaction effluent was collected in a separator that was placed inside an ice-water bath. For each experiment, it was repeated for three times with controlled experimental errors (< 3%) and average measurement values were provided as final results.

Figure 1. The schematic overview of experimental setup.

2.2. Sample analysis After the reaction was quenched, the organic and acid phases were separated by a separatory funnel. The organic phase was treated with the alkaline solution until it reached neutral. Then, the organic phase was analyzed by Agilent 7890B gas chromatography

(GC

with

flame

ionization

detector,

HP-5

column,

30m×0.32mm×0.25µm) for the determination of the conversion. For the determination of selectivity, a HPLC system (Shimadzu LC-16, Japan) equipped with a column (WondaSil C18-WR 5 µm, 4.6×150 mm) was used. The mass 7



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fractions of different kinds of naphthalene sulfonic acid were determined by using the UV-detector of HPLC at a wavelength of 230 nm32. A high-speed CCD camera (PhantomLab110-12G, USA) installed with a stereo microscope (Olympus, SZ2-CLS, Japan) was used for capturing snapshots of droplet flow and slug flow inside the capillary microreactor. In all experiments, the high-speed camera was set at a resolution of 1280×800 pixel2, with a captured area of about 19.9×12.5 mm2. The shooting of flow pattern was conducted at room temperature. Even the CCD camera could not capture the flow patterns in the PFA capillary microreactor immersed inside oil bath, the photos captured at the room temperature could be used to demonstrate the droplet coalescence phenomena and to implement relevant analysis. The sulfonation of naphthalene with sulfuric acid in the PFA capillary microreactor almost could not occur at the room temperature. In this case, the physical properties of two reactive phases (i.e., aqueous and organic phases) could be considered to maintain constant. Moreover, long dispersed phase slugs could be observed at the outlet of the PFA capillary microreactor due to the droplet coalescence when the sulfonation of naphthalene was conducted at 393 K, which were comparable with the dispersed phase slugs captured by the CCD camera at the room temperature. The optical instrument (Dataphysics OCA15) was used to measure the contact angle of the aqueous / organic phase on the PFA / stainless steel plate on the basis of the sessile drop method.

3. Results and discussion 8


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3.1. Effects of the residence time and the droplet coalescence on the reaction performance The effect of the residence time (t) on the conversion of naphthalene in the PFA capillary microreactor is shown in Figure 2. The reaction temperature was kept at 393 K and the sulfuric acid to naphthalene molar ratio was 5.0. The residence time was varied with different capillary lengths while keeping the flow rates of the organic and aqueous phases constant (Qor = 0.6433 ml/min and Qaq =0.1417 ml/min). It can be seen that the naphthalene conversion increased with increasing the residence time. It is worth noting that the increasing trend was more pronounced when the residence time was less than four minutes or longer than eight minutes under experimental conditions. However, the conversion had no significant change when the residence time was in the range of 4-8 min. This is mainly attributed to the flow pattern transformation with different residence times (capillary lengths) during the sulfonation in the capillary microreactors.

80 70

Conversion (%)

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60 50 40 30 20 10

0

2

4

6

8

Time (min) 9


10


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Figure 2. Effect of the residence time on the conversion of naphthalene in the PFA capillary microreactor (molar ratio of sulfuric acid to naphthalene q = 5.0, Qt = 0.785 ml/min and T = 393 K).

As shown in Figure 3, the flow pattern gradually changed from the droplet flow to the slug flow along the capillary microreactor with a length of 10 m, due to the coalescence of dispersed phase droplets. At the front part of the capillary microreactor (flow travelling distance L < 4 m), the dispersed droplets of aqueous phase were isolated by the continuous phase (organic phase) with the shape of a rugby ball with the width less than the inner diameter of the capillary, while the continuous phase existed in the form of liquid slugs (Figure 3a). As the travelling distance is more than 4 m (t > 4 min), the droplets began to coalescence to form bigger ones (Figure 3b and c). Such coalescence significantly reduced the contact area between the aqueous and organic phases, and thus significantly decreased the mass transfer rate of naphthalene from the organic phase to the aqueous phase and the reaction rate. Therefore, the naphthalene conversion did not increase obviously when the capillary length increased from 4 m to 8 m. As the travelling distance further increased to 10 m, the droplet coalescence resulted in the slug flow in the capillary microreactor, and the dispersed phase slugs were formed with the characteristic length longer than the inner diameter of the capillary (Figure 3d). The internal circulations inside both the dispersed phase slugs and the continuous phase slugs improved the surface renewal velocity and the mass transfer rate, leading to the increase in the reaction rate and the 10


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conversion of naphthalene26, 33. These results also indicated that the sulfonation of naphthalene was still controlled by the transport of naphthalene from the organic phase to the aqueous phase under involved experimental conditions even when the residence time was longer than 8 min (L > 8 m).

