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Electro-osmotic micromixers constitute a specialized class of active micromixers that apply alternating current (AC) to electrodes. This methodology promotes the formation of vortical structures within the fluid medium, resulting in a substantial increase in mixing homogeneity. In this study, the geometrical parameters of the electro-osmotic micromixer, for which two rigid baffles were implanted at the entrance, were optimized using the Taguchi method and response surface methodology (RSM). Data were obtained through a transient 2D model, simulated using COMSOL software based on the finite element method. After acquiring the optimized geometric parameters, the mixing index was assessed under various conditions, including inlet velocity, frequency, voltage, and phase lag of the alternating current. The optimized values of first baffle angle ( ), second baffle angle ( ), baffle length (L), the distance between baffles in the x direction (x), the distance between baffles in the y direction(y), and mixing chamber angle ( ) were obtained and resulted in a 10.58% improvement in the mixing process index. The implementation of rigid baffles improved the mixing index by 8%. Furthermore, increasing the applied voltage from 1 to 3 V resulted in a 27% average enhancement of the mixing index. A maximum mixing index of 99.37% was achieved at a phase lag, representing an average 20.1% improvement compared to the absence of a phase lag. This reflects an approximate 65% increase at the initial stage compared to the scenario without any phase lag.

Static mixers are widely used devices for efficient fluid mixing, homogenization, and enhancement of heat transfer, with applications ranging from chemical processing and pharmaceutical manufacturing to wastewater treatment. This review provides a structured overview of mixing processes and the key metrics used to assess mixing quality in static mixers. Conceptual models such as dispersive versus distributive mixing and the classification into macro-, meso-, and micromixing are introduced as a basis for understanding mixing phenomena. Subsequently, a comprehensive set of quantitative measures, including G-value, residence time distribution, intensity of segregation, coefficient of variation, striation-based descriptors, Lyapunov exponent, extensional efficiency, and shear rate, is discussed in detail. Correlations and relationships among these measures are highlighted to facilitate their application in characterizing mixing quality in static mixers. By systematically summarizing the theoretical background, definitions, and interconnections of mixing quality measures, this review aims to provide researchers and engineers with a clear framework for evaluating and comparing mixing quality in static mixers, thereby supporting both academic studies and practical design considerations.

In this study, a discrete element method is employed to simulate the mixing process of solid particles in a horizontal ribbon mixer with a double U-shaped vessel. A mixing index, i.e. the so-called Lacey index, is adopted to evaluate the mixing quality of particles. The effects of the operational and geometrical parameters including initial loading, particle size, impeller rotational speed, and inner blades on the mixing quality of particles have been investigated. Results suggest that the initial loading and the impeller rotational speed have significant effects on the mixing quality of particles, while the other two parameters have relatively small effects. Moreover, the effect of each parameter on the mixing quality has been explained by utilizing the relative velocity components between the centroids of particles after collision, and this ribbon mixer provides much more intense relative movements of particles along the vertical direction than the axial and side–side directions. Finally, the mixing performance between the ribbon mixers with respective single and double U-shaped vessels is compared. Results show that the ribbon mixer with a double U-shaped vessel shows better mixing performance under top–bottom and front–back initial loadings, however, worse mixing performance under side–side initial loading.

