Article pubs.acs.org/IECR
Cite This: Ind. Eng. Chem. Res. 2019, 58, 13357−13365
Mixing Performance and Application of a Three-Dimensional Serpentine Microchannel Reactor with a Periodic Vortex-Inducing Structure Mingzhao Guo,† Xingjian Hu,‡ Fan Yang,‡ Song Jiao,§ Yujun Wang,*,† Haiyan Zhao,‡ Guangsheng Luo,† and Huimin Yu§ †
State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, China State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China § Key Laboratory of Industrial Biocatalysis, Tsinghua University, The Ministry of Education, Beijing, 100084, China
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‡
ABSTRACT: A new type of three-dimensional (3D) serpentine microchannel reactor was fabricated by thermally bonding stacked polyimide films to greatly improve the mixing efficiency by transversal vortices at low Reynolds number (Re). The effects of Re, flow ratio R, and channel width on the mixing performance were investigated using the Villermaux−Dushman method, in which the segregation index XS was utilized to quantify the mixing efficiency. The results showed that XS decreased with increasing Re, decreasing R, and reducing channel width. Then, a computational fluid dynamics model was employed to analyze the flow characteristics. The vortices that varied periodically along the 3D serpentine microchannel significantly improved the mixing efficiency. Furthermore, the application of the 3D serpentine microchannel reactor in the biohydration of acrylonitrile demonstrated that the new design is very promising for fast reactions that are limited by mass transfer resistance.
1. INTRODUCTION
shown that if the advection is chaotic, rapid intermixing between multiple components can be achieved.6 The development of new methodologies for the fabrication of microreactors, such as soft lithography, three-dimensional (3D) printing, and laser ablation, has encouraged researchers to explore the geometric modifications of microchannel reactors.6 Mubashshir et al.10 fabricated a vortex micro Tmixer using the soft lithography technique. The structure in which the inlet channels join the mixing channel at an offset position could create vortex flow, which enhances the mixing performance. Okafor et al.11 manufactured a continuous flow oscillatory baffled reactor by 3D printing and synthesized nearly monodisperse silver nanoparticles in this reactor owing to its high mixing efficiency. He et al.12 created 3D helical microchannels with femtosecond laser irradiation. Kim et al.13 fabricated multilayered polyimide (PI) film microreactors through laser ablation and proved that the 3D serpentine structure could achieve submillisecond mixing and make
In recent years, microchannel reactors have received considerable attention from many researchers and companies because of their extensive applications in industrial processes such as polymerization, precipitation, pharmaceutical synthesis, and biocatalytic reactions.1,2 The benefits of microchannel reactors include high efficiency of heat and mass transfer, reduced energy consumption, and safety performance because of its large surface-to-volume ratio and the short transport path compared to other devices.3 The mixing performance has a significant influence on the conversion rate and selectivity of reactions in the liquid phase, especially when dealing with fast reactions.4 Because microchannel reactors, typically in submillimeter dimensions, generally operate at low Reynolds number (Re), the flow is predominantly laminar; thus, the mixing process has to mainly rely on molecular diffusion, which requires a considerable mixing time and channel length.5 To overcome this limitation and achieve a more efficient mixing, different geometric features, such as ridge/groove systems,6 a split−recombine structure,7 barriers, obstacles, rhombic micromixer,8 and serpentine microchannels,9 have been designed to induce transversal advection. It has been © 2019 American Chemical Society
Received: Revised: Accepted: Published: 13357
March 21, 2019 June 29, 2019 July 2, 2019 July 2, 2019 DOI: 10.1021/acs.iecr.9b01573 Ind. Eng. Chem. Res. 2019, 58, 13357−13365
Article
Industrial & Engineering Chemistry Research
thermal bonding PI films, patterned by ultraviolet laser, can precisely implement the design of 3D microchannels with excellent mechanical strength and sealing properties. The proposed design aims to enhance the mixing efficiency by inducing periodic vortices to strengthen the secondary flow in microchannels. The performance characteristics of the new 3D serpentine microchannels was evaluated through experimental and numerical investigations at low Re, and the mechanism of inducing periodic vortices in the new design was examined. The new design was then applied to the biohydration process of acrylonitrile catalyzed by Rhodococcus ruber TH3 free cells. Because this biocatalytic reaction system is limited by mass transfer and an excessive local concentration of acrylonitrile may inactivate cells, the improvement of mixing can accelerate the reaction rate.21 The results of the new design were also compared with those of the simple design without 3D turns. Through an evaluation of the mixing performance and an application to the acrylonitrile biohydration process, the new design of the 3D serpentine microchannel reactor with the vortex-inducing structure was proven to be very promising for rapid reactions limited by the mixing efficiency.
