Pressure drop in a split‐and‐recombine caterpillar micromixer in case of newtonian and non‐newtonian fluids

Microreactors are very promising tools for the design of future chemical processes. For example, emulsions of very narrow size distribution are obtained at much lower energy consumption than the one spent with usual processes. Micromixers play thereby an eminent role. The goal of this study is to better understand the hydrodynamic properties of a split‐and‐recombine Caterpillar micromixer (CPMM) specially with regard to handling viscoelastic fluids, a topic hardly addressed so far in the context of micromixers in general, although industrial fluids like detergent, cosmetic, or food emulsions are non‐Newtonian. Friction factor was measured in a CPMM for both Newtonian and non‐Newtonian fluids. For Newtonian fluids, the friction factor in the laminar regime is f/2 = 24/Re. The laminar regime exists up to Reynolds numbers of 15. For shear‐thinning fluids like Carbopol 940 or viscoelastic fluids like Poly Acryl Amide (PAAm) aqueous solutions, the friction factor scales identically within statistical errors up to a generalized Reynolds number of 10 and 0.01, respectively. Above that limit, there is an excess pressure drop for the viscoelastic PAAm solution. This excess pressure drop multiplies the friction factor by more than a decade over a decade of Reynolds numbers. The origin of this excess pressure drop is the high elongational flow present in the Caterpillar static mixer applied to a highly viscoelastic fluid. This result can be extended to almost all static mixers, because their flows are generally highly elongational. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2679–2685, 2013     

Numerical investigation of blade shape in static mixing

The mixing performance of the KMX and SMX static mixers have been compared using 3D high-resolution computational fluid dynamics (CFD) simulations. Although these mixers have a similar design composed of layers of blades, their blade shape is different: curved for the KMX and flat for the SMX. The flow of a Newtonian fluid in steady laminar regime has been considered as the benchmark of the study. The simulation was first validated by assessing the pressure drop vs. the number of mixer elements and the results were found to be in good agreement with experimental data. To evaluate the mixing quality, cross-section stream function, extensional efficiency, mean shear rate, residence time, intensity of segregation, stretching, and Lyapunov exponent have been selected. Analysis of the flow pattern and mixing parameters shows differences between the mixers and it appears that the curved blade is more efficient than the flat blade design at the expense of a slightly higher pressure drop. In practice, the KMX mixer should provide a higher mixing rate at high viscosity ratio than the SMX mixer. © 2004 American Institute of Chemical Engineers AIChE J, 51: 44–58, 2005     

Pressure drop during the flow of stokesian fluids through granular beds

The resistance to flow of Stokesian fluids (i.e. time—independent fluids with no yield stress) through granular beds is discussed. A definition of friction factor λ and generalized Reynolds number Re′_BK is proposed for fluids obeying the “power-law” shear stress—shear rate relation.The generalized Ergun equation, derived in this paper, gives the dependence of the friction factor on the generalized Reynolds number and flow behaviour index n. The validity of the generalized Ergun equation was proved experimentally. In the case of Newtonian fluid (for n = 1·0) a more exact form of the classical Ergun equation is obtained.     

A general correlation for pressure drop in a Kenics static mixer

A new pressure drop correlation in a Kenics static mixer has been developed. Pressure drop data were generated from computational fluid dynamics (CFD) calculations, avoiding the experimental limitations in obtaining comprehensive data enough for developing a reliable pressure drop correlation. Dimensional analysis reveals that the pressure drop characteristic of the Kenics static mixer can be described by three dimensionless groups, i.e., the friction factor, Reynolds number (Re), and aspect ratio of a mixing element (AR). A systematic graphical analysis led to a single master curve governing the pressure drop behavior of the Kenics static mixer, which had never been achieved before. We derived a pressure drop correlation fitting well with the obtained master curve in a general form into which the AR effect on the pressure drop is directly incorporated. Unlike the already existing correlations available in the literature, the correlation proposed in this study can cover the whole range of Re from laminar to turbulence. The reliability of the proposed correlation was validated by the comparison with various pressure drop data reported in the literature.     

