Numerical simulation and parameter optimization of micromixer device using fuzzy logic technique

The objective of this study is the design, simulation, and performance optimization of a micromixer device using the three input parameters of device structure, flow rate and diffusion coefficient of gold nanoparticles while the output parameters are concentration, velocity, pressure and time domain analysis. Each input parameter in the microfluidic chip influences the system output. The data were gathered through extensive study in order to optimize the diffusion control. The fuzzy logic approach is used to optimize the performance of the device with respect to the input parameters. In this study, we have chosen three different flow rates of 1, 5, and 10 μL min−1, three different diffusion coefficient values of low, average and high diffusivity gold nanofluids (15.3 e−12, 15.3 e−11, 15.3 e−10 m2 s−1) which are used in three different shapes of micromixer device, Y-shaped straight channel micromixer, herringbone-shaped micromixer, and herringbone shape with obstacles micromixer, and we measured the output performance, such as mixing efficiency, pressure drop, concentration across the microchannel and time domain. The data were obtained by fuzzy logic analysis and it was found that the herringbone shape with obstacles micromixer shows 100% mixing efficiency within a short duration of 5000 μm, and complete mixing was achieved within 10 seconds with a low pressure drop of 128 Pa.


Introduction
A microuidic device provides a powerful tool for lab on a chip (LOC) applications, such as sensing, 1 DAN amplication, 2 synthesis of nanoparticles 3 and blood cell separation. A micro-uidic device offers a portable diagnostic device for point-ofcare (POC) applications. There are several components in LOC and POC systems, such as microwells, microchannels, reservoirs, mixers, reactors, pumps and valves. A micromixer is an important component, which is used to mix uids in the range of micro-nano-pico liters. In microuidics for lab-on-a-chip applications, mixing performance remains a major challenge because uid ow is generally laminar. Generally, micromixers are classied into two types: active and passive micromixer devices. When an external force is required to mix the uids, we can call it an active micromixer. Different types of elds are used in an active micromixer, such as magnetic, 4,5 radio frequency, 6 electroosmotic 7,8 and surface acoustic wave. [9][10][11] Similarly, a passive micromixer device can have different physiological structures, such as Y-type, 12 T-shape, 13 grooves/ obstacles, 14 split-recombine, 15 serpentine 16 and herringbone type structures. 17 The construction of an active micromixer has greater complexity than a passive micromixer. Unfortunately, the driver voltage is too high, so the cost does not match the power. In addition, they are very difficult to make, so their uses are limited. At the same time, passive micromixers are simple, inexpensive devices and do not require an external eld to induce mixing efficiency. Additionally, they can be improved by modifying the microchannel structure, which helps improve mixing. 18,19 S. Camarri et al. 20 studied the engulfment regime of a T-type and T-joint micromixer device and reported the mixing efficiency and pressure drop. They reported that the conguration of a CA1 or CA2 device shows better efficiency than an isolated T-micromixer. When comparing the pressure drop between two the different congurations of CA1 and CA2 devices, the conguration of the CA1 device shows a lower pressure drop compared to CA2. X. Zhan et al. 21 designed a T-type micromixer with three different structural shapes: elliptical, rectangular and triangular shaped microchannels. Better mixing efficiency was found while using an elliptical cross-sectional microchannel. Z. Wu et al. 22 reported the design and numerical simulation of a three-dimensional T-shaped passive micromixer with three different obstacles: square, triangular and cylindrical. They reported a mixing efficiency of 96% while using the triangular obstacles with Re = 100 and 18 kPa pressure drop. E.
Tripathi et al. 23 designed and reported a spiral shaped micromixer which was investigated for a wide range of Reynolds numbers between 0.1 and 100. Better mixing was observed within the range of Reynolds number from 0.1 to 50. E. Nady et al. 24 studied the two inlets and two outlets of a Y-type passive micromixer with circular obstacles and tall walls. The total length of the device is 14 mm, the width of the channel is 200 mm, the thickness of the wall is 30 mm and the gaps between the walls are 170 mm and 70 mm. Better mixing was achieved in a short distance while using a circular channel with high number of tall wall structure and it act as an obstacles. Y. Liao et al. 25 reported a passive micromixer device with staggered herring bone structure and split-recombination microchannel. The mixing efficiency was analysed using a wide range of ow rates, 1-12 mL min −1 , and Reynolds numbers 3.3-40 and they achieved 98% mixing efficiency at 4.5-78 milliseconds. M. Ripoll et al. 26 designed a Y-type ring shaped micromixer which was used to produce lipid nanoparticles through the mixing of lipids and biomolecules. They reported the mixing performance to be linked with the characteristics of the lipid nanoparticles. O. Ulkir et al. 27 designed a T-shaped laminar diffusion-based micromixer with two inlets and two outlets. The mixing efficiency was studied using the diffusion coefficient 5 e −11 m 2 s −1 and inlet ow rate of 15 e −15 m 3 s −1 . For the output value of the system, the velocity was 0.09 mm s −1 , the pressure was 2 Pa and the concentration was 0.45 mol m −3 . Karthikeyan et al. 28 reported a Y-type herringbone shaped micromixer for mercury ion detection in water. They studied the pressure level and mixing efficiency of the device at different locations.