organic synthesis outpace the Fries rearrangement. Malecha et al.14 proposed an I-shape serpentine micromixer and proved that the energetic efficiency of the micromixer is comparable to efficiencies of classical mixers. In various microchannels with different shapes, the flow direction changes in three dimensions are crucial for the generation of convection. Therefore, how to easily design and fabricate effective 3D microchannels with a precise and reproducible technique is a research hotspot. Among various processing methods, laser ablation could complete the whole microfabrication in a few minutes for polymer chips; hence, it is widely used in microfluidic devices.15 The micromixing performance is important for the design of microfluidic devices and their consequent applications.2 Therefore, many rapid competing chemical reaction systems with mixing-sensitive reaction selectivities have been utilized to quantitatively analyze the micromixing efficiency. Among them, the Villermaux−Dushman method based on the iodide−iodate reaction system has been widely applied. Using this approach, many researchers have studied the mixing performance of various microreactors characterized by a segregation index in single and multiphase systems.1 However, such an experimental method cannot directly obtain the information on local distribution of flow velocity and component concentration, which can help in designing and optimizing the geometric features of microchannel reactors. Recently, along with the rapid development of computer capacity, numerical simulation by computational fluid dynamics (CFD) has become an economic and effective method of investigating the reactive flow and of exploring new geometries of microreactors through visualizing the mixing and reaction process.16,17 The simplest T-type and Y-type microchannel reactors have been studied by many researchers using the Villermaux−Dushman method and CFD simulation.1,2,4 For more complicated microreactors, researchers prefer to use just CFD simulations for studying the mixing performance. Alam et al.9 numerically analyzed the mixing performance in a curved microchannel with rectangular grooves in the sidewalls, and the grooved channel showed a higher mixing index than the smooth channel. Hossain et al. investigated the mixing of two flows in a planar serpentine micromixer with nonaligned inputs18 and a 3D serpentine split-and-recombine micromixer at different Re values by the CFD method.19 Clark et al. discussed the effect of planar serpentine micromixers with nonrectangular cross sections on mixing through computational work; the change in orientation of cross section increased the mixing performance.6 The above cited works by different researchers show that microchannels with repeating curved sections or serpentine turns have been a popular design to generate cross-sectional flows and induce convection that is capable of enhancing the mixing at low Re values.20 However, the fabrication and further scale-up of many of these complicated microchannels are difficult. In addition, although many numerical studies on mixing performance in various serpentine microchannels with specific cross-sectional shapes have been reported, comparative assessments on experimental and numerical research are limited. In this study, a novel periodic 3D serpentine microchannel reactor consisting of nonaligned perpendicular microchannels has been fabricated effectively using the method of ultraviolet laser ablation coupled with thermal bonding. The PI material used in this study offers a higher chemical and thermal stability than other polymers. Moreover, the fabrication method of
2. EXPERIMENTAL SECTION 2.1. Fabrication of 3D Serpentine Microchannel Reactor. The basic designs of the microchannel reactors used in this study are shown in Figure 1a. The novel 3D serpentine microchannel reactor consists of nonaligned T-joint and 3D turns, while the other one is a simple nonaligned Tjoint integrated with a straight microchannel as a comparison. The difference between the two microreactors is that the mixing region of the 3D serpentine microchannel reactor can change the orientation of fluids to be mixed periodically in three dimensions along the flow distance, which may create transversal flow and further induce the transition to chaotic advection at low Re. The microreactors used in this study were fabricated by thermally bonding stacked PI films, each of which was patterned by ultraviolet laser ablation.13,15 For the 3D serpentine microchannel reactors, first, six 125 μm thick PI films (Dupont, USA) were fully ablated by