Complete Mixing State Research Articles

Enhanced fluid mixing using a novel multi-stage static pipeline mixer: Numerical simulation and mechanism analysis

Static pipeline mixers play a crucial role in water treatment processes, and their mixing efficiency can be influenced by factors. Innovating mixer design to simultaneously reduce head loss and G-values while maintaining effective mixing across various flow conditions holds practical significance for improving treatment process performance. This study used a combination of numerical simulations and experimental validation to investigate the mixing process of a novel multi-stage static pipeline mixer. The results indicated that within the flow velocity range of 0.2–1.8 m/s, compared to the Kenics mixer, the new multi-stage static pipeline mixers (HOCM and COCM) achieved significant reductions in head loss (89.4 % for HOCM and 52.9 % for COCM) and G-values (67.3 % for HOCM and 31.3 % for COCM). The turbulent kinetic energy intensity of HOCM was much lower than that of COCM and Kenics mixers. Importantly, all mixers reached a state of complete mixing with the coefficient of variation (CoV) less than 0.05. In the HOCM mixer, the 2nd mixing stage was identified as the primary mixing zone, while in the COCM mixer, the 1st mixing stage played a crucial role in mixing. When the mixers achieved a mixing degree of 95 %, the head loss of HOCM and COCM was significantly lower than various types of traditional mixers (Kenics, SMX, SMV, ISG, Inliner Lightnin). This is attributed to the highly efficient mixing effect generated by the clockwise helical flow produced in the 1st and 2nd mixing stages.

Probing the Miscibility Gap of the Pt–Pd Binary System by Atom Probe Tomography

Abstract To solve the uncertainty of the platinum (Pt)–palladium (Pd) phase diagram, especially the existence of a suggested miscibility gap, atom probe tomography (APT) was used to determine the time evolution of the composition after heat treatment. Due to the extraordinarily slow diffusion in the temperature range of the controversial phase separation, the investigated volume was limited to nano-sized multiple layers deposited by ion beam sputtering (IBS). The evaporated volume was reconstructed from the obtained datasets and the respective diffusion coefficients were determined using the Fourier series solution of the diffusion equation. Beginning with pure Pt and Pd layers annealed at 673, 773, 873, and 973 K, the mixing appears to be purely diffusion controlled in the chosen annealing times, but the state of complete mixing was still not observed. Therefore, extended isothermal annealing sequences at 673 and 773 K with pre-alloyed layers have been carried out. They clearly suggest complete mixing even at the lowest investigated temperatures.

Study of the interference of plumes released from two near-ground point sources in an open channel

The dispersion and mixing of passive scalars released from two near-ground point sources into an open-channel flow are studied using direct numerical simulation. A comparative study based on eight test cases has been conducted to investigate the effects of Reynolds number and source separation distance on the dispersion and interference of the two plumes. In order to determine the nonlinear relationship between the variance of concentration fluctuations of the total plume and those produced by each of the two plumes, the covariance of the two concentration fields is studied in both physical and spectral spaces. The results show that at the source height, the streamwise evolution of the cross correlation between the fluctuating components of the two concentration fields can be classified into four stages, which feature zero, destructive and constructive interferences and a complete mixing state. The characteristics of these four stages of plume mixing are further confirmed through an analysis of the pre-multiplied co-spectra and coherency spectra. From the coherency spectrum, it is observed that there exists a range of ‘leading scales’, which are several times larger than the Kolmogorov scale but are smaller than or comparable to the scale of the most energetic eddies of turbulence. At the leading scales, the mixing between the two interfering plumes is the fastest and the coherency spectrum associated with these scales can quickly approach its asymptotic value of unity.

Experimental study of solute mixing at double-Tee junctions in water distribution systems

Recent studies have focused on mixing behavior at cross junctions, and incomplete mixing at cross junctions in water distribution systems was verified. Nevertheless, the research results on mixing at other junction configurations, such as double-Tee junctions, were insufficient. Double-Tee junctions can potentially be misrepresented as cross junctions because of network skeletonization. Hence, the diffusion and dilution of the contaminants at junctions were largely underestimated. To examine the mixing phenomenon and collect accurate mixing data at the double-Tee junction, a series of laboratory experiments was carried out with various Reynolds number ratios at the inlets and outlets combined with different dimensionless connecting pipe lengths (L/D). Results showed that the dimensionless connecting pipe length served an important function in mixing at double-Tee junctions. The cross junction was the special case of the double-Tee joint when L/D=0. The complete mixing state occurred when L/D→∞. The mixing degree of the double-Tee junction was between the cross junction and the complete mixing state. A conceptual model that described the mixing behavior at double-Tee junctions was developed. The model included the use of the dimensionless parameter φ, which defined the degree of departure from complete mixing.

