1. Introduction
Mixing is critical in chemical and biological processing and analysis. Adequate mixing can ensure the precision of chemical and biological processing and reaction analysis [
1]. The passive mixer based on the microchannel, the passive micromixer, has emerged as a novel alternative in recent decades. Micromixers have been widely employed for reagent mixing, reactant delivery, fluidic control, and particle separation, and it is an essential and decisive component in the Lab-On-a-Chip system (LOC) [
2,
3].
The width and depth in the cross-section of a passive micromixer are both in the range of 10–m. In such a scale, a mixing process has the following characteristics:
The flow in the microchannel is pumped or delivered with the limited velocity (≤
), resulting in a laminar state of low Reynolds number [
4]. Therefore, molecular diffusion is the dominant mass transfer process in a micromixer [
5];
The diffusion distance between two phases is small, promoting the flow mixing sufficiency in cross-section;
The specific surface area in a micromixer is generally much larger (up to 50 times) than the conventional mixing vessel. The higher specific surface area ensures a higher mixing and heat exchange efficiency.
Therefore, the micromixer is particularly suitable for mixing or synthetic reactions of small reaction volumes of high efficiency. In general, diffusion time, diffusion intensity, and vortex flow intensity are the most critical perspectives for mixing efficiency in a micromixer [
6,
7]. Several new micromixers have been designed in recent years (e.g., T-shaped mixer, E-shaped mixer, and Y-shaped mixer) to improve the aforementioned major factors of mixing efficiency. A heart-shaped micromixer, named Corning G1 micromixer, is a novel and highly efficient micromixer with a wide range of applications in the field of process engineering [
8].
Optimizing the microchannel structure is a critical procedure in microfluidic mixing [
9]. Several optimization techniques have recently been introduced to design a new microchannel. Lv et al. [
10] used single-objective optimization with different Reynolds numbers to maximize the mixing performance on the cantor fractal baffle structure. They combined the fractal principle with the simulated annealing algorithm to improve the mixing performance of a micromixer. Hossain et al. [
11] analyzed and optimized a modified Tesla micromixer through a three-dimensional Navier–Stokes analysis. In their study, the mixing and pressure-drop characteristics have been investigated in terms of two geometric parameters, i.e., the ratio of the diffuser gap to the channel width and the ratio of the curved gap to the channel width. The optimizations included three dimensionless design variables: ratios of the diagonal channel width to the pitch length, the main channel width to the pitch length, and the channel depth to the pitch length. Zhang et al. [
12] proved that the Koch fractal principle can effectively break the laminar flow in the microchannel and promote the generation of chaotic convection.
Response surface methodology (RSM) has emerged as a reliable search optimum method to suggest optimization by constructing a fitting surface from the limited data of discrete design conditions [
13]. The RSM can extensively search out the optimum across the entire region of the fitting surface rather than the local optima from the discrete points of the aforementioned methods [
14,
15]. RSM’s core principle is approximating the actual limit state function using the response surface function for subsequent analytical calculations [
16], seeking an optimal combination of factor levels and solving multivariate problems [
17]. With its short cycle and high precision, this technique fully captures the interactions between multiple factors. Therefore, this study adopts the RSM to optimize the G1 micromixer structure.
This paper focuses on the influence of feed pressure p and microchannel central width w of a Corning G1 micromixer on the mixing efficiency of two miscible fluids. Our optimization of this micromixer is conducted as the following steps:
(1) A 2D numerical model of a G1 micromixer for mixing two miscible fluids is generated;
(2) An estimation index for mixing efficiency, called the mixing index (), is adopted through the study;
(3) Numerical simulations with a series of working conditions were carried out to obtain the relationship for the , the feed pressure p, and the microchannel width w;
(4) The RSM was introduced to process the data from the CFD simulations. A proper fitting surface was constructed from the CFD discrete working conditions of , p, and w;
(5) A search optimum algorithm of PPSO was used to suggest the optimization of , p, and w across the entire region of the fitting surface;
(6) The suggestion of optimal parameters from the RSM method and the PPSO algorithm was validated by the CFD simulation again.
4. Conclusions
The simulation of miscible liquid–liquid two-phase flow in a Corning G1 micromixer was achieved using the mixture model. The microchannel’s feed pressure and central width effect on the flux and mixing efficiency were analyzed. A response surface model for the mixing index was subsequently proposed.
The most effective width for the channel and its associated mixing index were determined using PPSO for the response surface model. Those values were 1.634 mm and 0.9827, respectively. The numerical model of the micromixer was designed using the optimized parameter and was verified with CFD. The CFD values agree with the predicted values of the response surface model well, and their average relative errors for the flux and mixing index are 2.93% and 1.09%, respectively.
The optimized 1.634 mm microchannel improves the mixer’s flux and mixing efficiency of miscible liquid–liquid mixtures compared to the original Corning’s G1 mixer, i.e., the mixer with a 1.5 mm width under the pressure variant at 0.1 MPa, 0.2 MPa, and 0.3 MPa. On average, the flux increases by 13.51%, and mixing efficiency improves by 2.45%.
Besides the channel width, the key structural parameters of the arc baffle and cylindrical baffle, etc., may also affect the mixing performance of the G1 micromixer [
37,
38]. However, modifications of these structure parameters usually introduce manufacturing challenges and costs. On the contrary, a few studies [
39,
40,
41] have reported that the mixing performance is also sensitive to the microchannel width (
w), so simple modifications of the channel width may increase the mixing performance significantly. This study discusses the effects of microchannel width and feed pressure on mixing performance rather than other structural and manipulation parameters. The research interest specifically focuses on the mixing performance of HCl and ethylene glycol solutions. Although this work is based on a specific design and process, the workflow in this paper can provide the standard processing for optimizing other flow mixers.