Computational Analysis for Mixing of Fluids Flowing through Micro- Channels of Different Geometries

5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India Computational Analysis for Mixing of Fluids Flowing through Micro- Channels of Different Geometries Sankha Shuvra Das 1*, Binay Kumar Patawari 2, P.K. Patowari 3, S Halder 4 1*,3,4 Department of Mechanical Engineering, NIT Silchar, Assam, 788010, 2 Department of Mechanical Engineering, ISM Dhanbad, Jharkhand, 826004 Emails: 1* sankha.nita.2010@gmail.com, 2 vinayzzz26@gmail.com, 3 ppatowari@yahoo.com, 4 sudiptomec@gmail.com Abstract Rapid and uniform mixing is a key consideration in the design and development of micro-mixers. In micro scale, as the flow is laminar, mixing is dominated by molecular diffusion only. Hence, the presence of confluence or bends in the path of fluid flow causes rapid and uniform mixing of fluids. This paper presents a computational study of mixing of fluid in the micro-channel and investigates the mixing efficiency in straight, square wave and in three dimensional (3D) serpentine micro-channels. For all the geometries the basic dimensions as 400µm of width, 200µm of depth, 266.67 µm of hydraulic diameter and 11.5 mm of linear length are considered. The 3D models for all the geometries are developed using CATIA v6 and simulation is done using COMSOL Multiphysics software. The simulation is done for normal inflow velocity of 0.0002 m/s, 0.0004 m/s and 0.0006 m/s with Reynolds number (R e ) of 0.053, 0.106 and 0.160 respectively. To characterize the mixing efficiency, properties of water such as viscosity and density are considered as the fluid properties and fluid concentration of 0 mol/m 3 and 50 mol/m 3 are used through two different inlets respectively. The simulation results showed that at R e = 0.106, 3D serpentine micro-channel gives higher and uniform mixing than others. The analysis indicated that mixing efficiency is strongly dependent on the geometry of the micro-channel. In 3D serpentine micro-channel due to its change of plane, occurrence of fluid stirring and swirling vortexes are more, which enhances diffusion gradients resulting increase in mixing efficiency. The pressure drop during the fluid is also found out for straight, square wave and three dimensional serpentine micro-channels. The velocity vector plots showed the velocity profile and path of fluid flow throughout the length of channel. Keywords: Micro-channel, Micro-mixing, Micro-fluidics. 1. Introduction Micro-fluidics is the study of fluid flow in the channel of the micrometer dimensions. It is also a method for controlling or manipulating the fluid volume through micro dimensions. Now-a-days this technology is one of the major topics of research interest, as micro-scale devices are widely applied in biological systems, medical diagnostic, DNA sequencing, lab-on-a-chip devices, MEMS, and micro-reactors for chemical reactions [1, 2]. This technique is having the advantage over the conventional method (i.e. macro-fluidics) as because the process is less time consuming and also less quantity of sample and reagents are required for the analysis [3 5]. Micro-mixing is a primary requirement in many processes such as medical diagnostics, nano drug delivery, cell sorting, DNA sequencing, protein folding, lab-on chip application and many bio-chemical and biomedical processes. But mixing of more than one fluid is a critical issue in micro-channel as it is very difficult to achieve an effective mixing at the outlet of the micro-channel. It is very hard to achieve as because the flow in micro-channel is laminar which causes viscous effect in the fluid flow and as a result mixing is only dependent on molecular diffusion [6]. So, there should be some techniques which will enhance fluid mixing in micro-channel and also their application in biomedical and bio-chemical processes. Another application of the fluid micro-mixing technology is in micro-reactor which may bring revolutionary influence on modern chemistry. Microreactors can be used for chemical analysis of expensive materials with small amount of samples which may restrict the wastage of those materials. To work with the micro-fluidics, it is very much essential to first understand the physics associated with the microfluidics and also the factors that are most dominating at 236-1

