Optimization of a microfluidic mixer for studying protein folding kinetics

We have applied an optimization method in conjunction with numerical simulations to minimize the mixing time of a microfluidic mixer developed for protein folding studies. The optimization method uses a semideterministic algorithm to find the global minimum of the mixing time by varying the mixer geometry and flow conditions. We describe the minimization problem and constraints and give a brief overview of the optimization algorithm. We present results of the optimization, including the optimized geometry and parameter sensitivities, and we demonstrate the improvement in mixing performance with experiments using microfabricated mixers. The dye-quenching experiments of the original and optimized mixer designs show respective mixing times of 7 and 4 mus, a 40% reduction. The new design also provides more uniform mixing across streamlines that enter the mixer. The optimized mixer is the fastest reported continuous flow mixer for protein folding.     

Evaluation of the mixing effectiveness of a new powder mixer

The effectiveness of the new powder mixer Canguro J tumbler was evaluated using lactose, microcrystalline cellulose, and salicylic acid as chemical indicator with the ratio 88:10:2 (w/w). The mixing time, the speed of the tumbler (rpm), its inclination, and filling percentage were varied in order to assess the limits of the mixer and the best parameters to use for obtaining a mixture as uniform as possible. The same experiments were then repeated after addition of 1% (w/w) magnesium stearate to the mixture of powders. The efficiency in the distribution of this lubricant was estimated by the progressive hardness reduction of the tablets derived from the compression of the powders, at a constant applied force. Finally, a comparison between Canguro J and a very efficient V-shaped mixer of the same capacity was performed. The results show that all investigated parameters influenced the mixing capability of Canguro J. The best effectiveness of the mixer occurred at the filling rate of 50% and a rotation speed of 20 rpm; in this case, Canguro J is even a little more effective than the V-shaped mixer. However, even at the filling rate of 70%, the same distribution uniformity of the powders can be obtained after a mixing time protraction of a few minutes.     

通道式微混合器的设计及性能

利用计算流体力学和数字图像处理技术,研究"Y"型通道式微混合器的结构及混合性能,分析了混合器结构尺寸和流动条件对混合过程的影响.数值模拟结果表明,在混合通道入口夹角为60°、通道宽度为200μm、注入速度为0.02 m/s的流动条件下,可以取得比较满意的混合效果.利用数值模拟对比了扭曲通道混合器、导流块和直通道结构对混合过程的影响,结果表明使用导流块可以显著提高混合效果.依照模拟计算结果,设计并用MEMS工艺制作了双侧壁有内肋块的通道式微混合器,并进行了流体混合实验,观测了混合过程.拍摄混合实验图像,对比标准浓度-图像灰度关系曲线后识别出拍摄点混合指数.识别计算的结果也证实了所设计混合器性能上的优越性.最后对实验结果误差进行了分析,说明了误差来源并给出了相应的改进措施.     

The joint mixing action of the static pre-mixer and the rotating drum mixer – Discrete element method approach

In this study, the mixing performance of coupled mixing action of the Komax static mixer (which is used as a pre-mixer) and rotating drum (applied as the final mixer) was explored in the maize meal mixing operation. The main objective of this paper was to predict the behaviour of the previously grinded maize particles, during the mixing process in static mixer and drum mixer, and to explore the possibilities to shorten the mixing time in the main mixer (in order to reduce the energy consumption).Three different experiments were performed: in the first experiment, possibilities of static mixer were explored, second experiment showed the mixing performance of rotating drum, and the combination of these two mixing devices was investigated in the third experiment. Homogeneity of the obtained mixtures was determined experimentally, by the “Microtracers” method.The Discrete Element Method was used for modelling of granular flow in the pre-mixing and final mixing applications, and to predict the inter-particle mixing quality within a static mixer and the rotating drum mixer. The results of the numerical simulation are compared with appropriate experimental results. The possible industrial application of this model could be the optimization of parameters of mixing systems taking into account the quality and the duration of the mixing process.     

Stokes flow in a mixer with changing geometry

A slow-flow mixing device that mimics a natural mixing technique is described. Analytical, numerical and experimental results are presented for the `translating, rotating mixer', which illustrate its mixing effectiveness. In large part, this effectiveness is due to the fact that its geometry changes with time, a feature rare in mathematically tractable slow-flow mixing models. The mixer consists of a large circular cylinder filled with fluid, which is stirred by a circular cylindrical `rod' that moves around in the fluid. The stirring rod may also rotate about its axis. The velocity field is calculated explicitly for the mixer, and its mixing action is simulated numerically. Through a complex-variable formulation of the problem, the energy input required for various mixing protocols may readily be determined, and in turn suggestions for efficient mixing using the device are offered. To validate the analytical and numerical results, tracer-advection experiments are performed, using a simple experimental rig and a variety of mixing protocols, providing encouraging agreement with numerical simulation.     