Jeans’ criterion in nonextensive statistical mechanics

The Jeans’ gravitational instability in nonextensive statistical mechanics is studied and a general form of the generalized Jeans’ criterion is obtained that is related to the q-function c q=∑ i p i q . In this approach, the nonextensive model of classical ideal gas is applied to the Jeans’ problem instead of the ordinary one in extensive statistical mechanics and the generalized critical wavelength to describe the gravitational instability is deduced. This nonextensive modification of the Jeans’ criterion leads to a new critical length that depends not only on the nonextensive parameter q but also on the dimension D and the total particle numbers N of the system. When q→1−, the Jeans’ length is perfectly recovered. We also give the nonextensive parameter q a physical interpretation that q=1 represents an isothermal process of the gas, corresponding to the state of complete mixing, but 0< q<1 is nonisothermal, corresponding to the state of incomplete mixing, it measures the degree of mixing.

Modelling of microsegregation in ternary alloys: Application to the solidification of Al–Mg–Si

A fast numerical model has been developed for the quantitative prediction of microsegregation during solidification of ternary alloys. Considering a small volume of uniform temperature, the back-diffusion equations in the primary solid phase are solved in a 1-dimensional configuration using an implicit finite difference formulation with a Landau transformation onto a fixed [0,1] interval. The other phases which may precipitate during solidification are supposed to be stoichiometric and at equilibrium while the liquid is in a state of complete mixing. These calculations are coupled with phase diagram data through the use of mapping files: the liquidus surface, the monovariant lines and all the pertaining information are mapped through calls to Thermo-Calc [B. Sundman, B. Jansson and J. O. Andersson, CALPHAD, 9, 153 (1985)], prior to starting the microsegregation calculation itself. This very efficient microsegregation model can thus be coupled directly to macrosegregation computations performed at the scale of a whole casting: from the average enthalpy and concentrations variations computed at each mesh point of a casting during one time step, this microsegregation model is capable of predicting the variations of temperature, of the volume fractions of the various phases, of the liquid concentrations and of the average density. The efficiency of this coupling between microsegregation calculation and thermodynamic mapping files is demonstrated in the particular case of the Al–Mg–Si system.

Ion Beam Mixing of Au/In Bilayer Thin Film: Growth of Intermixed Layer

Ion beam mixing of Au/In bilayer thin film samples has been studied using electrical resistivity measurements and Rutherford backscattering spectrometry during bombardment with 400 keV Ar + at room temperature. These measurements indicate the growth of an intermixed layer at the interface. The increase in the resistivity of the film with fluence is correlated with the increase in the volume fraction of the intermixed layer. The volume fraction showed a square root dependence on ion fluence, suggesting that diffusional processes are responsible for the ion mixing. The saturation regime at high fluence (6 x 10 16 ions/cm 2 ) indicates a complete mixing state and the formation of a non-uniform solid solution of Au-In. These results are confirmed by Rutherford backscattering spectrometry measurements which indicate that the mixing rate reflects a square root dependence, and hence diffusional mechanisms are the dominant processes. Comparison between experimental mixing rate and calculated values indicates that mixing is due to both cascade and thermal spike mechanisms.

A DEFINITION OF QUALITY OF MIXEDNESS

To express the degree of mixing in chemical process equipment, a new, generally applicable definition of quality of mixedness is presented by making use of the entropy in information theory. The newly defined quality of mixedness varies from zero for the complete separate state or piston flow to values approaching unity for the final mixing state or the complete mixing state. The application of the newly defined quality of mixedness is explained with two types of examples.

Frequency shifts of self-oscillating magnetometer with cesium vapor

The frequency shifts of a self-oscillating magnetometer with cesium vapor are studied quantitatively by solving rate equations for cesium atoms undergoing the action of a circularly polarized pumping light beam. Particular attention is given to the frequency shifts due to the line asymmetry of the rf spectrum in the light transmitted through the vapor. The line asymmetry varies with the orientation of the light beam relative to the field to be measured, the intensity of the light, and the temperature of the absorption cell. As an effect of a buffer gas, two extreme cases are considered, i.e., the optically excited state is in the complete mixing state and in the nonmixing state. The results show the fact that the frequency shifts depend largely on the collisional mixing in the excited state and on the sense of the circular polarization of the light. In order to reduce the frequency shifts, a new type of magnetometer, called the symmetrized spectrum magnetometer, is discussed, in which two circularly polarized light beams with opposite sense are simultaneously applied to a partitioned absorption cell.