V. Vijayanandh et al. 29 reported a T-type micromixer with different shapes of ridges, such as triangular, square and curved. The mixing efficiency of the device was optimised using different shapes of micromixers and they reported that the best mixing efficiency was achieved while using a micromixer with triangular ridges. Karthikeyan et al. 16 studied the different shapes of micromixers such as a Y-type straight channel micromixer, and a serpentine shape micromixer with or without grooves. They reported the mixing efficiency and pressure drop. The best mixing efficiency was achieved with a short length while using a micromixer with grooves.
S. Hossain et al. 30 reported a serpentine micromixer with the crossing of two layers. They studied a mixing efficiency of 96% at low Reynolds numbers from 0.2 to 10 and low pressure drop. X. Dong et al. 31 designed a T-shaped micromixer for a non-Newtonian uid. They studied a mixing efficiency of 93.84% at Re = 0.24 while using a non-Newtonian uid and 93.90% mixing efficiency at Re = 8 while using a Newtonian uid.
Karthikeyan et al. 12 designed a Y-shaped micromixer with rectangular and triangular shaped obstacles to mix uids with very low diffusivity. The mixing efficiency observed for the triangular shaped micromixer shows 100% mixing efficiency compared with other micromixers with rectangular shaped obstacles at a ow rate corresponding to the Reynolds number (Re) of 25. I. Ertugrul et al. 32 reported a microuidic device for platelet separation using the fuzzy logic technique.
M. Hejazian et al. 33 reported a straight and serpentine shaped micromixer. The mixing efficiency of the device was studied using uorescence intensity proles with different ow rates of 20, 100 and 200 mL min −1 . A. Usean et al. 34 designed a Yshaped convergence and divergence-based micromixer for low ow rate applications. S. R. Bazaz et al. 35 developed three different shapes of passive hybrid planar micromixer with repetitive obstacles, such as teardrop, nozzle, ellipse, pillar and tesla shaped obstructions inside the mixing zone. R. A. Taheri et al. 36 reported a three-dimensional micromixer with split and recombine microchannel. They reported 96% mixing efficiency at a Reynolds number of 0.1, 90% mixing efficiency at a Reynolds number of 1 and 67% mixing efficiency at a Reynolds number of 10.
In this paper, we propose three dissimilar structures of micromixer: a Y-shaped straight channel micromixer (SCM), a herringbone serpentine channel micromixer (HSM), and a herringbone serpentine channel micromixer with obstacles (HSOM). The characteristic performance of the devices is discussed using the three input parameters of device structure, ow rate and diffusion coefficient, while the outputs are concentration, mixing efficiency, velocity, pressure and time domain analysis.

Y-shaped straight channel micromixer
A Y-shaped micromixer is one of the simplest models used to mix two liquids A and B. This micromixer contains a long straight channel of around 16 500 mm (16 mm) with two inlets each of about 2500 mm in length. The width of the microchannel is 200 mm and the diameter of the inlet and outlet reservoirs is 3000 mm. This device has a sensing zone diameter of 5000 mm. The structure of the Y-shaped micromixer with a straight channel and its dimensions are shown in Fig. 1.

Y-shaped herringbone serpentine channel micromixer
The Y-shaped herringbone serpentine channel micromixer contains many sharp bends in the microchannel. The width and overall length of the microchannel are around 200 mm and 16 mm (i.e. x-axis 16 mm), respectively, with two inlets each of 2500 mm length. The space between two bends is 200 mm. This device has a sensing zone diameter of 5000 mm. The structure of the Y-shaped herringbone serpentine channel micromixer and its dimensions are shown in Fig. 2.

Y-shaped herringbone serpentine channel micromixer with obstacles
The structure of the Y-shaped herringbone serpentine channel micromixer with obstacles and its dimensions are shown in Fig. 3. The obstacles are of quadrant shape, as shown in the insert to Fig. 3. The quadrant shaped obstacles have a smooth curved edge at the uid inlet, which provides smooth uid ow, and a vertical edge at the other end, which improves uid interaction. The obstacles improve the mixing efficiency over a short length. The grooves are kept at a spacing of 100 mm and there are 164 obstacles over the whole mixing length of 16 mm with two inlets each of 2500 mm length and an inlet port diameter of 3000 mm. This device has a sensing zone diameter of 5000 mm.