The current paper presents a three-dimensional study of the nitrogen and oxygen mixing process in a T-type micromixer. The micromixer with a height of 125 μm and a width of 550 μm has been considered for numerical investigation. Computations and solving governing equations have been done using the finite element method for Reynolds numbers of 26.9, 50.9, 78.4, and 109.3. The obtained mixing quality and pressure drop of a simple T-type micromixer have been validated against reference data which revealed admissible agreement. The main goal of this work is to enhance the mixing quality by presenting the novel design of the SAR (split-and-recombine) structures. SAR-type micromixers have attracted attention due to the low mixing ratio in simple T-type mixers. For this purpose, the mixing units and obstacles were added to the mixing channel of T-type micromixer and the comparative results have been reported in terms of mixing quality, concentration contours, and pressure drop. The results revealed that at low Reynolds numbers, due to the better molecular diffusion, the mixing quality is high for all simulated models. Besides, it is found that SAR micromixers improve the contact interface area of fluids, thus, the diffusion flux and consequently the mixing quality enhances. Furthermore, it has been concluded that by adding the obstacle before the mixing units, the mixing quality is higher than the state they have been added after the mixing units. On the other hand, the cross-section area of mixing units has been studied. The mixing quality is increasing by increasing the mentioned parameter. Finally, the most effective mixing efficiency (95%) and moderate dimensionless pressure drop (170) has been achieved at Re = 78.4 and b/DH = 0.429.

Clay–gravel mixture is an increasingly popular material used in geotechnical engineering for its engineering adaptability and easy accessibility. Among various granulometric factors, gravel content plays a critical role in the alteration of mixture microstructure. Its influence on mechanical behavior has been comprehensively investigated, yet the hydraulic models accounting for the paired impact of clay and gravel particles are seldomly discussed. In an effort to enhance the permeability prediction capability of this soil, a generalized binary model derived from a theoretical hydraulic conductivity expression is proposed, with the participation of two fundamental compound seepage models. High accuracy between test and calculation results indicates the reliability of this model, as well as its supremacy over conventional models. The parameter sensitivity analysis demonstrates that the proposed model, being of convincing parametric stability regardless of variant particle size distribution characteristics, has the potential to be applicable to a wide range of engineering-adapted CGMs. The predictive formula for cohesive fraction and the anomaly coefficient, as is integrated into the binary model, are explicitly discussed. Suitable for clay–gravel materials under a transitional soil state for engineering applications, this model provides a quantitative and reasonable evaluation of hydraulic conductivity with high practicality. The above findings might work as a perspective for the credible assessment of structure seepage safety behavior, as well as a quantitative evaluation method regarding the mixing quality of CGMs.

Highly filled plastics may offer a suitable solution within the production process for bipolar plates. However, the compounding of conductive additives and the homogeneous mixing of the plastic melt, as well as the accurate prediction of the material behavior, pose a major challenge for polymer engineers. To support the engineering design process of compounding by twin-screw extruders, this present study offers a method to evaluate the achievable mixing quality based on numerical flow simulations. For this purpose, graphite compounds with a filling content of up to 87 wt.-% were successfully produced and characterized rheologically. Based on a particle tracking method, improved element configurations were found for twin-screw compounding. Furthermore, a method to characterize the wall slip ratios of the compounded material system with different filler content is presented, since highly filled material systems often tend to wall slip during processing, which could have a very large influence on accurate prediction. Numerical simulations of the high capillary rheometer were conducted to predict the pressure loss in the capillary. The simulation results show a good agreement and were experimentally validated. In contrast to the expectation, higher filler grades showed only a lower wall slip than compounds with a low graphite content. Despite occurring wall slip effects, the developed flow simulation for the design of slit dies can provide a good prediction for both low and high filling ratios of the graphite compounds.

A theoretical analysis of the influence of the distribution of the local specific energy dissipation rate on the specific interfacial area, the surface and volumetric mass transfer coefficients in apparatuses with heterophase processes and a liquid continuous phase, as well as the quality of mixing in apparatuses with homophase reactions in the liquid phase, is performed. It is shown that the average value of the specific energy dissipation rate over the volume of the device is not a full-fledged criterion for assessing the useful effect since it does not take into account, on the one hand, the local level of energy dissipation in the active zones and, on the other hand, the features of the flow structure and the local residence time in the active zones, depending on the geometry of the device and the method of energy input into it. Limiting cases are discussed: (1) uneven energy distribution in the presence of a small volume with a high specific dissipation rate and (2) ideally uniform energy distribution throughout the entire volume of the device. In the first case, a significant part of the volume is used inefficiently; in the second case, an excessive amount of energy is spent. In this regard, the concepts of dosed distributed energy input for long-term processes and maximum energy concentration in a microvolume for fast-flowing processes are considered.