Applications of modern optimal control theory to environmental control of confined spaces and life support systems: Part 1—Modeling and Simulation

This paper is the first of a series of five containing the results of an original investigation of the temperature control of confined spaces such as those in any building and life support systems by means of the modern control theory. While much of the material presented in this work is original, the series has been prepared in sufficiently tutorial style that it can be used as a text self-study by practicing air-conditioning engineers. It is hoped that this work will stimulate the applications of and research on the modern optimal control theory to the environmental control of life support systems in general, including controls of humidity, purity and noise. Parts 2–5 will be published in the next three issues of Building Science. Several mathematical models of an environmental control system which consists of a confined space or cabin, a heat exchanger, and a feedback element such as a thermostat are presented. The performance equations of the system, which represent the dynamic characteristics of the system proper and of the heat exchanger (the control element of the system) are derived. In the basic model the flow of air in the confined space is considered to be in the state of complete mixing and the disturbance is caused by an impulse heat imput. The performance equations in which the heat disturbances are of the form such as the step function and cyclic function which are different from the impulse function are also derived. Also presented are the performance equations which represent the dynamic characteristics of flow of air in a confined space or cabin characterized by the two completely stirred tanks-in-series (2 CST's-in-series) model. To determine the goodness of the system model a computer simulation is carried out and the results are compared with the known characteristics of the system.

The Dissolving Process into Water for the Mixture of Powdered Substances with Different Solubilities (SiO&lt;sub&gt;2&lt;/sub&gt;-Na&lt;sub&gt;2&lt;/sub&gt;CO&lt;sub&gt;3&lt;/sub&gt; System)

A dissolving phenomenon of the mixed system (SiO2-Na2CO3 system) has been studied in this experiment. Thirty two kinds of mixed system were prepared by mixing the fixed amounts, e.g. Ag (A=2, 4, 6, 8), of Na2CO3 (Anhydrous) of constant meshes (40-80, 120-150 mesh) with (10-A) g of SiO2 of constant meshes (20-30, 35-60, 60-80, 80-120 mesh). Each mixture in the state of complete mixing was put into water in a special vessel. The amounts of Na2CO3 which dissolved into 1l H2O at a constant temperature, 40°C, for fixed times, 1, 2, 3 and 4 minutes, were determined by titrating with 0.01N HCl.As described in the previous paper, the relation between the amounts of dissolved Na2CO3 and the time was expressed by the following experimental formula, log(1-Mt/M∞)=Bt, Mt: Amounts of dissolved Na2CO3 at time t, M∞: Amounts of Na2CO3 which is able to dissolve.An agreement of the experimental results with this formula was examined by the analysis of variance. It was found that the dissolving phenomenon can be considered as a diffusion process with an apparent diffusion constant.As -B in the formula is regarded as a diffusion rate of Na2CO3, it can be used as a measure of the dissolving phenomenon. The relations between -B and the weights of Na2CO3 in the mixed system are shown in Fig. 1 and Fig. 2, which show that the dissolving rate of Na2CO3 decreases with increasing the weights of Na2CO3.Eight experimental formulae showing the relations among -B, the valume percentage of each constituent, and the porosity of the mixture were obtained by the regression analysis, and from these equations it was found that the volume percentage of Na2CO3 gives a negative factor but the porosity a positive factor to the dissolving rate, and the volume percentage of SiO2 gives a negative factor, with the exception of the case of SiO2 20-30 mesh.The value of B calculated by the use of Eq. (4. 3. 4) and the observed value of B were found to be in good agreement (Table 10 and 11). From this results, it was ascertained that -B satisfies the aclitivity relationship in reference to the volume percentage of Na2CO3, the volume percentage of SiO2 and the porosity as follows;-B=L[Na2CO3]volume%+N[SiO2]volume%+L[Porosity]L=0.0648-0.00250x-0.000392y+0.0000138xyN=0.0380-0.00104x-0.000247y+0.0000064xyM=-0.0226+0.00085x+0.000169y-0.0000051xyx: mean SiO2 mesh, y: mean Na2CO3 mesh.