Simulations of micromixers
Simulations were carried out with the Numerical Multiphysics CAD tool. The structures were drawn using the design values given in the previous section.

Analytical expressions for micromixing
The ow of an incompressible Newtonian liquid in a micromixer can be described by the Navier-Stokes equation and continuity equation, as shown in eqn (1) and (2), respectively.
where r is the uid density, u is the ow velocity, v is the dynamic viscosity of the uid, p is the uid pressure, and f is the body force. The species transport in the systems can be described by the convection diffusion equation, as shown in eqn (3), where c and D are the concentration and diffusion constant of the species. The term "pressure drop" refers to the drop in pressure across the geometry of any device. i.e. the difference between inlet pressure and outlet pressure.
Mathematically it can be represented as,  The mixing efficiency (M) of the micromixer can be calculated using the following formula, where N is the total number of sampling points across the crosssection in the channel, c i is the normalized concentration of the uid at each cross-section of the device, and c is the average concentration of the uid in the inlets. In accordance with eqn (5), the mixing efficiency, M = 0% indicates the completely unmixed state of the species, and M = 100% indicates the completely mixed state. An efficiency of mixing between about 80 and 100% is suitable for mixing applications. 37,38 3.2 Analysis of micromixer 3.2.1 Simulated micromixer device. We look at the micromixer model processes of a microuidic device for controlled mixing by diffusion. The device brings two different laminar streams into contact for a controlled time. The contact surface is well dened, and by controlling the ow rate, it is possible to control the number of species transferred from one stream to another by diffusion. Diagrams of the microuidic-based micromixer devices to be analyzed, each with two inputs and an output, are shown in Fig. 4, 5 and 6. Fig. 4 shows the concentration level across the device of a Yshaped straight channel micromixer. This device has two inlets in a Y-shape with a straight channel acting as a mixing zone followed by a sensing zone and outlet. Fig. 4 shows a simulation study of "Test case 1", which is presented in Table 1. Fig. 5 shows the concentration level across the device of a Y-shaped herringbone serpentine channel micromixer. This device has two inlets in a Y-shape with a herringbone serpentine channel acting as a mixing zone followed by a sensing zone and outlet. Fig. 5 shows the simulation study of "Test case 10", which is presented in Table 1. Fig. 6 shows the concentration level across the device of a Y-shaped herringbone serpentine channel micromixer with obstacles. This device has two inlets in a Yshape along with a herringbone serpentine channel with obstacles acting as a mixing zone followed by a sensing zone and outlet. Fig. 6 shows the simulation study of "Test case 19", which is presented in Table 1, Fig. 4, 5, and 6 show the mixing concentration prole across the device with different structures and the same input parameters. In Fig. 4, the uid ow is     4508 | RSC Adv., 2023, 13, 4504-4522 laminar due to the microchannel and it requires a greater length of microchannel to achieve complete mixing: in this case complete mixing was achieved at 17 500 mm. Therefore, Fig. 5 shows a Y-shaped herringbone serpentine channel with sharp edges for better mixing and mixing was achieved at 7500 mm. Then Fig. 6(a) and (b) present a Y-shaped herringbone serpentine channel with obstacles to achieve complete mixing within short length of under 5000 mm.
3.2.2 Optimization with fuzzy logic. The selection of input and output variables to be used is the rst stage in the fuzzy logic system modelling process. Diffusion control of A and B uids in the channels is the primary duty of the microuidicbased micromixer modelled in this work. The output parameters of the diffusion-related fuzzy logic approach must be taken into consideration in order to do this, and the rules must be expressed clearly. Using the fuzzy logic application, optimization procedures are undertaken in this study according to the input and output parameters.
The diffusion coefficient and inlet ow rate of the A and B uids entering the micromixer are the parameters that make up the system input. The system output parameters are the velocity, pressure, and concentration of the liquids. The diffusion of liquids A and B is made possible by the values of the diffusion coefficient. The pressure and velocity of uids in the micromixer channel are also inuenced by the inlet ow rate ratio. Fig. 7 displays the inputs and outputs of the fuzzy logic system.
According to the values of the upper and lower limits of the input and output parameters, the membership function values written for each input and output value are updated in the fuzzy logic approach. The COMSOL Multiphysics application has been used for dozens of different analytical procedures. The results of the analysis are used to develop rules and parameter values. Nine criteria were developed to specify the connection between the parameters aer the upper and lower bounds for modelling the necessary parameters using the membership function were chosen. The following table is the fuzzy logic test case (Table 1). We chose three different structures of micromixer devices: Y-shaped straight channel micromixer (SCM), Y-shaped herringbone serpentine shape micromixer (HBM) and Y-shaped herringbone serpentine shape micromixer with obstacles (HBM-OB). Each device structure has two input parameters of ow rate (1, 5 and 10 mL min −1 ), diffusion coefficient (15.3 e −10 , 15.3 e −11 and 15.3 e −12 m 2 s −1 ), and three output parameters of velocity, pressure and concentration. We chose 27 test cases using the fuzzy logic test case table below.