Tablet-to-Tablet Dissolution Variability and its Relationship to the Homogeneity of a Water Soluble Drug

The homogeneity of a water soluble drug in a tablet granulation was studied by mixing the granulated drug with excipients in a V-shaped tumbling mixer. Samples were withdrawn from five different locations of the mixer for homogeneity and dissolution studies at different mixing times. For dissolution studies, tablets were compressed at a constant compression load. Qualitatively, the coefficient of variation of mixing and dissolution looked similar, suggesting that the mixing homogeneity may have some relationship to the tablet-to-tablet dissolution variability. The addition of magnesium stearate resulted in an increase in the coefficient of variation of mixing and a decrease in the dissolution rate. A large decrease in the dissolution rate occured during the first minute of mixing with the magnesium stearate. The tablet crushing strength continuously decreased during the first 10 minutes of mixing with the magnesium stearate. The results suggested that the formulation in which a major portion of the excipients was not wet granulated with the drug resulted in higher tablet-to-tablet dissolution variability. The addition of sodium starch glycolate or sodium carboxymethyl cellulose to starch for enhancing disintegration neither improved the tablet-to-tablet dissolution variability nor increased the rate of drug dissolution.     

Design and Numerical Simulation of a Gas Mixer

A high precision gas mixer used to mix gases of small flow rapidly and uniformly was proposed in this paper. Nine simulation schemes were proposed based on orthogonal test. There were four factors including dilute gas flow rate, the length of mixing tube, the diameter of the mixing chamber and the width of the mixing chamber in orthogonal test and each factor had three levels. The numerical simulation was carried out to explore the relationship of the flow field and the four factors and to calculate the concentration of carbon monoxide at the mixer’s outlet. The primary factor that affected the mixing effectiveness was found out by means of range analysis. The heterogeneous degree of the distribution of carbon monoxide concentration at the mixer’s outlet was smaller than 0.002 under different conditions. The results reached uniform micromixing in engineering and met the requirement of measurement and detection.     

DEM simulation for optimal design of powder mixing in a ribbon mixer

A ribbon mixer is often employed in powder mixing in a wide range of engineering fields. The structure of the ribbon mixer is extremely complicated. This structure makes it difficult to understand the mixing mechanism by experimental approaches due to problems related to accurate sampling. At present, the mixing mechanism in the ribbon mixer is empirically identified as convection, despite a lack of precise assessment. Additionally, experimental investigations to find the optimal design of the ribbon mixer have not been sufficiently conducted because of its prohibitive cost. As such, there is a lack of sufficient discussion concerning the design for better mixing in the ribbon mixer. Numerical technologies represent a promising approach for solving the aforementioned problems. Significant improvements in computer hardware have enabled numerical models such as the discrete element method (DEM) to be positively employed in powder mixing. In the current study, an identification approach is developed for convective mixing, and besides, the study explores an effective parameter for better mixing in the ribbon mixer using the DEM. A swept volume measurement approach due to paddle movement is newly developed to identify the main mixing mechanism as convection. Sensitivity analyses are performed to find an effective parameter for better mixing. Through the sensitive analyses, the blade width is indicated as an important factor for achieving better mixing. Moreover, this study shows that the relationship between the swept volume and mixing index remains, even if the paddle width changes. Thus, the swept volume measurement method is revealed as useful for identifying the mechanism as convection in the ribbon mixer. Thus, not only novel finding regarding the blade width for better mixing but also the development of an approach for identifying convective mixing in the ribbon mixer is presented herein. Incidentally, convection being the dominant mechanism is consistent with the novel finding regarding blade width achieving better mixing.     

DEM study of the effect of impeller design on mixing performance in a U-shape ribbon mixer

The mixing of powders in a U-shape mixer is significantly influenced by the mixer design, especially impellers, but the studies on the mixing processes are still insufficient. In this study, the effect of impeller designs on mixing performance in an industrial-scale U-shaped ribbon mixer is studied using DEM simulations. Three impeller designs are studied: 2-bladed impeller spiralling in the same direction (i.e., Design I) and the opposite direction (i.e., Design II), and 4-bladed impeller (i.e., Design III). Different particle mixing behaviours in three different impeller designs are studied in aspects of mixing status, particle path line, velocity distribution, and forces. The radial direction has the highest dispersion coefficient while the axial direction has the lowest dispersion coefficient. Most particles in the mixers are imposed a weak force. Design III shows the best mixing performance among the three with the front-by-back and top-by-bottom loading used. Design II shows a better mixing performance used than Design I and III with the side-by-side loading but takes a longer time to reach the stable status. This work evaluates the effect of different impeller designs on the mixing performance in an industrial-scale U-shaped ribbon mixer and provides an effective way to assist industrial design in an economical and safe manner.     