Figure 3. Flow pattern characteristics of the two immiscible reactive phases in the PFA capillary microreactor at different capturing positions. (a) L = 2 m, t = 2 min, (b) L = 4 m, t = 4 min, (c) L = 8 m, t = 8 min, (d) L =10 m, t = 10 min.

In fact, the coalescence of droplets in reactors is rather complex and it only occurs when the interaction time of droplets is sufficient for the intervening film to drain out down to the critical rupture thickness34-35. Currently, there have been some references about the droplet coalescence in specific parts of microreactors such as junctions and 11



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chambers. However, the droplet coalescence in main channels of microreactors was not paid attention to. As the sulfonation of naphthalene processed along the flow direction in the capillary microreactor, the viscosity of the dispersed phase (droplets) increased. More importantly, the kinetic energy carried by the dispersed phase was much lower compared to the continuous phase due to the low volumetric flux ratio of the dispersed phase to the continuous phase, and the specific energy dissipation of the dispersed phase obviously was large with a long flow travelling distance (e.g., L > 4 m) especially when the direct contact between the dispersed phase and the capillary inner wall occurred36-38. Therefore, the movement of the dispersed phase droplets downstream was slower compared with that of the droplets upstream, making the contact and coalescence of consecutive dispersed phase droplets possible. In order to evaluate the effect of the droplet coalescence on the mass transfer performance in the capillary microreactor for the sulfonation of naphthalene, the specific interfacial area (a) is calculated. When the capillary number (Cad = µcUs/γ) is less than 0.04, the liquid film thickness between the dispersed phase droplet and the inner wall of the capillary can be negligible according to Equation 1 39-42: h = 1.34Ca 2/3 r

(1)

where h is the liquid film thickness between the dispersed phase droplet and the inner wall of the capillary, and r is the inner radius of the capillary, respectively. The value of µcis about 1×10-3 Pa·s, and the value of γ is about 0.0256 N/m. The value of Ca is then obtained (Ca = 0.65×10-3), giving the liquid film thicknesses about 5 µm. In other words, the dispersed phase droplets could be considered to directly contact with 12


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the inner wall of the capillary, and thus the shape of these droplets before the coalescence looked like the rugby ball (Figure 3a). It may be attributed to that there was no wetting of the droplet on the capillary wall surface43. The contact angles of the aqueous and organic phases on the PFA plate were 80° and 49°, respectively. The similar wetting properties of the PFA capillary wall regarding to both the aqueous and organic phases may be the another reason for the shape of droplets looking like the rugby ball. Figure 4 shows the schematic diagram of a unit of the slug flow in which the dispersed phase slug with a length of several fold inner diameter of the capillary is formed due to the coalescence of several smaller droplets. In Figure 4b, the dispersed phase slug can be considered as the combination of two ellipsoid caps and a cylinder, and its volume can be calculated by the following equation44: l 4 Vs = π × r 2 × l + × π × r × ( 0 ) 2 3 2

(2)

where l is the length of the cylinder in the middle part of the dispersed phase slug. The interfacial area between the two immiscible liquid phases (As) can be calculated as follows.

l  4  As = × π ×  r × l0 + ( 0 ) 2  +2 × π × r × l 3 2  

(3)

The volume of a dispersed phase droplet before the coalescence can be calculated based on its rugby shape (Figure 4a): Vd =

l 4 × π × r × ( 0 )2 3 2

(4)

where l0 is the initial length of the droplet. Therefore, the number of the dispersed phase droplets (nd) that join in the coalescence for the formation of the slug flow unit 13



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can be calculated by the following equation:

nd =

Vs Vd

(5)

Moreover, the area of a dispersed phase droplet (Ad) before the coalescence can be calculated by the following equation. Ad =

l  4  × π ×  r × l0 + ( 0 ) 2  3 2  

(6)