Computational Analysis for Mixing of Fluids Flowing through Micro-Channels of Different Geometries the micro-scale [7]. The factors which are dominant in micro-fluidics include laminar flow, fluidic resistance, surface area to volume ratio, diffusion, and surface tension [8]. Therefore, it is very much essential to understand the fluid flow in micro-channel and also the micro-mixing. Moreover, mixing in micro-scale depends on the geometry of the micro-channel [9] and it may enhance if any lateral obstacle present in the path of the fluid flow [10]. The mixing performance may also increase if the residence time of fluid particle inside the chamber increases [11]. The objective of this work is to find out mixing efficiency of two fluids in microchannels of three different geometries: straight, square wave and 3D serpentine using computational analysis. 2. Computational Analysis 2.1 Modelling The design of the straight, square wave and 3D serpentine micro-channels were developed using CATIA v6 modelling software which is shown in Figure1. The total mixing length of all the channels was taken as 11.5 mm. The cross sections of all these microchannels were rectangular with 400µm wide and 200µm depth. Figure 1 (a) Straight micro-channel (b) square wave micro-channel (c) 3D serpentine micro-channel 2.2 Meshing (a) (b) (c) For analysis, the models were imported to COMSOL software and meshing was performed using structured meshing method and also by selecting extremely coarser element size. After meshing, the whole geometry for all these cases was divided into tetrahedral, prism, triangular and quadrilateral elements with 6859, 9986 and 9024 number of elements for straight, square wave and 3D serpentine micro-channel respectively. 2.3 Simulation The computational analysis of all the micro-channels was performed using COMSOL Multiphysics software. For the flow analysis, Laminar flow model was selected under Single Phase Fluid Flow of model wizard. As this was a mixing based problem so Transport of Diluted Species model was selected under Chemical Species Transport of model wizard and to solve the problem Stationary Solution was considered. 2.3.1 Simulation of Micro-channel For the analysis, water and benzoic acid were considered. Here, density of water and benzoic acid were used as 1000 kg/m 3 and 500 kg/m 3 respectively whereas viscosity was considered as 0.001 Pa.s. and 0.00126 Pa.s. The diffusion co-efficient of benzoic acid in water at 25ºc is 1 10-9 m 2 /s and this value was used for simulation. The simulation was performed in three different inlet velocities such as 0.0002 m/s, 0.0004 m/s and 0.0006 m/s for all these three micro-channel models. The Table 1 shows the input parameters used for simulation. The boundary conditions such as average velocity were imposed to both the inlets and the outlet was kept at atmospheric pressure. The channel walls were assigned to no slip conditions. On the other hand, concentration was assigned to both inlets, convective flux was imposed at outlet and walls were assigned to no flux conditions. The concentration for the inlet 1 and 2 was taken as 0 mol/m 3 and 50mol/m 3 respectively. So, the average concentration was 25 mol/m 3 and for getting proper mixing, it was considered that concentration range should be 25 ± 0.1mol/m 3. So, the concentration difference should be 0.2 mol/m 3. Table 1 Input parameters used for simulation of the micro-channels Hydraulic Sl. Width Depth Diameter, No. (µm) (µm) D h (µm) 1. 400 200 266.67 2. 400 200 266.67 3. 400 200 266.67 Area, A (m 2 ) Flow rate, Q (m 3 /s), V R e 0.08 10-6 1.6 10-11 0.0002 0.053 0.08 10-6 3.2 10-11 0.0004 0.106 0.08 10-6 4.8 10-11 0.0006 0.160 236-2

5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India The straight micro-channel was initially chosen as because of its ease of fabrication. Square wave and 3D serpentine micro-channel were chosen for compactness in the design and to study the effect on mixing due to their non-uniform shapes. Case I: Straight Micro-channel After the simulation, it was found that at the outlet there was no mixing occurred as the two liquids still separated from each other and could not diffuse properly at the outlet. This means that for this particular inlet velocity either the mixing length should be increased or the flow velocity should be decreased to get proper mixing. The concentration difference at the outlet was obtained as 4mol/m 3 whereas for getting proper mixing the concentration difference should be 0.2 mol/m 3. The simulation result is given in Figure 2. obtained after simulation along the width of straight micro-channel at various positions along the mixing length. Table 3 gives the pressure drop and streamline velocities at different inlet conditions for straight channel. (a) (a) (b) Figure 3 (a) Pressure drop during the fluid flow in straight micro-channel (b) streamline velocity (b) Figure 2 (a) Simulation of straight micro-channel at 0.0002 m/s (b) concentration difference at outlet Besides finding out a better mixing at the outlet, it was very much required to find out the pressure drop occurred during the flow. It was also required to find out the streamline velocity which will give idea regarding the fluid flow along the length of the microchannel. Figure 3 shows the pressure drop and streamline velocities during the flow in straight microchannel. Table 2 shows the concentration difference Sl. Table 2 Concentration difference along width at different location Difference of concentration along the width of straight No. channel (mol/m 3 ) 0 mm 5mm 11.5 mm 1. 0.0002 50 20 4 2. 0.0004 50 30 18 3. 0.0006 50 40 27 Table 3 Pressure drop and streamline velocity at different inlet velocity Sl. No. Pressure Drop (Pa) Maximum 1. 0.0002 2.1271 0.00079 2. 0.0004 4.2544 0.00158 3. 0.0006 6.3819 0.00237 236-3