The effects of prolonged heat and drought stress and cool growing conditions on dough mixing quality traits of spring wheat (Triticum aestivum L.) were studied in fifty-six genotypes grown in 2017 and 2018 in southern Sweden. The mixing parameters evaluated by mixograph and the gluten protein characteristics studied by size exclusion high-performance liquid chromatography (SE-HPLC) in dough were compared between the two growing seasons which were very different in length, temperature and precipitation. The genotypes varying in gluten strength between the growing seasons (≤5%, ≤12%, and ≤17%) from three groups (stable (S), moderately stable (MS), and of varying stability (VS)) were studied. The results indicate that most of the mixing parameters were more strongly impacted by the interaction between the group, genotype, and year than by their individual contribution. The excessive prolonged heat and drought did not impact the buildup and mixing time expressed as peak time and time 1–2. The gluten polymeric proteins (unextractable, %UPP; total unextractable, TOTU) and large unextractable monomeric proteins (%LUMP) were closely associated with buildup and water absorption in dough. Major significant differences were found in the dough mixing parameters between the years within each group. In Groups S and MS, the majority of genotypes showed the smallest variation in the dough mixing parameters responsible for the gluten strength and dough development between the years. The mixing parameters such as time 1–2, buildup, and peak time (which were not affected by prolonged heat and drought stress) together with the selected gluten protein parameters (%UPP, TOTU, and %LUMP) are essential components to be used in future screening of dough mixing quality in wheat in severe growing environments.

The computational fluid dynamics (CFD) study on micromixers in this paper illustrates the effect of confluence angle on mixing performance at different Reynolds numbers and flow rate ratios. The mixing performance parameters such as mixing quality and effectiveness increases with the increase in Reynolds number for all the micromixer geometries. For any value of Reynolds number, the angle of confluence is found to have a significant effect on flow behavior in the mixing channel and thus on mass transfer. The formation of vortices and the interlacing of fluid streams are identified as the favorable phenomena due to which mass transfer or mixing of fluid streams is enhanced. The mixing effectiveness is mostly observed to be high in case of unequal flow rates in the two feed/inlet channels. The optimum value of confluence angle depends of flow rate ratio. When flow rate ratio is high, T-shaped micromixer ( θ  = 180°) provides better performance while for other ratios, micromixers with relatively large angles of confluence are found more suitable.

Passive micromixers are of great importance in biomedical engineering (lab-on-chips) and chemical processing (microreactors) fields. Various hydrodynamic principles such as lamination, flow separation, and chaotic advection were employed previously to improve mixing in passive mixers. However, mixing enhancement due to velocity gradients in the flow, which is known as the Taylor dispersion effect, has been seldom studied. In the present study, thin rectangular slabs oriented in the flow direction are placed in the mixing channel of a T-micromixer. The thin rectangular slabs are referred to as Taylor Dispersion Obstructions (TDOs) as they are designed to create velocity gradients in the flow. The mixing performance of T-micromixer with and without TDOs is estimated in the Re range of 0 to 350. It is observed that there is no effect on mixing in the presence of TDOs in the low Re (0 < Re < 100), as the velocity gradients created in the flow are considerably small. The vortex formed in the flow for Re of 100 to 220 damped the gradients of velocity created in the flow (due to the presence of TDOs) which resulted in negligible improvement in the quality of mixing. However, considerable enhancement in mixing performance is obtained at high Re (250 to 350) with the presence of TDOs in the mixer. The increase in inertial effects at higher Recreated larger gradients of velocity near the walls of TDOs and mixing channel walls and thereby a significant enhancement in mixing performance is obtained due to Taylor dispersion.