Velocity prole of the device
Analyses of the microuidic based micromixer device were performed using COMSOL Multiphysics soware. Twenty-seven The inow velocity of the uid in both inlets is considered to be the same (1, 5, 10 mL min −1 ) and the uid concentrations (c) in inlets A and B are taken as 1 mol m −3 and 10 mol m −3 , respectively. Fig. 8 shows the velocity across the Y-shaped straight channel micromixer with different ow rates of 1 mL min −1 , 5 mL min −1 and 10 mL min −1 . The peak velocity was achieved in the middle of the microchannel and the velocity was reduced at the wall of the microuidic channel due to uid sticking onto the channel wall. Fig. 9 shows the velocity across the Y-shaped herringbone serpentine channel micromixer with different ow rates of 1 mL min −1 , 5 mL min −1 and 10 mL min −1 .
The peak velocity was achieved in the middle of the microchannel and the velocity was reduced at the wall of the micro-uidic channel due to uid sticking onto the channel wall. Fig. 10 shows the velocity across the Y-shaped herringbone serpentine channel micromixer with obstacles, with different ow rates of 1 mL min −1 , 5 mL min −1 and 10 mL min −1 . The peak velocity was achieved in the middle of the microchannel and the velocity was reduced at the wall of the microuidic channel due to uid sticking onto the channel wall.

Concentration analysis across the device
A concentration study of the device was carried out with different test cases as given in Table 1. Fig. 11 shows the concentration across the Y-shaped straight channel micromixer at different ow rates of 1 mL min −1 (11(A)), 5 mL min −1 (11(B)), and 10 mL min −1 (11(C)) with a diffusion co-efficient of 15.3 × 10 −10 m 2 s −1 . Fig. 11(A), (B) and (C) show the concentration across the uidic channel at different locations of 1000 mm, 5000 mm, 7500 mm, 10 000 mm, 15 000 mm and 20 000 mm. When uids enter into the straight channel from the inlets, the uid ow is laminar and the uid-uid interaction time is greater when the uid ow is at a low ow rate of 1 mL min −1 (11(A)), so better mixing concentration is observed. Similarly, when the uid ow is increased to 5 mL min −1 (11(B)) and 10 mL min −1 (11(C)), the uid-uid interaction is reduced, so the mixing concentration level is reduced at different locations. Fig. 12 shows the concentration across the Y-shaped straight channel micromixer at different ow rates of 1 mL min −1 (12(A)), 5 mL min −1 (12(B)), and 10 mL min −1 (12(C)) with a diffusion coefficient of 15.3 × 10 −11 m 2 s −1 . At different locations along the uidic channel (1000 mm, 5000 mm, 7500 mm, 10 000 mm, 15 000 mm, and 20 000 mm), Fig. 12(A), (B) and (C) show the concentrations along the uidic channel at different locations. In a straight channel, uid enters from the inlets in a parallel ow. The observed mixing concentration is higher when the uid ow rate is 1 mL min −1 (12(A)), which results from greater uid-uid interaction time.
Fluid ow is laminar when it enters the straight channel from the inlets. At low ow rates, such as 1 mL min −1 (13(A)), the uid-uid interaction time is greater, resulting in a better mixing concentration. Additionally, as the uid ow increases to 5 mL min −1 (13(B)) and 10 mL min −1 (13(C)), the uid-uid interaction reduces, thereby decreasing the mixing concentration at different locations. Fig. 14 shows the concentration across the Y-shaped herringbone serpentine channel micromixer at different ow rates of 1 mL min −1 (14(A)), 5 mL min −1 (14(B)), and 10 mL min −1 (14(C)) with a diffusion co-efficient of 15.3 × 10 −10 m 2 s −1 . This gure illustrates the concentration of uids across the uidic channel across a number of locations of 1000 mm, 5000 mm, 7500 mm, 10 000 mm, 15 000 mm, and 20 000 mm. The uid ow in a herringbone serpentine channel is laminar when it enters from the inlets. When uid ow is maintained at a low ow rate of 1 mL min −1 (14(A)), the amount of uid-uid interaction is greater, resulting in a better mixing concentration. Furthermore, the mixing concentration level is reduced at different locations as the uid ow increases to 5 mL min −1 (14(B)) and 10 mL min −1 (14(C)). Fig. 15 shows the concentration across the Y-shaped herringbone serpentine channel micromixer at different ow rates of 1 mL min −1 (15(A)), 5 mL min −1 (15(B)), and 10 mL min −1 (15(C)) with a diffusion coefficient of 15.3 × 10 −11 m 2 s −1 . At different locations within the uidic channel, of 1000 mm, 5000 mm, 7500 mm, 10 000 mm, 15 000 mm and 20 000 mm, Fig. 15(A), (B) and (C) illustrate the concentrations.