Computational Analysis for Mixing of Fluids Flowing through Micro-Channels of Different Geometries Case II: Square wave Micro-channel For square wave micro-channel, the simulation result is given in Figure 4 and it was found that, mixing occurred at the outlet section of the square wave micro-channel. In this case, for the same inlet velocity, mixing is better than that of straight micro-channel and this may be due to the presence of obstacles in the path of fluid. As in the micro-channel, mixing depends on molecular diffusion only, presence of any bend or confluence in the path of fluid causes fluid stirring resulting in rapid and uniform mixing at the outlet. The concentration difference at the outlet occurred as 0.02 mol/m 3 whereas for getting better mixing the concentration difference at the outlet should be 0.2 mol/m 3. So, for the same dimensions and same inlet conditions mixing length required for square wave micro-channel was less than the straight micro-channel. Simulation was performed for other inlet velocities also and the result is given in Table 4. It shows the concentration difference obtained after simulation along the width of square wave microchannel at various locations from the origin of the mixing length. Table 5 gives the pressure drop and streamline velocities at different inlet conditions for square wave micro-channel. Table 5 Pressure drop and streamline velocity at different inlet velocity Sl. No. Pressure Drop (Pa) Maximum 1. 0.0002 3.4787 0.00081 2. 0.0004 6.9576 0.00163 3. 0.0006 10.437 0.00245 Case III: 3D Serpentine Micro-channel The analysis of the 3D serpentine micro-channel was performed and the simulation result is given in Figure 5. From simulation it was found that, mixing occurred at the outlet section of the 3D serpentine micro-channel. In this case, mixing occurred at the early of the mixing length and also it was observed that in this case mixing enhanced than that in case of square wave microchannel. This may be due to the presence of confluence or bends in the path of the flow and moreover they are not in a same plane as like as square wave microchannel which may increase the fluid stirring and also turbulence during the flow and causes early mixing. The concentration difference at the outlet occurred as 0 mol/m 3 whereas for getting better mixing the concentration difference at the outlet should be 0.2 mol/m 3. So, for the same dimensions and same inlet conditions mixing length required for 3D serpentine channel was less than the straight and square wave micro-channel. The variation in concentration was found out for other inlet velocities also and the result is given in Table 6. It shows the concentration difference along the width of 3D serpentine micro-channel at various locations from the origin of the mixing length. Table 7 gives the pressure drop and streamline velocities at different inlet conditions for 3D serpentine micro-channel. Figure 4 Variation of concentration in square wave micro-channel at 0.0002 m/s Table 4 Concentration difference along width at different location Difference of concentration Sl. No. along the width of square wave micro-channel (mol/m 3 ) 0 mm 5mm 11.5 mm 1. 0.0002 50 1.6 0.02 2. 0.0004 50 2 0.05 3. 0.0006 50 2.5 0.07 Figure 5 Simulation of 3D serpentine micro-channel at 0.0002 m/s. 236-4

5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India Sl. No. Table 6 Concentration difference along width at different location Difference of concentration along the width of 3D serpentine channel (mol/m 3 ) 0 mm 5mm 11.5 mm 1. 0.0002 50 0.12 0 2. 0.0004 50 0.5 0.004 3. 0.0006 50 0.8 0.009 geometries concentration difference at the outlet was close to zero that means mixing enhances in the case of square wave and 3D serpentine than straight microchannel. Moreover, in this particular inlet velocity mixing occurred at 5mm linear distance from the origin of the mixing length of the 3D serpentine micro-channel which means that for same inlet conditions mixing is much better in 3D serpentine micro-channel than straight micro-channel and moderately better than square wave micro-channel. Sl. No. Table 7 Pressure drop and streamline velocity at different inlet velocity Pressure Drop (Pa) Maximum 1. 0.0002 3.5012 0.00079 2. 0.0004 7.0026 0.00159 3. 