The specific interfacial areas for the slug flow unit and the droplet flow without the coalescence are respectively defined as a1anda2: As V nd × Ad a2 = V a1 =

(7) (8)

Therefore, the degree of the decrease in the specific interfacial area due to the droplet coalescence (Ds) can be calculated as follows:

DS =

a2 − a1 a2

(9)

It can be concluded that the decrease of the specific interfacial area caused by the droplet coalescence in the PFA capillary microreactor could reach 93% when the liquid film thickness could be negligible (Figure 4c). Furthermore, the degree of the decrease in the specific interfacial area was also evaluated when the liquid film thickness between the dispersed phase droplet and the inner wall of the capillary would not be neglected. In this case, the interfacial area between this thin layer of the organic phase and the dispersed droplet (slug) greatly contributed to the specific interfacial area. Figure 4c shows the variation of Ds along the capillary microreactor 14


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with and without neglecting the liquid film thickness between the dispersed phase droplet and the inner wall of the capillary. As can be seen in Figure 4c, the degree of the decrease in the specific interfacial area could reach 25% even the interfacial area between this thin layer of the organic phase and the dispersed droplet was considered to contribute to the specific interfacial area.

Figure 4. Schematic diagram of the droplet flow without the coalescence (a), the slug flow (b) and the variation of Ds (c), for estimating the change of the specific interfacial area due to the droplet coalescence.

3.2. Effect of the reaction temperature on the reaction performance The temperature usually plays an important role on reaction rate and product selectivity in the sulfonation of aromatics45. Figure 5 shows the conversion of naphthalene at different reaction temperatures. The sulfuric acid to naphthalene molar ratio was 5.0 and the residence time was maintained at 10 min. The conversion of naphthalene increased with increasing the reaction temperature. It was observed that the conversion of naphthalene was significantly increased from 30% to 75%, when 15



the reaction temperature increased from 373 K to 393 K. A further increase in the reaction temperature from 393 K to 413 K did not obviously improve the conversion of naphthalene. The reaction rate constant typically increases with the increase of the temperature according to Arrhenius Equation. Moreover, with the increase of the temperature the mass transfer rate increased due to the increased diffusivity of naphthalene in the aqueous phase46. Both the reaction rate constant and the mass transfer rate increased with the increase of the reaction temperature. The reaction kinetics dominated the sulfonation in the range of 373-393 K, while the mass transfer limitation played a key role in the range of 393-413 K. As a consequence, the conversion of naphthalene significantly increased and then smoothly increased with the increase of the reaction temperature.

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60 50 40 30 20 370

380

390

400

410

420

Temperature (K)

Figure 5. Effect of the reaction temperature on the conversion of naphthalene in the PFA capillary microreactor (q = 5.0, Qor = 0.6433 ml/min, Qaq = 0.1417 ml/min and t 16


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= 10 min).

Table 1 showed the selectivity of this sulfonation reaction conducted in the PFA capillary microreactor. It can be found that the percentage of α- naphthalene sulfonic acid decreased with the increase of the reaction temperature, while that of β-naphthalene sulfonic acid increased with increasing the reaction temperature. According to the reaction characteristics, the generation of α- naphthalene is easier than that of β-naphthalene sulfonic acid. However, the thermal stability of β-naphthalene sulfonic acid is higher than that of α-naphthalene sulfonic acid. The percentage of naphthalene disulfonic acid was almost kept the same when the temperature was varied from 373 K to 413 K, indicating that the selectivity of naphthalene disulfonic acid is not sensitive to the change of reaction temperature.

Table 1. Effect of temperature on the selectivity of the sulfonation reaction w (α- naphthalene

w (β-naphthalene

w (naphthalene

sulfonic acid) / %

sulfonic acid) / %

disulfonic acid) / %

373

56.02

5.32

38.66

383

54.87

7.09

38.04

393

43.85

19.36

36.79

403

39.31

26.54

34.15

413

8.92

57.29

33.79

Temperature/K

17



3.3. Effect of the molar ratio of sulfuric acid to naphthalene on the reaction performance The effect of the mole ratio of sulfuric acid to naphthalene on the conversion of naphthalene was investigated by changing the flow rate ratio of the aqueous phase to the organic phase at the reaction temperature of 393 K and the residence time of 10 min. The total flow rate of the organic and aqueous phases was kept constant (0.785 ml/min). The conversion of naphthalene obviously increased with the increase of the mole ratio of sulfuric acid to naphthalene, as shown in Figure 6. A higher mole ratio of sulfuric acid to naphthalene provided more active sulfonating components for the sulfonation, resulting in the increase of the reaction rate and the conversion of naphthalene47.