an ultraviolet laser technique (355 nm, Bellin Laser Co. Ltd., China) to form the desired rectangular cross-sectional shape and holes (1.60 mm diameter circles for inlet/outlet and alignment holes). Then, the ablated films were cleaned and coated with thermaladhesive fluoroethylene−propylene (FEP, Dupont, USA, 50% solids content, 200 nm nanopowder aqueous dispersion) by spin coating. After being dried, these PI films were stacked with precise alignment and finally sealed by one-step bonding at 300 °C under a pressure of 0.5 MPa for at least 2 h (Figure 1b). After bonding, the cross-sectional SEM images showed that the FEP layers were uniformly distributed with a thickness of 5 μm and tightly sealed between PI films (Figure 1e). Consequently, the 3D serpentine microchannels were formed with a height of 125 μm, mixing channel length of 23 mm, and widths of 200, 300, and 400 μm. The simple nonaligned Tmixer with a width of 200 μm, height of 125 μm, and mixing channel length of 23 mm was fabricated with four layers of PI films through the same procedure. For both microchannel reactors, stream A and stream B were introduced through inlet A and inlet B, respectively, by two syringe pumps (703005, Harvard Apparatus). 2.2. Villermaux−Dushman Method. The micromixing performance was investigated by using the Villermaux− 13358
DOI: 10.1021/acs.iecr.9b01573 Ind. Eng. Chem. Res. 2019, 58, 13357−13365
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H2BO3− and further form I3− according to reactions 2 and 3. The segregation index XS is generally used to quantify the mixing performance of microreactors. It is defined as follows: Y YST
XS =
(4)
In the above equation, Y is the ratio of acid consumed by reaction 2, and YST is the value of Y, according to stoichiometric allocation, which means that the mixing process is infinitely slow. Y=
2(VA + VB)([I 2]+[I−3 ]) VB[H+]0
(5)
6[IO−3 ]0 6[IO−3 ]0 + [H 2BO−3 ]0
(6)
YST =
where VA and VB are the volumetric flow rates of mixtures A and B, which are injected into the two inlets, respectively. In this study, mixture A contains H2BO3−, I−, and IO3− as stream A, while mixture B is a sulfuric acid solution as stream B. Thus, the value of XS is in the range of 0 to 1, where XS is equal to 0 for perfect quick micromixing and XS is equal to 1 for complete segregation. To obtain the value of XS, the concentration of I3− can be measured by a sampling examination using a UV spectrophotometer (UV-2450, Shimadzu, Japan) at 288 nm, and the concentration of I2 can be calculated by an equilibrium constant KB of reaction 3 expressed as follows:
Figure 1. Design and fabrication of microchannel reactors: (a) geometry of the 3D serpentine microchannel reactor (left) and simple nonaligned T-mixer (right); (b) scheme for fabricating the 3D serpentine microchannel reactor by thermally bonding the stacked patterned PI films; (c) optical image of the microchannel reactor assembly with tubes; (d) optical image of the 3D serpentine microchannel (top view); (e) cross-sectional SEM image of the FEP layer uniformly distributed and tightly sealed between PI films.
KB =
k1
log10 KB =
k2
k3
(3)
k4
555 + 7.355 − 2.575 log10 T , T
KB (L/mol)
The effects of the microchannel width, Re, and flow ratio of the two fluids on the segregation index were investigated in the 3D serpentine microchannel reactors, and the temperature was maintained at 25 °C with a water bath. The experimental setup is shown in Figure 2a. For comparison, the segregation indices of the asymmetrical T-mixer with nonaligned inlets at different Re values were also measured with other conditions unchanged. Here, Re was defined by the average velocity at the outlet and the hydraulic diameter (dh) of the mixing channel:
(2)
I− + I 2 V I−3
(7)
(8)
(1)
5I− + IO−3 + 6H+ → 3I 2 + 3H 2O
C I2C I−
Here, KB is a temperature-dependent factor:23
Dushman reaction based on the iodide−iodate reaction system as shown below:22 H 2BO−3 + H+ → H3BO3
C I−3
+
Reaction 1 and 2 are competing for H in defect stoichiometrically, while reaction 1 is quasi-instantaneous and reaction 2 is much slower (Table 1). In a perfect mixing condition, the acid will be homogeneously dispersed in an instant and completely consumed by borates according to reaction 1; thus, no I2 will be generated in the reaction system. Conversely, local overconcentrated acid, owing to slow micromixing, can react with I− and IO3− to yield I2 after complete consumption of
Re =
ρ d hu μ
(9)
The concentration of H+ in mixture B was adjusted by the following equation to keep the molar ratio of the iodide− iodate reaction system invariable.