Laminar ow occurs when uid is introduced into the herringbone serpentine channel from the inlets. At a low ow rate of 1 mL min −1 (15(A)), there is more uid-uid interaction time, resulting in a higher mixing concentration. In a similar manner, as the uid ow increases to 5 mL min −1 (15(B)) and 10 mL min −1 (15(C)), the uid-uid interaction is reduced, which results in a reduction in mixing concentration levels at various locations. Fig. 16 shows the concentration across the Y-shaped herringbone serpentine channel micromixer at different ow rates of 1 mL min −1 (16(A)), 5 mL min −1 (16(B)), and 10 mL min −1 (16(C)) with a diffusion co-efficient of 15.3 × 10 −12 m 2 s −1 . In Fig. 16, the concentrations are depicted at different points in the uidic channel for different distances of 1000 mm, 5000 mm, 7500 mm, 10 000 mm, 15 000 mm, and 20 000 mm. From the inlets, uid ows in a laminar fashion through the herringbone  serpentine channel. With a low uid ow rate of 1 mL min −1 (16(A)), the uid-uid interaction time is greater, resulting in a better mixing concentration. In the same way, as the uid ow increases to 5 mL min −1 (16(B)) and 10 mL min −1 (16(C)), the uid-uid interaction is reduced, resulting in a reduction in mixing concentration levels at differing locations. Fig. 17 shows the concentration across the uidic channel at different locations of 1000 mm, 5000 mm, 7500 mm, 10 000 mm, 15 000 mm and 20 000 mm with different ow rates of 1 mL min −1 (17(A)), 5 mL min −1 (17(B)), and 10 mL min −1 (17(C)) with a diffusion co-efficient of 15.3 × 10 −10 m 2 s −1 . In the present study, we observe that a laminar uid ow is observed when uid enters the micromixer devices from the inlets. A higher mixing concentration is observed when the ow rate is low at 1 mL min −1 (17(A)), so the uid-uid interaction time is greater. Furthermore, an increase in uid ow rate decreases the time required for uid-uid interaction, resulting in a decrease in mixing concentration. For the proposed device, quadrantshaped obstacles are introduced inside the microchannel for improved mixing within a short period of time, which allows for a reduction in the length of the device. It is considered that the mixing process has been completed once the uid concentration reaches the average concentration of the uid inow (5.5 mol m −3 ). According to the results, at a ow rate of 1 mL min −1 , the concentration level is saturated throughout a distance of 5000 mm.
This study shows that a better mixing concentration is achieved compared with the other two micromixer devices: Yshaped straight channel micromixer and Y-shaped herringbone serpentine shape micromixer without obstacles. When the ow rate is increased to 5 and 10 mL min −1 (17(B) and 17(C)), the mixing concentration level is reduced slightly compared with the other two micromixer devices. Fig. 18 shows the concentration across the uidic channel at different locations of 1000 mm, 5000 mm, 7500 mm, 10 000 mm, 15 000 mm and 20 000 mm with different ow rates of 1 mL min −1 (18(A)), 5 mL min −1 (18(B)), and 10 mL min −1 (18(C)) with a diffusion co-efficient of 15.3 × 10 −11 m 2 s −1 . In this study, we can observe that when uids enter into micromixer device from the inlets, the uid ow is laminar and uid-uid interaction time is greater when the uid ow is at low ow rate of 1 mL min −1 (18(A)) so a better mixing concentration is observed. Similarly, when the uid ow rate is increased, the uid-uid interaction time is reduced because the mixing concentration is reduced. The proposed device has quadrant shaped obstacles introduced inside the microchannel for better mixing within a short duration, reducing the length of the device. It is discovered that the concentration level is saturated throughout a 5000 mm length at a ow rate of 1 mL min −1 .  This study shows that better mixing concentration is achieved compared with the other two micromixer devices: Yshaped straight channel micromixer and Y-shaped herringbone serpentine shape micromixer without obstacles. When the ow rate is increased to 5 and 10 mL min −1 (18(B) and 18(C)), the mixing concentration level is reduced slightly compared with the other two micromixer devices. Fig. 19 shows the concentration across the uidic channel at different locations of 1000 mm, 5000 mm, 7500 mm, 10 000 mm, 15 000 mm and 20 000 mm with different ow rates of 1 mL min −1 (19(A)), 5 mL min −1 (19(B)), and 10 mL min −1 (19(C)) with a diffusion co-efficient of 15.3 × 10 −12 m 2 s −1 . It was observed that the uid ow into the micromixer device is laminar when it enters the mixing zone. When the uid ow is low, 1 mL min −1 (19(A)), the uid-uid interaction time is greater, so the mixing concentration is better. When the ow rate is low (19(A)), the uid-uid interaction time is longer, resulting in a better mixing concentration. Similarly, an increasing ow rate reduces the uid-uid interaction time, which reduces the mixing concentration. An obstacle of quadrant shape has been introduced into the microchannel for better mixing within a short period of time and to reduce the size of the device. The concentration level is saturated over a length of 5000 mm by mixing at a rate of 1 mL min −1 . In this study, it was shown that the mixing concentration was higher compared with the other two micromixers: Yshaped straight channel micromixers and Y-shaped herringbone serpentine micromixers without obstructions. The mixing concentration level is slightly reduced when the ow rate increases to 5 mL min −1 and 10 mL min −1 (19(B) and 19(C)), in comparison with the other two micromixers. From Fig. 20, we are able to see three different micromixer devices: Y-shaped straight channel micromixer (SCM), Y-shaped herringbone serpentine shape micromixer (HBM) and Y-shaped herringbone serpentine shape micromixer with obstacles (HBM-OB).