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60 50 40 30 20 10 0

2

4

6

8

10

Mole ratio (sulfuric acid/naphthalene)

Figure 6. Effect of the mole ratio on the conversion of naphthalene in the PFA capillary microreactor (Qt = 0.785 ml/min, T = 393 K and t = 10 min). 18


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The flow characteristics in the PFA capillary microreactor with different flow rate ratios of the aqueous phase to the organic phase are shown in Figure 7. The photos were captured at the flow travelling distance of 2 meters in the capillary microreactor. The total flow rate of the organic and aqueous phases was kept constant. As can be seen in Figure 7, the dispersed phase droplets began to coalescence when the flow rate ratio of the aqueous phase to the organic phase was more than 0.22. Consequently, the mass transfer rate and the reaction rate did not increase obviously as the flow rate ratio of the aqueous phase to the organic phase was larger than 0.22, and the optimal flow rate ratio of the aqueous phase to the organic phase was considered to be 0.22.

19



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Figure 7. Flow characteristics in the PFA capillary microreactor with different flow rate ratios of the aqueous phase to the organic phase, (a) Qaq : Qor = 0.044, (b) Qaq : Qor = 0.13, (c) Qaq : Qor = 0.22, (d) Qaq : Qor = 0.31, (e) Qaq : Qor = 0.40.

3.4. Effect of capillary wall wetting properties on the reaction performance The effect of capillary wall wetting properties on the sulfonation of naphthalene was studied by the comparison between the PFA capillary microreactor and the stainless steel capillary microreactor at the reaction temperature of 393 K and the sulfuric acid to naphthalene molar ratio of 5.0. Both the PFA capillary microreactor and the stainless steel capillary microreactor had the same length (10 m) and the same 20


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inner diameter (1 mm). The contact angles of the aqueous and organic phases on the stainless steel plate were measured, and their values were 74° and 32°, respectively. Such a contact angle difference (42°) indicated that the aqueous phase tends to be more easily dispersed when it contacts with the organic phase in the stainless steel capillary microreactor compared with the PFA capillary microreactor. As shown in Figure 8, the capillary wall wetting properties had significant influence on the sulfonation performance and the conversion of naphthalene in the stainless steel capillary microreactor was much higher compared with the PFA capillary microreactor. Under optimized conditions in the PFA capillary microreactor, the conversion of naphthalene could reach 90% in the stainless steel capillary microreactor at the residence time of 10 min.

90 PFA capillary Stainless steel capillary

80

Conversion (%)

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70 60 50 40 30 0

2

4

6

8

10

Time (min)

Figure 8. Effect of capillary wall wetting properties on the conversion of naphthalene (Qt = 0.785 ml/min, q = 5.0 and T = 393 K).

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In order to determine the flow pattern, the outlet of an 8 m length stainless steel capillary was closely connected with a PFA capillary with the same inner diameter through a transparent plastic hose (Figure 9a). As shown in Figure 9b, a photo was captured at the position right after the joint between the stainless steel capillary and the PFA capillary, which can be used to reflect the flow characteristics inside the stainless steel capillary at the travelling distance of 8 m. It is obvious that the regular slug flow was formed and the droplet coalescence phenomena could be neglected in the stainless steel capillary microreactor. It may be the main reason for the higher conversion of naphthalene when the stainless steel capillary microreactor was applied for conducting the sulfonation of naphthalene compared with the PFA capillary microreactor (Figure 8).

Figure 9. (a) Photo of the connection of the stainless steel capillary and the PFA capillary, (b) flow characteristics at the position right after the joint between the stainless steel capillary and the PFA capillary (Qor = 0.6433 ml/min, Qaq = 0.1417 ml/min, L = 8 m and t = 8 min).