Table 1. Kinetic Parameters of Villermaux−Dushman Reaction at 25 °C.1 Reprinted from ref 1. Copyright 2012 American Chemical Society reaction
kinetics
k
Reaction 1 Reaction 2 Reaction 3
r1 = k1[H+][H2BO3−] r2 = k2[IO3−][I−]2[H+]2 r3 = k3[I−][I2] − k4[I3−]
k1 = 1011 m3/(kmol·s) k2 = 4.27 × 108 m12/(kmol4·s) k3 = 5.90 × 109 m3/(kmol·s), k4 = 7.50 × 109 s−1 13359
DOI: 10.1021/acs.iecr.9b01573 Ind. Eng. Chem. Res. 2019, 58, 13357−13365
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reaction was terminated by equal volume mixing with 1.0 mol/ L HCl through a T-type micromixer with a bore size of 50 μm. The reaction mixture was collected at the outlet and centrifuged to remove the cells; then the acrylamide concentration of the mixture was measured using an ultraperformance liquid chromatography system (UPLC IClass, Waters, USA) equipped with a C18 column (1.8 μm; 2.1 × 100 mm) and PDA detector. The entire microchemical system was submerged in a water bath to maintain the temperature at approximately 20 °C. With a delay tube length of 20 cm, the reaction rates of acrylonitrile in the 3D serpentine microchannel reactor were obtained under different flow ratios (16 to 50) of the continuous fluid to dispersed fluid, using various enzymatic activities (100 to 400 U/mL). Meanwhile, the reaction rates in the simple nonaligned Tmixer with the same setup were also measured under different enzymatic activities to verify the acceleration of reaction due to the enhancement of micromixing. The flow rate of cell solutions was fixed as 1.0 mL/min; hence, the residence time was approximately 9 s, and each experiment was repeated three times. 2.4. Materials. The acrylonitrile (AN, 99.5%), acrylamide (AM, 99%), potassium iodide (KI, 99%), potassium iodate (KIO3, 99%), and boric acid (H3BO3, 99.5%) were purchased from J&K Scientific Ltd. (Beijing, China). The sodium hydroxide (NaOH, 97%), sulfuric acid (H2SO4, 98%), and hydrochloric acid (HCl, 70%) were purchased from Beijing Chemicals Co. (Beijing, China).
Figure 2. Experimental setup of (a) the Villermaux−Dushman reaction for quantifying the mixing performance in the 3D serpentine microchannel reactor and (b) the biohydration process of acrylonitrile in the 3D serpentine microchannel reactor.
NA VC RCA = A A = = constant NB VBC B CB
(10)
where R represents the flow ratio of the stream A to stream B. The reactant concentrations of streams A and B in the experiments are presented in Table 2 according to a previous report,24 for which the concentration of H+ in stream B refers to the completely dissociated concentration.
3. CFD MODEL Although the segregation index in the Villermaux−Dushman method is a widely utilized indicator of the overall mixing performance achieved by the mixer, it could not provide local information on flow velocity and component concentration. The CFD simulation is recognized as a powerful characterization method to analyze local mixing and reveal the mechanism by solving the equations of conservation of momentum, mass, and energy. 3.1. Mathematical Model of Transport. The flow fields inside each microchannel can be described by the incompressible model including the governing equations for continuity, momentum, energy, and species at steady state. The gravity effect is considered to be negligible.
Table 2. Concentration of Reactants in Villermaux− Dushman Experiments stream
IO3− (mol/L)
I− (mol/L)
H2BO3− (mol/L)
H+ (mol/L)
Stream A Stream B (R = 1) Stream B (R = 2) Stream B (R = 4) Stream B (R = 8)
0.00236 0 0 0 0
0.0118 0 0 0 0
0.0909 0 0 0 0
0 0.06 0.12 0.24 0.48
2.3. Biohydration Process of Acrylonitrile. The biohydration of acrylonitrile is indicated in eq 11. The bacterial strain used as biocatalyst was R. ruber TH3, which was cultured according to a previously reported method.25 The enzymatic activity of the R. ruber TH3 free cells containing NHase was obtained by measuring the production rate of acrylamide per volume unit of fermentation broth at the optimal condition of 28 °C and pH = 7.0. One unit (U) of NHase activity was defined as the amount of free cells capable of catalyzing the formation of acrylamide at a rate of 1 μmol/ min.