Mixing efficiency of the devices
In this study, we can observe that the mixing efficiencies of the SCM device at the above-mentioned locations are 50. 68%   When comparing the mixing efficiency of all three types of micromixer device and mixing length, the best mixing efficiency was achieved in the HBM-OB device due to the structural dimensions of the device and the obstacles. The obstacleinduced uid-uid interaction caused better mixing, which was achieved in a short duration compared with the other two types of micromixer device. Fig. 21 shows the mixing efficiency across the uidic channel at different locations of 1000 mm, 2500 mm, 5000 mm, 7500 mm, 10 000 mm, 12 500 mm, 15 000 mm, 17 500 mm and 20 000 mm with a constant ow rate and a diffusion co-efficient of 15.3 × 10 −11 m 2 s −1 . In Fig. 21, we can see three different Y-shaped micromixer devices: a Y-shaped straight channel micromixer (SCM), a Y-shaped herringbone serpentine shape micromixer (HBM), and a Y-shaped herringbone serpentine shape micromixer with obstacles (HBM-OB). During this study, we could observe that the mixing efficiencies of the SCM device at the above-mentioned locations were 42     that the HBM-OB device had the best mixing efficiency, owing to the structure and the obstacles of the device. In comparison with the other two types of micromixer device, the obstacles induce uid-uid interaction, which results in improved mixing in a short period of time. Fig. 22 shows the mixing efficiency across the uidic channel at different locations of 1000 mm, 2500 mm, 5000 mm, 7500 mm, 10 000 mm, 12 500 mm, 15 000 mm, 17 500 mm and 20 000 mm with a constant ow rate and a diffusion co-efficient of 15.3 × 10 −12 m 2 s −1 . From Fig. 22, we are able to see three different micromixer devices: Y-shaped straight channel micromixer (SCM), Y-shaped herringbone serpentine shape micromixer (HBM) and Y-shaped herringbone serpentine shape micromixer with obstacles (HBM-OB). In this study, we can observe that the mixing efficiencies of the SCM device at the above-mentioned locations are 41 . When comparing the mixing efficiency of all three types of micromixer device and mixing length, the best mixing efficiency was achieved in the HBM-OB device due to the structural dimensions of the device and the obstacles. The obstacles induce uid-uid interaction, which causes better mixing, which was achieved over a short duration compared with the other two types of micromixer device. Fig. 23 shows the mixing efficiency across the uidic channel at different locations of 1000 mm, 2500 mm, 5000 mm, 7500 mm, 10 000 mm, 12 500 mm, 15 000 mm, 17 500 mm and 20 000 mm with a constant ow rate and a diffusion co-efficient of 15.3 × 10 −10 m 2 s −1 . From Fig. 23, we are able to see three different micromixer devices: Y-shaped straight channel micromixer (SCM), Y-shaped herringbone serpentine shape micromixer (HBM) and Y-shaped herringbone serpentine shape micromixer with obstacles (HBM-OB).