Improving mixing performance by curved-blade static mixer

This article addresses design modification to a flat-blade static mixer to enhance mixing performance. The static mixer elements used in this work consist of four blades with curvature made to intensify turbulent-like flow, while reducing the pressure drop. The blades were mounted on a cylindrical housing with 45° rotation relative to the axial direction. The mixer assembly was used in three different arrangements of 8, 10, and 14 elements for a range of Reynolds number between 600 and 7,000. The coefficient of variance (COV) of samples was used to measure the mixing quality. The curved-blade mixer provides considerable improvement in mixing quality compared with the flat-blade mixer and comparable to the SMX mixer. Compared with the flat-blade static mixer, the new design reduces the COV by up to about 50%. This effect is more pronounced when the number of mixing elements increases. Furthermore, the friction factors for the modified mixer, obtained at a wide range of Reynolds number, were apparently smaller than those for the flat-blade, SMX, and SMV mixers. The correlation presented for the friction factor, when all mixer arrangements and aspect ratios were considered, supports the experimental data with ±15% deviation.     

Power Requirement for Mixing Shear‐Thinning Fluids with a Planetary Mixer

The optimal control of processes dealing with non‐Newtonian liquids requires the knowledge and control of the power demand of the mixing equipment. In this context, an extension of the Metzner and Otto concept to planetary mixers is proposed to adapt this concept to planetary mixers. The theoretical part of this work defines modified expressions of Reynolds and power numbers. These definitions introduce a characteristic velocity u_ch that is used to define the parameter K_s. A planetary mixer is employed to experimentally ascertain this guideline. Power consumption measurements carried out by mixing shear‐thinning fluids permit to determine the K_s factor. This factor varies only slightly with the flow behavior index and may be regarded as a defined constant for this geometry. Finally, experiments with an additional shear‐thickening fluid confirm the validity of this approach.     

Velocity profiles and frictional pressure drop for shear thinning materials in lid-driven cavities with fully developed axial flow

A finite element numerical study has been carried out on the isothermal flow of power law fluids in lid-driven cavities with axial throughflow. The effects of the tangential flow Reynolds number (Re_U), axial flow Reynolds number (Re_W), cavity aspect ratio and shear thinning property of the fluids on tangential and axial velocity distributions and the frictional pressure drop are studied. Where comparison is possible, very good agreement is found between current numerical results and published asymptotic and numerical results. For shear thinning materials in long thin cavities in the tangential flow dominated flow regime, the numerical results show that the frictional pressure drop lies between two extreme conditions, namely the results for duct flow and analytical results from lubrication theory. For shear thinning materials in a lid-driven cavity, the interaction between the tangential flow and axial flow is very complex because the flow is dependent on the flow Reynolds numbers and the ratio of the average axial velocity and the lid velocity. For both Newtonian and shear thinning fluids, the axial velocity peak is shifted and the frictional pressure drop is increased with increasing tangential flow Reynolds number. The results are highly relevant to industrial devices such as screw extruders and scraped surface heat exchangers.     

Laminar flow and chaotic advection mixing performance in a static mixer with perforated helical segments