Continuity equation: (12)
∇·u = 0
NHase
CH 2CHCN + H 2O ⎯⎯⎯⎯⎯⎯→ CH 2CHCONH 2 (11)
Momentum equation: ÄÅ ÉÑ ÅÅ ∂u Ñ Å ρÅÅ + (u ·∇)uÑÑÑÑ = −∇p + μ∇2 u ÅÇÅ ∂t ÑÖÑ
(13)
Energy equation: ÄÅ ÉÑ Å ∂T Ñ + (u ·∇)T ÑÑÑÑ = ∇·(k∇T ) + q ρcpÅÅÅÅ ÇÅÅ ∂t ÖÑÑ
(14)
Species equation:
As shown in Figure 2b, pure acrylonitrile (as a dispersed fluid) and the R. ruber TH3 free cell solution (as a continuous fluid) were pumped into the microchemical system by syringe pumps. The reactant solutions were first mixed in the microchannel reactor and then delivered via a Teflon helical delay tube with an inner diameter of 1 mm. Finally, the
∂(ρi ) ∂t
+ ∇·(ρi u) = ∇·(Di∇ρi ) + ri
(15)
where u is the velocity vector, ρ is the fluid density, μ is the fluid viscosity, t is the time, p is the pressure, cP is the specific 13360
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Industrial & Engineering Chemistry Research heat of the species, T is the temperature, k is the thermal conductivity, q is the internal heat source term, ρi is the mass concentration of species i, Di is the diffusion coefficient of species i, and ri is the formation rate of species i. 3.2. Simulation Procedure. The equations above were discretized based on the finite volume method, and the numerical simulations were performed using the FLUENT 14.0 (ANSYS, INC.) software operated in a double precision model. The 3D geometry of the experimental device was drawn by using the preprocessor Gambit 2.4.6 (ANSYS, Inc.), which generated structured meshes with hexahedral elements. The typical number of elements used for simulations was approximately 4.7 × 105, which was tested to be sufficient for a mesh-independent solution. To conform to the experimental conditions of the Villermaux−Dushman reaction, suitable boundary conditions of simulations were adopted: no-slip walls at constant temperature (25 °C), uniform velocity profile for inlets, and outflow condition for outlets. Meanwhile, the species transport equations and laminar finite rate model were employed for the reaction, the kinetics of which were detailed above. The diffusion coefficients and enthalpies of formation for all species were obtained from other studies as presented in Table 3. Because liquid water accounted for more than 99%
Figure 3. Effect of Re on segregation index XS (Wc = 200 μm and R = 1).
microchannel were examined separately in detail, while other operating conditions remained unchanged. When the volumetric flow ratio R was fixed as 1, the variation of the segregation index with Re in the 3D serpentine microchannel with different widths (Wc = 200, 300, and 400 μm) is depicted in Figure 4a. Obviously, the smaller is the channel width, the better is the mixing performance; meanwhile, the difference in
Table 3. Diffusion Coefficients (in Aqueous Solution) and Enthalpies of Formation of All Species.1 Reprinted from ref 1. Copyright 2012 American Chemical Society species +
H H2BO3− IO3− I− I2 I3− H3BO3 H2O
diffusion coefficient (m2/s) −9
9.311 × 10 1 × 10−9 1.078 × 10−9 2.045 × 10−9 1.360 × 10−9 1 × 10−9 1 × 10−9
enthalpies of formation (kJ/mol) 0 −1072.8 −221.3 −56.78 0 −51.5 −1072.8 285.83
volume of streams, for simplicity, the physical properties of each stream were assumed to be the same as those of water at 25 °C.