In this study, we can observe that the mixing efficiencies of the SCM device at the above-mentioned locations are 41 When the mixing efficiency of all three types of micromixer device and mixing length are compared, the best mixing efficiency was achieved in HBM-OB. Fig. 24 shows the mixing efficiency across the uidic channel at different locations of 1000 mm, 2500 mm, 5000 mm, 7500 mm, 10 000 mm, 12 500 mm, 15 000 mm, 17 500 mm and 20 000 mm with a constant ow rate and a diffusion co-efficient of 15.3 × 10 −11 m 2 s −1 . This gure displays three different types of micromixers: a Y-shaped straight channel micromixer (SCM), a Y-shaped herringbone serpentine shape micromixer (HBM) and a Y-shaped herringbone serpentine shape micromixer with obstacles (HBM-OB). As a result of this study, we observed 39.94%, 53.05%, 58.60%, 62.59%, 72.95% and 86.81% mixing efficiencies for the SCM device at each of the above-mentioned locations. This graph shows the mixing efficiencies of the HBM device as 38 A comparison of the mixing efficiency of all three types of micromixers and mixing length shows that the HBM-OB device has the best mixing efficiency due to its structural dimensions and the obstacles. Compared with the other two types of micromixer device, the obstacles induced uid-uid interaction, resulting in better mixing in a short period of time. Fig. 25 shows the mixing efficiency across the uidic channel at different locations of 1000 mm, 2500 mm, 5000 mm, 7500 mm, 10 000 mm, 12 500 mm, 15 000 mm, 17 500 mm and 20 000 mm with a constant ow rate and a diffusion co-efficient of 15.3 ×  10 −12 m 2 s −1 . From Fig. 25, we are able to see three different micromixer devices: Y-shaped straight channel micromixer (SCM), Y-shaped herringbone serpentine shape micromixer (HBM) and Y-shaped herringbone serpentine shape micromixer with obstacles (HBM-OB). In this study, we can observe that the mixing efficiencies of the SCM device at the above-mentioned locations are 39 . When the mixing efficiency of all three types of micromixer device and mixing length are compared, the best mixing efficiency was achieved in the HBM-OB device due to the structural dimensions of the device and the obstacles. The obstacles induce uid-uid interaction, causing the better mixing to be achieved over a short duration compared with the other two types of micromixer device. Fig. 26 shows the mixing efficiency across the uidic channel at different locations of 1000 mm, 2500 mm, 5000 mm, 7500 mm, 10 000 mm, 12 500 mm, 15 000 mm, 17 500 mm and 20 000 mm with a constant ow rate and a diffusion co-efficient of 15.3 × 10 −10 m 2 s −1 . From Fig. 26, we are able to see three different micromixer devices: Y-shaped straight channel micromixer (SCM), Y-shaped herringbone serpentine shape micromixer (HBM) and Y-shaped herringbone serpentine shape micromixer with obstacles (HBM-OB). In this study, we can observe that the mixing efficiencies of the SCM device at the above-mentioned locations are 41 . When the mixing efficiency of all three types of micromixer device and mixing length are compared, the best mixing efficiency was achieved in the HBM-OB device due to the structural dimensions of the device and the obstacles. Fig. 27 shows the mixing efficiency across the uidic channel at different locations of 1000 mm, 2500 mm, 5000 mm, 7500 mm, 10 000 mm, 12 500 mm, 15 000 mm, 17 500 mm and 20 000 mm with a constant ow rate and a diffusion co-efficient of 15.3 × 10 −11 m 2 s −1 . Fig. 27 illustrates three different types of micromixers: a Y-shaped straight channel micromixer (SCM), a Y-shaped herringbone serpentine shape micromixer (HBM) and a Yshaped herringbone serpentine shape micromixer with obstacles (HBM-OB Due to the structural dimensions of the device and the obstacles present, the HBM-OB device showed the best mixing efficiency when comparing the mixing efficiency of the three types of micromixer. In comparison with the other two types of micromixer device, the obstacles induce uid-uid interaction, which results in improved mixing in a short period of time. Fig. 28 shows the mixing efficiency across the uidic channel at different locations of 1000 mm, 2500 mm, 5000 mm, 7500 mm, 10 000 mm, 12 500 mm, 15 000 mm, 17 500 mm and 20 000 mm with a constant ow rate and a diffusion co-efficient of 15.3 × 10 −11 m 2 s −1 .   From Fig. 28, we are able to see three different micromixer devices: Y-shaped straight channel micromixer (SCM), Y-shaped herringbone serpentine shape micromixer (HBM) and Y-shaped herringbone serpentine shape micromixer with obstacles (HBM-OB). In this study, we can observe that the mixing efficiencies of the SCM device at the above-mentioned locations are 39 . When the mixing efficiency of all three types of micromixer device and mixing length are compared, the best mixing efficiency was achieved in the HBM-OB device due to the structural dimensions of the device and the obstacles.
Generally, a conventional mixer device requires a greater volume of samples and reagents and other existing micromixer devices also work in high ow rates to achieve complete mixing. This high ow rate will create a greater pressure drop (more than 10 kPa). This proposed and optimized micromixer device provides complete mixing in a shorter length with shorter timing and with a lower pressure drop.