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3.5. Variation of Hatta number with the droplet coalescence According to literature, the sulfonation of naphthalene with sulfuric acid is a third-order reaction, and it is first order with respect to naphthalene and second order with respect to sulfuric acid48. The following equation has been often used to express the sulfonation rate of aromatics in the sulfuric acid solution:

－d [ Ar ] / dt = k[ Ar ] AH 2SO4 2 / Aw

(10)

where [Ar] denotes the concentration of naphthalene to be sulfonated, AH2SO4 is the activity factor of sulfuric acid, and Aw is the activity factor of water, which is proportional to the water concentration. k is the reaction rate constant, and t is the reaction time. The mole ratio of sulfuric acid to naphthalene was 5.0, indicating that the amount of sulfuric acid was much excess in this sulfonation. Therefore, Equation (10) can be simplified as Equation (11) with the assumption that the concentrations of sulfuric acid and water were kept nearly constant during the sulfonation in the capillary microreactor. －

dC = k1 × C dt

(11)

where k1 represents the pseudo first-order reaction rate constant, C is the substrate concentration at time t. After integration, Equation (11) can be further transformed to the following equation:

－ln(1 − X ) = k1 × t

(12)

If the rate is first order with respect to naphthalene, a plot of –ln(1-X) vs t will fit a straight line. As shown in Figure 10, there is a strictly linear relationship between – ln(1-X) and t when the stainless steel capillary microreactor was applied for this 23



sulfonation. For the PFA capillary microreactor, a plot of –ln(1-X) vs t fits a straight line when the residence time was less than 4 min. However, the linear relationship could not be maintained when the residence time was more than 4 min due to the mismatching between the intrinsic reaction kinetics and the mass transfer rate resulting from the influence of the droplet coalescence in the PFA capillary microreactor.

3.0 Stainless steel capillary PFA capillary

2.5 2.0 -ln(1-x)

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

1.5 1.0 0.5 0

1

2

3

4

5

6

7

8

9

10 11

time (min)

Figure 10. Reaction kinetics characteristics of the sulfonation of naphthalene in the PFA capillary microreactor and the stainless steel capillary microreactor (Qt = 0.785 ml/min, q = 5.0 and T = 393 K).

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Figure 11. Schematic diagram of film model for calculating the Hatta number.

Moreover, the Hatta number (Ha) can be calculated, which compares the rate of reaction in the liquid film to the rate of diffusion through the film based on a film model49. Due to the droplet coalescence along the flow direction in the capillary microreactor, the mass transfer could gradually become the controlling step during the sulfonation. The naphthalene diffused across the film with the thickness of δ and reacted with sulfuric acid in the bulk of the aqueous phase. The concentration difference driving this diffusion is (CAi-CA), as shown in Figure 11. In present work, the concentration of sulfuric acid was much higher than the solubility of naphthalene in the aqueous phase (CB≫ CAi), and the reaction was pseudo first order in naphthalene with the rate constant being kCB. Then, a reaction time constant for the consumption of naphthalene in the film is (kCB-1) 4. The transport of naphthalene through this film was driven by the molecular diffusion, for which Fick’s second law gives a time constant (δ2/DB, where DB is the diffusivity of naphthalene in the aqueous phase). This proportionality is often termed as the liquid film mass transfer coefficient 25



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(kl), giving the following definition. kl =

DB

(13)

δ

When the diffusion is fast relative to the reaction, hardly any naphthalene can react in the film. This occurs when the following inequality is satisfied:

δ 2 / DB 2.5 l0 

(17)

The value of DB is about 1.1×10-9 m2/s53 and kCB can be calculated according to the experimental data obtained from the stainless steel capillary microreactor. The values of l and l0 were obtained depending on the droplet coalescence inside the PFA capillary microreactor, and the value of ε was treated as 1.5 when l/l0 was more than 2.5. The value of Hatta number was then obtained. Figure 12 shows the variation of Ha number caused by the droplet coalescence in the PFA capillary microreactor. It should be noted that for the stainless steel capillary microreactor the phenomena of droplet coalescence were neglected and the mass transfer coefficient was considered to maintain constant based on the reaction performance of sulfonation and the flow patterns inside this capillary microreactor.

4.0 3.5 PFA capillary

PFA capillary

3.0 2.5

Ha

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2.0 1.5 1.0 stainless steel capillary

PFA capillary

0.5 0.0 1

2

3

4

5

l/l0 27


6

7


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

Figure 12. The variation of Ha number caused by the droplet coalescence in the capillary microreactor.