4. RESULTS AND DISCUSSION 4.1. Mixing Performance of Novel 3D Serpentine Microchannel by Villermaux−Dushman Method. The effect of Re on the segregation index XS was first investigated through the experimental method by adjusting VA and VB from 0.2 to 1.0 mL/min, keeping the volumetric flow ratio R as 1. As shown in Figure 3, XS decreased sharply from 3.3 × 10−2 to 3.8 × 10−4 with Re ranging from 10 to 205 in the novel 3D serpentine microchannel with a width of 200 μm. In contrast, the XS value of the simple nonaligned T-mixer with the same width changed from 0.19 to 0.011 when Re increased from 61 to 410, indicating that the increase in flow rate favors micromixing. Impressively, the XS value of the novel 3D serpentine microchannel is approximately 2 orders of magnitude smaller than that of the simple nonaligned Tmixer, reaching the order of 10−4 when Re is greater than 60, which shows that almost no I2 and I3− are generated in the 3D serpentine microchannel due to the extremely efficient mixing performance. Furthermore, the effects of channel width and volumetric flow ratio R on the mixing performance in the 3D serpentine
Figure 4. Effects of (a) channel width when R = 1 and (b) volumetric flow ratio R when Wc = 200 μm on segregation index XS in the 3D serpentine microchannel. 13361
DOI: 10.1021/acs.iecr.9b01573 Ind. Eng. Chem. Res. 2019, 58, 13357−13365
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Industrial & Engineering Chemistry Research the XS value under three microchannel widths reduced significantly with increasing Re at a range of 10−150, after which the XS values of three widths approached a very small and constant value that represented the chemical kinetics regime without a mixing effect. This indicates that in the 3D serpentine microchannel, the mixing efficiency is more sensitive to Re, rather than the channel width, which seems to determine the convection intensity. Then, the effect of the volumetric flow ratio R on segregation index XS was investigated for four cases (R = 1, 2, 4, and 8) in the 3D serpentine microchannel with a width of 200 μm. In this section, stream A (iodate of 0.00236 mol/L, iodide of 0.0118 mol/L, and borate ions of 0.909 mol/L) was pumped through inlet A into the microreactor at flow rates ranging from 0.05 to 3.20 mL/min, while completely dissociated concentration of H+ in stream B was 0.06, 0.12, 0.24, and 0.48 mol/L, and VB was adjusted accordingly to keep the molar ratio of reactants constant. As shown in Figure 4b, XS decreased with decreasing R, mainly because a larger R value corresponded to a larger difference between the two mixture flows and higher concentration of H+ according to eq 10, making mixture B more difficult to disperse uniformly into A. Therefore, the local excess H+ would be consumed by reaction 2 to form more I2 and I3−, leading to a higher XS. In addition, increasing R made concentrations of all reactants increase in equal proportion after mixing, such that the reaction rate of reaction 2 in the Villermaux−Dushman reaction system increased more than that of reaction 1, according to the kinetics of reactions in Table 1, which would cause the value of XS to increase as well. Nevertheless, the 3D serpentine microchannel still has a good mixing performance at high R and intermediate Re, for example, when R is 8 and Re is 369, XS reaches 0.011. 4.2. Numerical Analysis by CFD Simulation. 4.2.1. Validation of Computational Model. The proposed computational model was validated by comparing the CFD results with experimental data, with respect to the Villermaux−Dushman method at R = 1, for the 3D serpentine microchannel with a width of 200 μm at different Re values, as shown in Figure 5a. It can be observed that the simulation results predicted by the computational model are in good agreement with the experimental data. The reason why the discrepancy between numerical and experimental results is noticeable when Re is 20 may be that the wall roughness of the microchannel, fabricated with PI films, intercepts the fluid adjacent to the rough wall at a small Re, increasing the mass transfer resistance near the wall surface.26 However, as Re increases, the effect of wall roughness on the mixing efficiency becomes negligible. Therefore, the proposed computation model is carried forward for further analysis. The contours of the molar concentration of H+ along the length of the microchannel are also depicted in Figure 5b, where it can be seen that the reactions are almost finished at a channel length of 8 mm when the Re value is 41, indicating that the length of the microchannel was enough. 4.2.2. Enhancement of Mixing by Vortices in the 3D Serpentine Microchannel. To reveal the mechanism of mixing efficiency enhancement in the 3D serpentine microchannel, a CFD simulation was employed to visually analyze the flow and concentration fields. As shown in Figure 6, the evolution of the concentration of H+ along the microchannels with a width of 200 μm indicated the visible distinction of species distribution between the two designs when Re was 102. Apparently, in the simple nonaligned T-mixer, the two fluids introduced into the system remained mostly separated (Figure 6a), which limited
Figure 5. Validation of computational model: (a) comparison of simulation results and experimental data (Wc = 200 μm and R = 1); (b) contour of molar concentration (mol/L) of H+ (Wc = 200 μm, R = 1, and Re = 41).