The laminar flow and chaotic mixing characteristics of a high-viscosity fluid in static mixers with staggered perforated helical segments were numerically investigated in the range of Re=0.1-150. The numerical results of pressure drop of Kenics static mixer have a good agreement with the reported data from the literature. The effects of aspect ratio A _r and Reynolds number on the mixing performance of Modified Kenics Static Mixers (MKSM) were evaluated by Darcy friction coefficient, shear rate, stretching rate, and Lyapunov exponent, respectively. The product of f×Re for MKSM linearly increased with the increase of Re, but it was constant under Re<10. The values of shear rate in the first perforated hole of mixing elements gradually became much larger by 1.10%-11.78% than those in the second perforated hole with the increasing Re. With the increase of dimensionless axial mixing length, the stretching rate increased linearly and the sensitivity for initial condition gradually weakened. A larger A _r is beneficial for micro-mixing in creeping flow. The average Lyapunov exponent linearly increases with the increase of Re. The profiles of Lyapunov exponent at different dimensionless perforated diameter (d/W) and perforated spacing (s/W) indicate that the chaotic mixing in MKSM is much more sensitive to d/W than s/W. A dimensionless parameter η taking into account the mixing degree and pressure drop was employed to evaluate the mixing efficiency. The optimization of perforated helical segments with the highest mixing efficiency at Re=100 was d/W=0.55 and s/W=1.2.     

Effects of geometry and flow rate on secondary flow and the mixing process in static mixers—a numerical study

A method based on computational fluid dynamics (CFD) for the characterization of static mixers using the Z factor, helicity and the rate of striation thinning is presented. These measures were found to be well-suited for the characterization of static mixers as they reflect the pressure drop, the formation of secondary flow, i.e. vortices, and their effect on the mixing process. Two commercial static mixers, the Kenics KM and Lightnin Series 45, have been characterized. In the mixers investigated, secondary flow is formed in the flow at the element intersections and due to the curvature of the mixer elements. The intensity of the vortices is higher in the Lightnin than the Kenics mixer due to edges in the middle of the Lightnin mixer elements. The formation of vortices affects the Z factor by an increase in the power requirement, and the rate of striation thinning by an increase in the stretching of the striations. The formation of vortices was observed at a Reynolds number of 10 in both mixers with aspect ratios of 1.5. However, the intensity of the vortices was greater in the Lightnin than the Kenics mixer, which was observed in not only the magnitude of the helicity, but also the Z factor, rate of striation thinning and the distribution of striation thickness.The distribution in striation thickness is shifted towards thin striations as the flow rate is increased from below to above the Reynolds numbers of which vortices were first observed, but some striations still pass the mixer elements almost unaffected, which can be seen in the skewness of the distribution of the striation thickness, which shifts from being negative to positive.     

FRICTION FACTOR IN STATIC MIXER AND DETERMINATION OF GEOMETRIC PARAMETERS OF SMX SULZER MIXERS

Pressure drops were determined in fluid flow through SMX Suizer static mixer of different sizes. In order to investigate a large range of Reynolds number, the experiments were performed with fluids of different viscosities. Pressure drops measurements in static mixer considered as a porous medium, are analysed with a capillary model for the determination of the geometric parameters of static mixers: pore diameter and tortuosity. These parameters allow the expression of pressure drops in terms of friction factor,f_c as a function of pore Reynolds number, Re_pA universal equation is obtained for the friction factor:f_c=16/Re_p+,0.194 which covers both viscous and inertial flow regimes.     

数值模拟静态混合器结构对PS/CO_2熔体温度的影响

利用专用CFD软件Polyflow对SMX型和Kenics型静态混合器中PS/CO_2发泡溶液进行数值模拟计算,分析比较不同板厚在不同元件个数条件下两种静态混合器消耗的压力损失,以及不同CO_2浓度对静态混合器压力损失的影响;并引入"离散系数"分析比较两种静态混合器出口温度均匀性的变化.数值模拟的结果表明:SMX型静态混合器冷却效果优于Kenics型静态混合器,并且SMX型静态混合器出口温度均匀性高于Kenics型静态混合器.     

Power Requirement when Mixing a Shear‐Thickening Fluid with a Helical Ribbon Impeller Type

The optimal design of close clearance impellers requires the knowledge of the power demand of the mixing equipment. In non‐Newtonian mixing, this can be readily obtained using the Metzner and Otto concept [1]. In this work, this concept and the determination of the K_s value for an atypical helical agitator (PARAVISC system from Ekato firm) have been revised in the case of shear‐thinning fluids and a shear‐thickening fluid. For poor shear‐thinning fluids, it has been shown that for our mixing system the K_s value does not vary strongly with the flow behavior index, and may be regarded as a constant for the mixing purpose design. By contrast, for the shear‐thickening fluid, power consumption measurements indicate that the relationship between the K_s values and the flow behavior index is much more complex due to a partial solidification of the product around the impeller.     

