Mechanisms of mixing and creation of structure in laminar stirred tanks

Álvarez, Mario Moisés; Zalc, Jeffrey M.; Shinbrot, Troy; Arratia, Paulo E.; Muzzio, Fernando J.

doi:10.1002/aic.690481005

Cited by 114 publications

(82 citation statements)

References 23 publications

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“…Figure 6 shows a sample of experimental and numerical trajectories, passing through the same position at the inlet of the mixer. The deviation between the trajectories is quantified by 2 (t) = (∆x(t)) 2 + (∆y(t)) 2 + (∆z(t)) 2 , where ∆ indicates the difference between experimental and numerical positions. Further analysis shows that the deviation increases in time and the maximum deviation is found to be 0.89 mm.…”

Section: Performance Analysis Of the Modified 3d Ptv Proceduresmentioning

confidence: 45%

Scalar transport in inline mixers with spatially periodic flows

et al. 2017

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Spatially persisting patterns form during the downstream evolution of passive scalars in three-dimensional (3D) spatially periodic flows due to the coupled effect of stretching and folding mechanisms of the flow field. This has been investigated in many computational and theoretical studies of 2D time-periodic and 3D spatially periodic flow fields. However, experimental studies, to date, have mainly focused on flow visualization with streaks of dye rather than fully 3D scalar field measurements. Our study employs 3D particle tracking velocimetry and 3D laser-induced fluorescence to analyze the evolution of 3D flow and scalar fields and the correlation between the coherent flow/scalar field structures in a representative inline mixer, the Quatro static mixer. For this purpose an experimental setup that consists of an optically accessible test section with transparent internal elements accommodating a pressure-driven pipe flow has been built. The flow and scalar fields clearly underline the complementarity of the experimental results with numerical simulations and provide validation of the periodicity assumption needed in numerical studies. The experimental procedure employed in this investigation, which allows studying the scalar transport in the advective limit, demonstrates the suitability of the present method for exploratory mixing studies of a variety of mixing devices, beyond the Quatro static mixer.

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Section: Performance Analysis Of the Modified 3d Ptv Proceduresmentioning

confidence: 45%

Scalar transport in inline mixers with spatially periodic flows

et al. 2017

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“…Alvarez et al 20 determined that the flow within a torus can be chaotic depending on the symmetry of the flow and the rotational protocol of the impeller(s). Similarly, Fountain et al, 19,21 using both computational and experimental techniques, developed a theory for predicting regions of regularity (which are centered about elliptical points) and chaos (which contain hyperbolic points, and enhance mixing due to the stretching and folding of fluid elements) in a 3D flow.…”

Section: Apparatus and Proceduresmentioning

confidence: 47%

Particle migration in the rotating flow between co‐axial disks

2006

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We experimentally examine a dilute suspension of non-neutrally buoyant spherical particles migrating in a simple mixing tank at small but finite Reynolds numbers. We observe that the particles spontaneously migrate to repeatable non-trivial asymptotic locations within toroidal structures, located above and below at-disk impellers. The asymptotic migration positions include both the exact center of the torus and intermediate higher-order cluster locations within the flow whose stability is dependent on flow andparticle conditions. Furthermore, we note that the particle clusters seem to coincide with the location of unmixed islands within the underlying fluid flow. We also observe a migratory competition when multiple particles are introduced into the flow.

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“…2 Laminar mixing also has a wide application in many industrial processes, including polymer processing 3 and food and pharmaceutical industries. 4,5 In compounding of various substances, it is necessary to obtain fluid mixtures with specified homogeneity properties, such as necessary for solutions, emulsions, and suspensions. The general mechanisms that make laminar mixing effective, independently of the process being either natural or artificial, are the repetitive stretching and folding of material elements leading to a reduction of the characteristic length scales, 6 and to an increase of the intermaterial contact area.…”

Section: Introductionmentioning

confidence: 45%

Spectral analysis of mixing in chaotic flows via the mapping matrix formalism: Inclusion of molecular diffusion and quantitative eigenvalue estimate in the purely convective limit

2012

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This paper extends the mapping matrix formalism to include the effects of molecular diffusion in the analysis of mixing processes in chaotic flows. The approach followed is Lagrangian, by considering the stochastic formulation of advection-diffusion processes via the Langevin equation for passive fluid particle motion. In addition, the inclusion of diffusional effects in the mapping matrix formalism permits to frame the spectral properties of mapping matrices in the purely convective limit in a quantitative way. Specifically, the effects of coarse graining can be quantified by means of an effective Péclet number that scales as the second power of the linear lattice size. This simple result is sufficient to predict the scaling exponents characterizing the behavior of the eigenvalue spectrum of the advection-diffusion operator in chaotic flows as a function of the Péclet number, exclusively from purely kinematic data, by varying the grid resolution. Simple but representative model systems and realistic physically realizable flows are considered under a wealth of different kinematic conditions-from the presence of large quasi-periodic islands intertwined by chaotic regions, to almost globally chaotic conditions, to flows possessing "sticky islands"-providing a fairly comprehensive characterization of the different numerical phenomenologies that may occur in the quantitative analysis of mapping matricesultimately of chaotic mixing processes. © 2012 American Institute of Physics

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Mechanisms of mixing and creation of structure in laminar stirred tanks

Cited by 114 publications

References 23 publications

Scalar transport in inline mixers with spatially periodic flows

Scalar transport in inline mixers with spatially periodic flows

Particle migration in the rotating flow between co‐axial disks

Spectral analysis of mixing in chaotic flows via the mapping matrix formalism: Inclusion of molecular diffusion and quantitative eigenvalue estimate in the purely convective limit

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