Figure 6. Concentration distribution of H+ along the channel of (a) the simple nonaligned T-mixer and (b) the 3D serpentine microchannel (Wc = 200 μm, R = 1, and Re = 102).
the mixing to the molecular diffusion at the boundary, and the uneven distribution of H+ caused reaction 2 to occur. On the other hand, for the 3D serpentine microchannel with 3D turns, which changed the orientation between the serpentine sections, the fluids were confined to move along the serpentine channel, where the crossflow and mixing efficiency were remarkably increased due to the formation of vortices. The result was that the fluids homogeneously mixed after 3 turns, and at the same time, the reactions were completed (Figure 6b). As shown in Figure 7, arrow plots based on the velocity field in the 3D serpentine microchannel confirmed that the topology used induced rotating transversal flows, and the direction of vortices changed periodically as the flow orientation changed. The streamwise vorticity is expressed as follows: 13362
DOI: 10.1021/acs.iecr.9b01573 Ind. Eng. Chem. Res. 2019, 58, 13357−13365
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Figure 8. Periodic variation of the vortex intensity in the 3D serpentine microchannel (Wc = 200 μm and R = 1).
Figure 7. Arrow plots of the velocity field in the 3D serpentine microchannel (Wc = 200 μm, R = 1, and Re = 102).
∂uy zy ji ∂u zz ωx = jjj z − zz j ∂y z ∂ k {
channel due to the considerable viscous forces at low Re, and the rate of decrease depends strongly on the length of the straight section. Figure 8 shows that the maximum value of vortex intensity varies from 428 to 1563 s−1 as Re increases from 41 to 102, indicating that a stronger inertia force could significantly strengthen the vortices. Therefore, in the 3D serpentine microchannel, stronger periodic vortices are induced at higher Re, thereby resulting in stronger transversal flow and higher mixing efficiency. Table 4 shows the total
(16)
where ωx stands for the vorticity component in the x-direction, and uz and uy are the components of velocity in the z- and ydirections, respectively. The circulation on the yz-plane (cross section) is calculated by integrating the streamwise vorticity over the entire cross-sectional area of the microchannel, which is expressed as follows when flowing in the x-direction: Γx =
∫A
∂uy yz ij ∂uz jj z jj ∂y − ∂z zzz dy dz yz ‐ plane k {
Table 4. Total Energy Dissipation Rate Per Unit Mass for the 3D Serpentine Microchannel (Wc = 200 μm and R = 1)
(17)
In this study, the intensity of the vortices in the flow direction is represented by the area-averaged circulation, which has a significant positive effect on the mixing efficiency: IntensityVor =
Γx A yz ‐ plane
Re
ΔP (Pa)
εT (m2/s3)
41 61 82 102
5218 8663 12708 17343
92.7 231.0 451.8 770.8
energy dissipation rate per unit mass, εT, required to achieve the vortex intensity in Figure 8, and εT is expressed as follows:14
(18)
where Ayz‑plane represents the cross-sectional area. The microchannel in the red dotted lines, as shown in Figure 8, was selected to demonstrate the periodic variation of the vortex intensity with distance. In the 3D serpentine microchannel, this region is a typical repeating unit, where the variation of the vortex intensity is divided into four stages corresponding to the four sections of the unit: increasing from the inlet of the first turn, decreasing through the first straight section, increasing in the reverse direction at the inlet of the second turn, and finally decreasing to near zero through the second straight section. The vortex intensity can approach the highest values at the exits of the 3D turns after acceleration from the inlets. In addition, after the peak, the vortex intensity decreases as the fluid passes through any straight section of the
εT =
(VA + VB)ΔP ρV
(19)
where ΔP is the pressure drop obtained from simulation results and V represents the volume of the mixing region. Obviously, higher mixing efficiency requires more energy input. 4.3. Characteristics of the Biohydration Process in Microchannel Reactors. With the delay tube length of 20 cm, the effects of the flow ratio of the two fluids and the enzymatic activity on the reaction rate were investigated in the 3D serpentine microchannel with a width of 200 μm. As shown in Figure 9a, the reaction rate peaks at a flow ratio of 40, and the maximum reaction rate varies from 3.7 to 15.6 mol/(m3·s), 13363
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5. CONCLUSION A novel 3D serpentine microchannel reactor with a periodic vortex-inducing structure was fabricated by thermally bonding stacked PI films with high reproducibility, durability, and low cost. The Villermaux−Dushman method, which was utilized to analyze the mixing quality of the microreactors, indicated that XS decreased with increasing Re, decreasing R, and reduced channel width, reaching 3.8 × 10−4 as Re increased to 205 with a channel width of 200 μm and R of 1, showing the excellent mixing efficiency of the new design. A three-dimensional CFD model was developed to investigate the flow characteristics in the microreactors, and the numerical results agreed well with the experimental data. The contours of species concentration and arrow plots of velocity were visualized to reveal the vortices that varied periodically along the serpentine channel. The maximum vortex intensity reached 1563 s−1 as Re increased to 102, indicating that a stronger inertia force could lead to a stronger transversal flow and higher mixing efficiency. Furthermore, owing to the excellent mixing, the application of the 3D serpentine microchannel reactor in the biohydration of acrylonitrile greatly promoted the reaction rate, which demonstrated that the proposed microdevice is very promising for fast reactions limited by mass transfer resistance.