Design and characterization of a Low-pressure-drop static mixer

Four-blade static mixer was designed for inline mixing of Newtonian fluids at Reynolds numbers from 700 to 6800. The mixer consists of four equally spaced blades mounted on cylindrical housing with 45° rotation relative to the circumference. It was tested in three different compartments of 6, 8, and 10 mixing elements; each element rotated 45° relative to the adjacent one. Multipoint sampling was used to measure concentration downstream the mixer. The mixing quality was measured by the coefficient of variance (CoV). The CoV decreases as the energy input per unit mass increases. This effect is more pronounced when the number of mixing elements increases. For the case of 10 mixing elements, a good mixing performance (typically more than 95% mixedness or CoV < 0.05) achieved, although a marginally good mixing performance could also be achieved by eight mixing elements. The friction factors were correlated as f = C₁/Re + C₂/Reⁿ with an average deviation of ±10% from experimental data. Furthermore, experimental friction factors were compared with existing models. For a wide range of Reynolds numbers, the friction factors are apparently smaller than those from SMV, KMX, and baffle-type static mixers. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1126–1133, 2019     

On the performance of static mixers: A quantitative comparison

The performance of industrially relevant static mixers that work via chaotic advection in the Stokes regime for highly viscous fluids, flowing at low Reynolds numbers, like the Kenics, the Ross Low-Pressure Drop (LPD) and Low-Low-Pressure Drop (LLPD), the standard Sulzer SMX, and the recently developed new design series of the SMX, denoted as SMX(n) (n, N_p, N_x) = (n, 2n − 1, 3n), is compared using as criteria both energy consumption, measured in terms of the dimensionless pressure drop, and compactness, measured as the dimensionless length. Results are generally according to expectations: open mixers are most energy efficient, giving the lowest pressure drop, but this goes at the cost of length, while the most compact mixers require large pressure gradients to drive the flow. In compactness, the new series SMX(n), like the SMX(n = 3) (3, 5, 9) design, outperform all other devices with at least a factor 2. An interesting result is that in terms of energy efficiency the simple SMX (1, 1, 4, θ = 135°) outperforms the Kenics RL 180°, which was the standard in low pressure drop mixing, and gives results identical to the optimized Kenics RL 140°. This makes the versatile “X”-designs, based on crossing bars, superior in all respects.     

Investigations of heat transfer and pressure drop between parallel channels with pseudoplastic and dilatant fluids

Central to the problem of heat exchangers design is the prediction of pressure drop and heat transfer in the noncircular exchanger duct passages such as parallel channels. Numerical solutions for laminar fully developed flow are presented for the pressure drop (friction factor times Reynolds number) and heat transfer (Nusselt numbers) with thermal boundary conditions [constant heat flux (CHF) and constant wall temperature (CWT) ] for a pseudoplastic and dilatant non‐Newtonian fluid flowing between infinite parallel channels. A shear rate parameter could be used for the prediction of the shear rate range for a specified set of operating conditions that has Newtonian behavior at low shear rates, power law behavior at high shear rates, and a transition region in between. Numerical results of the Nusselt number [constant heat flux (CHF) and constant wall temperature (CWT) ] and the product of the friction factor and Reynolds number for the Newtonian region were compared with the literature values showing agreement within 0.36% in the Newtonian region. For pseudoplastic and dilatant non‐Newtonian fluids, the modified power law model is recommended to use because the fluid properties have big discrepancies between the power law model and the actual values in low and medium range of shear rates. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3601–3608, 2003     

Pressure drop and mixing behaviour of non‐Newtonian fluids in a static mixing unit