Grid independence verication
The entire geometry is represented by an unstructured triangular mesh. Fig. 30 illustrates a typical mesh used in this study. A large number of ow gradients exist near the inlet, mixing zone, sensing zone, outlet, and close to the wall boundary in these regions. In order to capture the most detailed information possible, the mesh element size is rened in the regions of the obstacles. In addition to our simulations, we are also experimenting with mesh independence to determine the best mesh element size that will yield independent results. The average concentration at the channel outlet is given in Table 2 for three different mesh sizes for the main geometric design depicted in Fig. 3. Due to the negligible variation in concentration values   from the third to the fourth row in Table 2, the mesh is determined based on the conditions found in the third row. Karthikeyan et al. 16 provided numerical results that were compared to the simulation results of the current numerical method. Table 3 shows a comparison of different types of passive micromixer device with different specications. This study was carried out for 120 seconds from inlet to outlet. At the initial stage of 500 mm, there was a wide concentration level between 1 and 10 mol m −3 and there was not complete mixing; when it was measured at 2500 mm, the concentration range was between 3.80 and 7.40 mol m −3 . Similarly, at 5000 mm, there was a broad concentration level between 4.8 and 6.1 mol m −3 and there was not complete mixing; when it was measured at 10 000 mm, the concentration range was between 5 and 6 mol m −3 .

Time domain analysis across the device
Finally, at 20 000 mm, the concentration level was almost narrow: 5.5 mol m −3 at 24 seconds. Fig. 32 shows a time domain study of the HBM device at a low ow rate of 1 mL min −1 with a diffusion co-efficient of 15.3 × 10 −10 m 2 s −1 (TC10). At different locations of the device, of 500 mm, 2500 mm, 5000 mm, 10 000 mm, and 20 000 mm, the xaxis represents time in seconds and the y-axis represents concentration in mol m −3 .
An analysis of concentration levels over time at different locations and timings is presented in this study. During this experiment, the inlet and outlet were monitored for 120 seconds. Initially, the concentration level was wider at 500 mm, ranging from 1-10 mol m −3 , while at 2500 mm, the concentration range was between 3.93 and 7.10 mol m −3 . A similar concentration level was observed at 5000 mm when it was measured at 21 seconds,   and it was 5.5 moles m −3 when it was measured at 10 000 mm and 20 000 mm at 41 seconds and 91 seconds, respectively. Fig. 33 shows a time domain study of the HBM-OB device at a low ow rate of 1 mL min −1 with a diffusion co-efficient of 15.3 × 10 −10 m 2 s −1 (TC19). The x-axis denotes the time (seconds) and the y-axis denotes the concentration (mol m −3 ) at different locations of the device of 500 mm, 2500 mm, 5000 mm, 10 000 mm and 20 000 mm. This time domain study shows the change in concentration level at different locations and timings. This study was carried out for 120 seconds from inlet to outlet. At the initial stage of 500 mm, there is a wide concentration level between 1 and 10 mol m −3 and there was not complete mixing; when it was measured at 2500 mm, the concentration range was between 4.8 and 6 mol m −3 . Similarly, at 5000 mm, the concentration level was almost narrow at 5.5 mol m −3 at 16 seconds, and at this stage the uid was completely and well mixed; when it was measured at 10 000 mm and 20 000 mm, the concentration level was almost saturated at 5.5 mol m −3 at 40 and 48 seconds. When comparing Test cases 1, 10 and 19, Test case 19 shows the best mixing efficiency within a short duration compared with the other test cases.

Conclusion
In this study, we have taken three different passive micromixer devices, SCM, HBM and HBM-OB, that have two inlets, a sensing zone and one outlet for mixing two uids with three different diffusivities and three different ow rates, designed and analyzed using COMSOL Multiphysics soware. In order to study the mixing performance of two different concentrations of inlet uid (10 mol m −3 and 1 mol m −3 ) when the uids are mixed completely the concentration will reach 5.5 mol m −3 and this will be considered as the point of complete mixing. Achieving this mixed point will be different from device to device, based on the structural dimensions as well as the input parameters.
A fuzzy logic program was used to classify the data obtained from the analyses, and optimization procedures were performed on the data. During the optimization process, the parameters were changed to obtain the data. Changes in input parameters were applied to the same design in order to obtain output data.
As a result of the analysis and optimization processes, the optimum input parameters that should be applied to the HBM-OB micromixer device in order to achieve complete mixing from the inlet uids with ow rates of 1, 5, and 10 mL min −1 and a wide range of diffusivity 15.3 e −10 , 15.3 e −11 , and 15.3 e −12 m 2 s −1 were determined. If the input parameters are applied to the microuidic device in these value ranges, it is understood that the pressure in the output channel is in the range of 128-1289 Pa and complete mixing was achieved within a short length of less than 5000 mm and a short time of 10 seconds due to the structural dimensions of the device as well as the input parameters (TC19). The proposed HBM-OB micromixer device is most suitable for low-diffusivity uids and its applications such as biosensing, blood plasma analysis, blood cell analysis and heavy metal ion sensing.

Conflicts of interest
There are no conicts to declare.