■
AUTHOR INFORMATION
Corresponding Author
*Tel.: 86-10-62783870. Fax: 86-10-62770304. E-mail:
[email protected]. ORCID
Yujun Wang: 0000-0002-8495-9811 Notes
Figure 9. Enhancement of biohydration process by improvement of mixing efficiency: (a) effects of flow ratio and enzymatic activity on the reaction rate in the 3D serpentine microchannel (Wc = 200 μm); (b) comparison of reaction rates in the two microreactors (Wc = 200 μm).
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation (Grant No. 21878169).
an increase of ∼4.2 times when the enzymatic activity increased from 100 to 400 U/mL. Impressively, compared with the reaction rates in a membrane dispersion microreactor of our previous work,27 with the enzymatic activity varying from 100 to 400 U/mL at a flow ratio of 20, the reaction rates in the 3D serpentine microchannel are 2.2, 4.3, 7.7, and 11.0 mol/m3/s, respectively, at least 35% higher than those of the membrane dispersion microreactor. The reason for the increase in rate before the peak is that as the proportion of the cell solution increases, acrylonitrile is more likely to dissolve in a short time, thereby reducing the inhibition of cells and increasing the reaction rate. However, once the flow ratio reached 40, the continued increase in the proportion of cell solution resulted in the mass fraction of acrylonitrile being less than 2.0%, which significantly reduced the reaction rate due to a decrease in substrate concentration. In comparison, when the flow ratio is the optimal value of 40, the reaction rates in the simple nonaligned T-mixer only reached approximately 60% of the reaction rates in the 3D serpentine microchannel, as shown in Figure 9b, indicating that a high mixing efficiency could dramatically accelerate the biohydration. From the discussion above, the novel 3D serpentine microchannel reactor with a periodic vortex-inducing structure is very promising for reactions limited by mass transfer resistance owing to its excellent mixing performance.
NOMENCLATURE Ayz‑plane = cross-sectional area of microchannel on yz-plane, m2 cP = specific heat of mixture, J/(kg·K) Di = diffusion coefficient of species i dh = hydraulic diameter of mixing channel, m KB = equilibrium constant of reaction 3 k = thermal conductivity, W/(m·K) kj = kinetic constant for reaction j P = pressure, Pa q = internal heat source term, J/(m3·s) R = flow ratio of stream A to stream B ri = formation rate of species i Re = Reynolds number T = temperature, K u = velocity vector, m/s uz = component of velocity in z-direction, m/s VA = flow rate of stream A, mL/min VB = flow rate of stream B, mL/min Wc = width of microchannel, μm XS = segregation index Y = product yield in the iodide−iodate reaction YST = value of Y in total segregation case Γx = circulation in the x-direction, m2/s
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DOI: 10.1021/acs.iecr.9b01573 Ind. Eng. Chem. Res. 2019, 58, 13357−13365
Article
Industrial & Engineering Chemistry Research μ = fluid viscosity, mPa·s ρ = fluid density, kg/m3 ωx = vorticity component in the x-direction, s−1 εT = total energy dissipation rate per unit mass (m2/s3)
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