Static or motionless mixers have received wide application in chemical and allied industries due to their low cost and high efficiency. The pressure drop and mixing behaviour of such mixers have been widely studied. However, the available information for non‐Newtonian fluids is scanty. The results of pressure drop and mixing studies conducted with a locally made motionless mixer (MALAVIYA mixer) and four non‐Newtonian fluids—aq. CMC, PVA, and PEG solutions are reported in this article. The new mixer causes less pressure drop compared to some of the commercial mixers. Mixing behaviour of the unit is more closer to plug flow and a two‐parameter model correlates the dispersion data.     

CFD studies of dynamic gauging

Dynamic gauging is a non-contact technique for measuring the thickness of soft deposit layers on solid surfaces immersed in liquid environments, in situ and in real time. The technique works by inducing a flow into a nozzle located close to, and normal to, the deposit surface; the relationship between pressure drop and mass flow rate yields a measure of the distance between the nozzle and the deposit, whence the thickness of the deposit can be deduced.Computational fluid dynamics (CFD) studies were performed to illuminate the fluid dynamics of this technique, with particular focus on the flow patterns and on the stresses imposed on the surface. The governing Navier-Stokes equations were solved using the augmented Lagrangian method implemented by the commercial partial differential equation solver, Fastflo^TM. The code was first tested successfully against previous studies in the literature featuring confined, slow Homann flows, where fluid flowed out of a nozzle. Then, simulations of gauging flows, where fluid enters a nozzle from a confined entry region, were compared with experimental data; good agreement was observed. Laminar Newtonian flows have been investigated, with Reynolds number at the nozzle throat in the range 0<Re_t<2200. The shear and normal stresses on the gauged surface were predicted using the output from the CFD simulations. An initial comparison of experimental results for power-law fluids (aqueous carboxy-methyl-cellulose solutions) demonstrated the versatility of the technique and implied its applicability to more complex fluids, which would be useful for industrial application. The success of this study will enable (i) use of the gauge to measure the strength of deposits, (ii) optimization of the shape of the nozzle for different tasks and (iii) extension of the technique to power-law fluids.     

Generalized correlation for friction loss in drag reducing polymer solutions

The definition of the pipe flow friction factor has been extended to include the effect of fluid viscoelastic properties on energy dissipation in turbulent tube flow. The resulting friction factor includes a characteristic fluid relaxation time, which can be determined directly from rheological measurements, and reduces to the usual Fanning friction factor for inelastic fluids. The use of this more general friction factor enables turbulent tube flow data for both fresh and shear degraded “concentrated” drag reducing polymer solutions of various concentrations in various tube sizes to be correlated by the usual f vs. N_Re relation for Newtonian fluids in smooth tubes.     

Numerical investigation of the performance of several static mixers

The performance of six static mixer (Kenics, Inliner, LPD, Cleveland, SMX and ISG) are compared using 3D numerical simulations in laminar creeping flow regime. Numerical pressure drop results are tested against experimental ones, showing overall a good agreement. Besides pressure drop, four criteria (extensional efficiency, stretching, mean shear rate and intensity of segregation) are chosen to compare the static mixers. It appears that Kenics, Inliner, LPD and Cleveland mixers are rather similar. The ISG mixer seems better than this first group of mixers, but pressure drop is too high compared to other advantages. From our numerical results, SMX appears to be the most efficient of the six compared static mixers.     

Drop Breakup in an SMX Static Mixer in Laminar Flow

The mechanism of drop breakup inside SMX static mixers in the laminar flow regime was studied using experimental observations and computational fluid dynamics (CFD). The deformation and breakup of a single drop was simulated using the volume of fluid (VOF) model. It was observed that drops break up after collision with the leading edges and cross‐points of the bars in the SMX static mixer. It was found that drop collision with the bar cross‐points of the SMX static mixer elements is most effective for drop breakup. Elongation and folding result in drop breakup at the cross‐points.