When the sulfonation was conducted in the stainless steel capillary microreactor, the value of Ha number was kept constant. This indicated that the mass transfer rate could match the characteristic reaction rate and the conversion increased with the increase of the residence time (Figure 8). However, the value of Ha number varied along the flow direction in the PFA capillary microreactor due to the droplet coalescence. Moreover, the value of Ha number for the PFA capillary microreactor was larger than that for the stainless steel capillary microreactor, which again proved the importance of microreactor wall surface properties. In fact, the values of Ha number for both the stainless steel capillary microreactor and the PFA capillary microreactor was in the range of 1-3, indicating that the sulfonation was a fast reaction and occurred at both the liquid-liquid interface and the bulk of the aqueous phase 49.

4. Conclusion The sulfonation of naphthalene with sulfuric acid to produce naphthalenesulfonic acid as a model reaction was conducted in capillary microreactors in order to study the droplet phenomena and its influence on the reaction performance of liquid-liquid heterogeneous processes. It was found that the naphthalene conversion increased with increasing the residence time in the PFA capillary microreactor. However, it did not 28


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obviously change when the residence time was in the range of 4-8 min, which was due to the reduced specific interfacial area resulting from the droplet coalescence in the PFA capillary microreactor. The degree of the decrease in the specific interfacial area due to the droplet coalescence even reached 93% based on a simplified mathematical calculation. Higher reaction temperature led to higher conversion of naphthalene and higher selectivity of β-naphthalene sulfonic acid. An increase in the molar ratio of sulfuric acid to naphthalene not only resulted in higher naphthalene conversion, but also aggravated the droplet coalescence to form the slug flow. The microreactor wall surface properties was highly related to the droplet coalescence and thus significantly affected the reaction performance. The naphthalene conversion in the stainless steel capillary microreactor could reach 90% under optimized conditions, and it was obviously higher than that in the PFA capillary microreactor. Furthermore, the Hatta number calculated based on a film model indicated the competition between the mass transfer rate and the reaction rate in the sulfonation for both the PFA capillary microreactor with the droplet coalescence and the stainless steel capillary microreactor without droplet coalescence.

Acknowledgement We would like to acknowledge financial support from the National Natural Science Foundation of China (No. 21676164) and China Postdoctoral Science Foundation (2017M611565).

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List of figure captions Figure 1. The schematic overview of experimental setup. Figure 2. Effect of the residence time on the conversion of naphthalene in the PFA capillary microreactor (molar ratio of sulfuric acid to naphthalene q = 5.0, Qt =0.785 ml/min and T = 393 K). Figure 3. Flow pattern characteristics of the two immiscible reactive phases in the PFA capillary microreactor at different capturing positions. (a) L = 2 m, t = 2 min, (b) L = 4 m, t = 4 min, (c) L = 8 m, t = 8 min, (d) L =10 m, t = 10 min. Figure 4. Schematic diagram of the droplet flow without the coalescence (a), the slug flow (b) and the variation of Ds (c) for estimating the change of the specific interfacial area due to the droplet coalescence. Figure 5. Effect of the reaction temperature on the conversion of naphthalene in the PFA capillary microreactor (q = 5.0, Qor = 0.6433 ml/min, Qaq = 0.1417 ml/min and t = 10 min). Figure 6. Effect of the mole ratio on the conversion of naphthalene in the PFA 37



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capillary microreactor (Qt= 0.785 ml/min, T = 393 K and t = 10 min). Figure 7. Flow characteristics in the PFA capillary microreactor with different flow rate ratios of the aqueous phase to the organic phase, (a) Qaq :Qor= 0.044, (b) Qaq :Qor= 0.13, (c) Qaq :Qor = 0.22, (d) Qaq :Qor = 0.31, (e) Qaq :Qor= 0.40. Figure 8. Effect of capillary wall wetting properties on the conversion of naphthalene (Qt = 0.785ml/min, q = 5.0 and T = 393 K). Figure 9. (a) Photo of the connection of the stainless steel capillary and the PFA capillary, (b) flow characteristics at the position right after the joint between the stainless steel capillary and the PFA capillary (Qor = 0.6433 ml/min, Qaq = 0.1417 ml/min, L = 8 m and t = 8 min). Figure 10. Reaction kinetics characteristics of the sulfonation of naphthalene in the PFA capillary microreactor and the stainless steel capillary microreactor (Qt = 0.785ml/min, q = 5.0 and T = 393 K). Figure 11. Schematic diagram of film model for calculating the Hatta number. Figure 12. The variation of Ha number caused by the droplet coalescence in the capillary microreactor.

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Droplet Coalescence Phenomena during LiquidâLiquid

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