Fluid Motion and Mixing

Brodkey, Robert S.

doi:10.1016/b978-0-12-395633-0.50007-7

Cited by 9 publications

(4 citation statements)

References 128 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The submillimeter size of the microchannel in this design is much larger than the average free path of the molecule, which indicates that the microfluidics still has the basic characteristics of macroscopic fluid motion [36,37]. The inertia force is very small and the viscous force plays a dominant role in the macroscopic movement of the fluid [38].…”

Section: Numerical Analysismentioning

confidence: 97%

Performance evaluation of a 3D split-and-recombination micromixer with asymmetric structures

Jiao¹,

Zhang²,

Zhang³

et al. 2022

J. Micromech. Microeng.

View full text Add to dashboard Cite

Micromixers are widely used in lab-on-a-chip devices for analytical chemistry, bioengineering, and biomedicine to achieve rapid mixing and analysis of samples. However, the existing micromixers are mostly two-dimensional structures with low mixing efficiency. Even three-dimensional micromixers with complex structures have low mixing efficiency in the low Reynolds number range. In this paper, a three-dimensional (3D) split-and-recombination (SAR) micromixer inspired by the horseshoe transform principle is proposed to further improve the mixing efficiency. There 3D SAR micromixers with different subchannel sizes were designed and tested in the Reynolds numbers range of 0.1 to 100 . The optimal size of the micromixer was revealed through computational fluid dynamics (CFD) simulations and experimental test results. A minimum mixing index of 91% is achieved in the range of Reynolds numbers from 0.1 to 100. Especially, for Re ≥ 20, the mixing index is higher than 99%. The results obtained indicate that this 3D SAR micromixer with an asymmetric structure shows a satisfactory choice in the fluid mixing process of microfluidic systems, and has a potential application in the field of microchip-based biochemical analysis.

show abstract

Section: Numerical Analysismentioning

confidence: 97%

Performance evaluation of a 3D split-and-recombination micromixer with asymmetric structures

Jiao¹,

Zhang²,

Zhang³

et al. 2022

J. Micromech. Microeng.

View full text Add to dashboard Cite

show abstract

“…The dominant mixing mechanism of viscous liquids such as polymeric melts is bulk diffusion (6), or simply convection. Turbulent or eddy diffusion is generally non-existent in such systems and molecular diffusion is of limited significance.…”

Section: Strain Distribution Functions For Batch and Continuous Systemsmentioning

confidence: 99%

Theoretical analysis of residence time distribution functions and strain distribution functions in plasticating screw extruders

Lidor

Tadmor

1976

Polymer Engineering & Sci

View full text Add to dashboard Cite

The residence time distribution (RTD) function in a single screw plasticating extruder was theoretically calculated. The calculation is based on the solids conveying, melting, and melt conveying models in extruders. The screw channel is divided into small axial increments and the path of each exiting fluid particle is followed from hopper to die. In addition to the residence times the total shear deformation or strain imposed on the fluid particles was also calculated. This together with the RTD function has led to the definition and calculation of the strain distribution function (SDF). This function is proposed for quantitative characterization of the mixing performance of screw extruders as well as other laminar mixers. Some simple idealized batch and continuous laminar mixers are analyzed in terms of the SDF. Finally, the effect of extruder operating conditions and screw design on the RTD and SDF were investigated by computer simulations.

show abstract

“…Others rely on the idea that sufficient repetitive branching will give the resulting systems a level of self-similarity (Eshel, 1998 ; Dannowski and Block, 2005 ), which is justified in principle. Repetition of the same steps in the generative process is important to the emergence of strict or statistical self-similarity in both mathematical (as illustrated in Figure 1 ) and natural (Brodkey, 1966 ) fractals and reiterative growth is commonly cited as a source of complexity in plant architecture (Barthélémy and Caraglio, 2007 ; Costes et al, 2013 ). If we can find self-similarity in some part of plant anatomy, this may suggest that its developmental process is dominated by reiteration over a great range of scales, an idea exploited by so-called fractal root system models (van Noordwijk et al, 1994 ; Ozier-Lafontaine et al, 1999 ).…”

Section: Introductionmentioning

confidence: 99%

Box-Counting Dimension Revisited: Presenting an Efficient Method of Minimizing Quantization Error and an Assessment of the Self-Similarity of Structural Root Systems

2016

View full text Add to dashboard Cite

Fractal dimension (FD), estimated by box-counting, is a metric used to characterize plant anatomical complexity or space-filling characteristic for a variety of purposes. The vast majority of published studies fail to evaluate the assumption of statistical self-similarity, which underpins the validity of the procedure. The box-counting procedure is also subject to error arising from arbitrary grid placement, known as quantization error (QE), which is strictly positive and varies as a function of scale, making it problematic for the procedure's slope estimation step. Previous studies either ignore QE or employ inefficient brute-force grid translations to reduce it. The goals of this study were to characterize the effect of QE due to translation and rotation on FD estimates, to provide an efficient method of reducing QE, and to evaluate the assumption of statistical self-similarity of coarse root datasets typical of those used in recent trait studies. Coarse root systems of 36 shrubs were digitized in 3D and subjected to box-counts. A pattern search algorithm was used to minimize QE by optimizing grid placement and its efficiency was compared to the brute force method. The degree of statistical self-similarity was evaluated using linear regression residuals and local slope estimates. QE, due to both grid position and orientation, was a significant source of error in FD estimates, but pattern search provided an efficient means of minimizing it. Pattern search had higher initial computational cost but converged on lower error values more efficiently than the commonly employed brute force method. Our representations of coarse root system digitizations did not exhibit details over a sufficient range of scales to be considered statistically self-similar and informatively approximated as fractals, suggesting a lack of sufficient ramification of the coarse root systems for reiteration to be thought of as a dominant force in their development. FD estimates did not characterize the scaling of our digitizations well: the scaling exponent was a function of scale. Our findings serve as a caution against applying FD under the assumption of statistical self-similarity without rigorously evaluating it first.

show abstract

Fluid Motion and Mixing

Cited by 9 publications

References 128 publications

Performance evaluation of a 3D split-and-recombination micromixer with asymmetric structures

Performance evaluation of a 3D split-and-recombination micromixer with asymmetric structures

Theoretical analysis of residence time distribution functions and strain distribution functions in plasticating screw extruders

Box-Counting Dimension Revisited: Presenting an Efficient Method of Minimizing Quantization Error and an Assessment of the Self-Similarity of Structural Root Systems

Contact Info

Product

Resources

About