Numerical study of the mixing process of binary-density particles in a bladed mixer

Discrete element method (DEM) simulations of binary mixing of particles with different densities were conducted to study the influence of density ratio, blade speed, and filling level on the particle dynamics and mixing performance in a bladed mixer. Four particles with different densities at different locations were tagged to discuss the influence of three factors on the particle trajectory and velocity field in the mixer. A method based on cubic polynomial fitting of relative standard deviation was used to determine the critical revolution during the mixing process. It was found that the non-dimensional tangential velocity decreases with the increase of the blade speed and filling level, the fluctuation of vertical velocity increases with the radial location, blade speed, and filling level, and it is more pronounced than the fluctuation of tangential and radial velocity during the mixing process. Results obtained indicate that the mixing performance of particles with different density increases with the decrease of density ratio and filling level, while it increases with the increase of blade speed.     

Investigation of the staggered herringbone mixer with a simple analytical model

An analytical model is presented for the three-dimensional flow in the recently introduced staggered herringbone mixer for microchannels. In this model, the flow in the cross-section of the channel is treated as a lid-driven cavity flow. The model is shown to reproduce the advection patterns that were observed experimentally in the staggered herringbone mixer. The model is then used to study the quality of mixing in this flow as a function of geometry. Analysis is performed with Poincaré maps, mixing simulations, and residence time distributions. A range of optimal geometries is identified.     

Monitoring of concrete homogenisation with the power consumption curve

Homogenisation time increases for superplasticized concrete slowing down their industrial production. Monitoring power consumption measurement capability to control concrete homogeneity during mixing is explored. Various High Performance Concrete and Self-Compacting Concrete was batched in a 1 m³ pan mixer, with increasing mixing time. Rheology and compressive strength were measured and compared for different mixing times. Correlations were established between power consumption and compressive strength evolutions. Also, power consumption for the longest mixing time and concrete rheological parameters (yield stress and plastic viscosity) are related. On the another hand, tests show that mixing difficulty for a given mix-design is reduced with increased mixer capacity and when fast planetary tools are implemented in the mixer. As a conclusion, the power consumption evolution can be very useful information to control concrete homogeneity during mixing, to control material flowability, and to compare the capability of different mixers.     

Compartmental residence time estimation in batch granulators using a colourimetric image analysis algorithm and Discrete Element Modelling

In this paper we present an experimental technique and a novel colourimetric image analysis algorithm to economically evaluate particle residence times within regions of batch granulators for use in compartmental population balance models. Residence times are extracted using a simple mixing model in conjunction with colourimetric data. The technique is applied to the mixing of wet coloured granules (binary and ternary systems) in a laboratory scale mixer. The resulting particle concentration evolutions were in qualitative agreement with those from the mixing model. It was seen that the algorithm was most stable in the case of the binary colour experiments. Lastly, simulations using the Discrete Element Method (DEM) were also performed to further validate the assumptions made in the analysis of the experimental results. Particle concentrations from the simulations showed the same trends as the experiment and highlighted the importance of particle size distributions on the DEM residence times.     

Scale-up and flow behavior of cohesive granular material in a four-bladed mixer: effect of system and particle size

Flow of cohesive granular materials with different moisture contents was examined in a four-bladed mixer via the discrete element method (DEM). Firstly, the mixer diameter (D) was increased while keeping the particle diameter (d) constant. It was observed that when the mixer diameter to the particle diameter ratio (D/d) was larger than a certain critical size (D/d ≥ 75), granular flow behaviors and mixing kinetics followed simple scaling relations. For D/d ≥ 75, flow patterns and mixing kinetics were found to be independent of system size, and velocities of particles scaled linearly with the tip speed of the impeller blades and particle diffusivities scaled with the tip speed of the blades and mixer diameter. These results suggest that past a certain system size the flow and mixing of cohesive particles in large-scale units can be predicted from smaller systems. Secondly, system size was kept constant and particle diameter was changed and it was observed that by keeping the Bond number constant (by changing the level of cohesion) the flow behavior and mixing patterns did not change, showing that larger particles can be used to simulate flow of smaller cohesive particles in a bladed mixer by matching the Bond numbers.     