0.0006 10.504 0.00239 2.4 Result and Discussion Graphs have been plotted against the concentration difference along the width of the micro-channel vs. position along the mixing length of the channel using the data obtained from above simulation of three geometries. From Figure 7, it was observed that in case of straight micro-channel no mixing occurred for all these three inlet velocities and also found that as the inlet velocity increases mixing get deteriorated at the outlet. But in the case of square wave micro-channel in Figure 8, concentration difference at the outlet was close to zero for all the inlet velocities which means that mixing enhancement occurred in the square wave micro-channel and also mixing efficiency is more than the straight micro-channel. From Figure 9 it was found that at 0.0002 m/s inlet velocity, mixing occurred at 5mm linear distance from the origin of the mixing length in the case of 3D serpentine channel. In this case, mixing occurred for all the inlet velocities and moreover mixing at the outlet is better than square wave microchannel. The pressure drop for straight micro-channel was less as compared to square wave and 3D serpentine micro-channel and increases with the increase in inlet velocity. The streamline velocity which will give the idea regarding the fluid flow was almost same for all the geometries in all the three flow conditions. Figure 10 shows the plot for concentration difference vs. position along the mixing length of the channel for all the three geometries for inlet velocity 0.0002 m/s and it was found that for straight micro-channel mixing is not occurred at the outlet. But in the other two Figure 7 Concentration difference vs. position along the mixing length of the straight micro-channel Figure 8 Concentration difference vs. position along the mixing length of the square wave micro-channel Now the same analysis can be performed in other inlet velocities also (except the above velocities). For the straight channel, it may not be possible to get proper mixing at the outlet if velocity increases from 0.0006 m/s but in other two shapes it may be possible. 236-5

Computational Analysis for Mixing of Fluids Flowing through Micro-Channels of Different Geometries Figure 9 Concentration difference vs. position along the mixing length of the 3D serpentine microchannel Figure 10 Concentration difference vs. position along the mixing length for the three micro-channels at 0.0002 m/s inlet velocity 3. Conclusions The design for all the three geometries of micro channels straight, square wave and 3D serpentine were developed using CATIA v6 and simulation was performed successfully using COMSOL Multiphysics software. From the simulation it was observed that to achieve uniform fluid mixing it is vital to create some swirling vortexes within the mixing chamber. For the same inlet conditions, fluid mixing is much better in 3D serpentine micro-channel and moderately better in square wave micro-channel than that in case of straight micro-channel. The formation of more obstacles in the path of fluid flow is not recommended because it may cause back pressure leading to lateral flow. Acknowledgment The authors would like to acknowledge the National MEMS Design Centre (NMDC) of National Institute of Technology, Silchar under National Programme on Micro and Smart Systems (NPMASS) of Government of India. References [1] Yang J.T., Wang L., Lyu P.C. (2007), An overlapping crisscross micromixer, Journal of Chemical Engineering Science, Vol. 62, pp. 711-720. [2] Bothe D., Lojewski A., Warnecke H. J. (2011), Fully resolved numerical simulation of reactive mixing in T-shaped micro-mixer using parabolised species equations, Chemical Engineering Science, Vol. 66, pp. 6424-6440. [3] Teruo Fujii (2002), PDMS-based micro-fluidic devices for biomedical applications, Microelectronic Engineering, Vol. 61 62, pp. 907 914. [4] McClain M.A., Culbertson C.T., Jacobson S.C., Nancy, Sims L.C.E., Ramsey J.M. (2003), Microfluidic devices for the high-throughput chemical analysis of cells, Analytical Chemistry, Vol. 75 (21), pp. 5646 5655. [5] Ye M.Y., Yin X. F., Lun Z. (2005), DNA separation with low-viscosity sieving matrix on micro-fabricated polycarbonate microfluidic chips, Analytical and Bioanalytical Chemistry, Vol. 381, pp. 820 827. [6] Wang H., Iovenitti P., Harvey E., Masood S., (2003), Numerical investigation of mixing in micro-channels with patterned grooves, Journal of Micromechanics and Micro-engineering, Vol. 13, pp. 801-808. [7] Gravesen P, Branebjerg J, Jensen O. (1993), Micro-fluidics a review, Journal of Micromechanics and Microengineering, Vol. 3, pp. 168-82. [8] Purcell E. (1977), Life at low Reynolds number, American Journal of Physics, Vol. 45, pp. 3-11. [9] S. Naher, D. Orpen, D. Brabazon, C.R. Poulsen, M.M. Morshed, (2011), Effect of micro-channel geometry on fluid flow and mixing, Simulation Modelling Practice and Theory, Vol. 19, pp. 1088-1095. [10] P. K. Sahu, A. Golia, A. K. Sen, (2013), Investigations into mixing of fluids in microchannels with lateral obstructions, Microsystem Technology, Vol. 19, pp.493-501. [11] Y. Z. Liu, B.J. Kim, H. J. Sung, (2004), Twofluid mixing in a micro-channel, International Journal of Heat and Fluid Flow, Vol. 25, pp. 986-995. 236-6