Statistical comparison of high-shear versus low-shear granulation using a common formulation

Experimental combinations from the ranges assigned to the independent factors were studied using both a low-shear (planetary) mixer and a high-shear mixer for granulation. The independent factors studied were X₁ calcium phosphate/mannitol ratio, X₂ pregelatinized starch, X₃ magnesium stearate, X₄ mixer type, and X₅ compression pressure. To optimize the tablet properties fully, the experimental range was varied from -2 to +2 experimental units, with the exception of X₄, which was assigned -1 for the planetary mixer and +1 for the high-shear mixer. Drug dissolution did not seem to be affected by mixer type, but tablet hardness was affected by mixer type.     

A Comparison of Free-Flowing, Segregating and Non-Free-Flowing, Cohesive Mixing Systems in Assessing the Performance of a Modified V-Shaped Solids Mixer

The performance of a modified V-shaped solids mixer, i.e., uneven leg or offset angle, has been reassessed by using a binary cohesive mixture, made up of 1% sodium salicylate and 99% microcry stalline cellulose, as the mixing system. The performance of the mixer was defined in terms of relative standard deviation from the measured mean. The results generated from the present study were compared with the previously published data generated by using a free-flow mixing system. It appears in the present study that the free-flowing, segregating materials may be used as a mixing model to predict the trend of the performance of a modified V-shaped blender for the non-free-flowing, cohesive materials. However, in the equilibrium state, the non-free-flowing, cohesive mixture has much better quality of the mix than that of the free-flowing, segregating system in terms of the scale and intensity of segregation.     

A picoliter-volume mixer for microfluidic analytical systems

Mixing confluent liquid streams is an important, but difficult operation in microfluidic systems. This paper reports the construction and characterization of a 100-pL mixer for liquids transported by electroosmotic flow. Mixing was achieved in a microfabricated device with multiple intersecting channels of varying lengths and a bimodal width distribution. All channels running parallel to the direction of flow were 5 microm in width whereas larger 27-microm-width channels ran back and forth through the parallel channel network at a 45 degrees angle. The channel network composing the mixer was approximately 10 microm deep. It was observed that little mixing of the confluent solvent streams occurred in the 100-microm-wide, 300-microm-long mixer inlet channel where mixing would be achieved almost exclusively by diffusion. In contrast, after passage through the channel network in the approximately 200-microm-length static mixer bed, mixing was complete as determined by confocal microscopy and CCD detection. Theoretical simulations were also performed in an attempt to describe the extent of mixing in microfabricated systems.     

Analysis of the process of mixing of a passive impurity in a jet mixer

The experimental results for two regimes of mixing of a passive impurity in an axisymmetric jet mixer — the mixing of a turbulent jet and a cocurrent flow to form a recirculation zone behind the nozzle and an analogous mixing without the formation of a recirculation zone (Re_d = 10,000) — have been presented. The velocity field has been measured in the mixer cross sections at different distances from the nozzle (0.1 < x/D < 9.1) with a one-component Doppler laser anemometer, whereas the scalar field (concentration of the passive impurity) has been diagnosed by the laser-induced fluorescence method. Based on the scalar distributions obtained, the autocorrelation function and the integral scale have been computed, the form of the probability density function has been restored, and the distributions of the asymmetry and excess coefficients have been constructed. Visualization of flow in the mixer has been carried out. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 2, pp. 46–59, March–April, 2007.     

CONTACT NUMBER AS AN INDEX OF TRANSVERSE MIXING IN A MOTIONLESS MIXER

A geometrical and microscopic mixing index defined by the contact number was used to study the transverse mixing in a Kenics motionless mixer. The mixing index, a measure of transverse mixing, increased exponentially as the number of helices in the motionless mixer increased. The helices in the mixer also had the significant effect of reducing the void fraction of the mixture. The relationship between the coordination number and the compaction in the mixture through the mixer was studied. The mean coordination number indicates that the packing of these mixtures are between the cubic and hexagonal packings.     

CONTACT NUMBER AS AN INDEX OF TRANSVERSE MIXING IN A MOTIONLESS MIXER

ABSTRACT

A geometrical and microscopic mixing index defined by the contact number was used to study the transverse mixing in a Kenics motionless mixer. The mixing index, a measure of transverse mixing, increased exponentially as the number of helices in the motionless mixer increased. The helices in the mixer also had the significant effect of reducing the void fraction of the mixture. The relationship between the coordination number and the compaction in the mixture through the mixer was studied. The mean coordination number indicates that the packing of these mixtures are between the cubic and hexagonal packings.