[Show abstract][Hide abstract] ABSTRACT: 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, Np, Nx) = (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.
[Show abstract][Hide abstract] ABSTRACT: Some lab-on-a-chip applications require to establish a controlled spatial concentration gradient of (chemical) species, for example for iso-electrical focusing or to study chemotactic properties of cells. We show that covering a microchannel floor with special grooves or ridges, well-controlled concentration gradients can be created, depending on the geometrical design of the grooves or ridges. In our case, the pattern consists of ridges that are slanted with respect to the main channel direction. Similar patterns have been applied in the past to achieve mixing by introducing chaotic advection. We present experimental and numerical results that prove the mixing effectiveness of the ridges. In addition, making use of the local mixing capabilities of the ridge patterns, we show, using numerical simulations, how to achieve a concentration gradient across a microfluidic channel.
[Show abstract][Hide abstract] ABSTRACT: Motivated by the three-dimensional serpentine channel (Liu etal. in J Microelectromech Syst 9:190–197, 2000), we introduce
a chaotic serpentine mixer (CSM) and demonstrate a systematic way of utilizing a mapping method to find out an optimal set
of design variables for the CSM. One periodic unit of the mixer has been designed to create two streamlines portraits crossing
each other. As a preliminary study, flow characteristics and mixing in the original serpentine channel has been reinvestigated.
The working principle of the CSM is demonstrated via a particle-tracking method. From the design principle and the flow characteristics
of the CSM, we choose three key design variables with an influence on mixing. Then, simulations for all possible combinations
of the variables are carried out. At proper combinations of the variables, almost global chaotic mixing is observed in the
Stokes flow regime. The design windows obtained can be used to determine an optimal set of the variables to fit with a specific
Microfluidics and Nanofluidics 12/2009; 7(6):783-794. DOI:10.1007/s10404-009-0437-2 · 2.53 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this study, we explore the spectral properties of the distribution matrices of the mapping method and its relation to the distributive mixing of passive scalars. The spectral (or eigenvector-eigenvalue) decomposition of these matrices constitutes discrete approximations to the eigenmodes of the continuous advection operator in periodic flows. The eigenvalue spectrum always lies within the unit circle and due to mass conservation, always accommodates an eigenvalue equal to one with trivial (uniform) eigenvector. The asymptotic state of a fully chaotic mixing flow is dominated by the eigenmode corresponding with the eigenvalue closest to the unit circle (``dominant eigenmode''). This eigenvalue determines the decay rate; its eigenvector determines the asymptotic mixing pattern. The closer this eigenvalue value is to the origin, the faster is the homogenization by the chaotic mixing. Hence, its magnitude can be used as a quantitative mixing measure for comparison of different mixing protocols. In nonchaotic cases, the presence of islands results in eigenvalues on the unit circle and associated eigenvectors demarcating the location of these islands. Eigenvalues on the unit circle thus are qualitative indicators of inefficient mixing; the properties of its eigenvectors enable isolation of the nonmixing zones. Thus important fundamental aspects of mixing processes can be inferred from the eigenmode analysis of the mapping matrix. This is elaborated in the present paper and demonstrated by way of two different prototypical mixing flows: the time-periodic sine flow and the spatially periodic partitioned-pipe mixer.
Physics of Fluids 09/2009; 21(9). DOI:10.1063/1.3231601 · 2.03 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In microfluidics the Reynolds number is small, preventing turbulence as a tool for mixing, while diffusion is that slow that time does not yield an alternative. Mixing in microfluidics therefore must rely on chaotic advection, as well-known from polymer technology practice where on macroscale the high viscosity makes the Reynolds numbers low and diffusion slow. The mapping method is used to analyze and optimize mixing also in microfluidic devices. We investigate passive mixers like the staggered herringbone micromixer (SHM), the barrier embedded micromixer (BEM) and a three-dimensional serpentine channel (3D-SC). Active mixing is obtained via incorporating particles that introduce a hyperbolic flow in e.g. two dimensional serpentine channels. Magnetic beads chains-up in a flow after switching on a magnetic field. Rotating the field creates a physical rotor moving the flow field. The Mason number represents the ratio of viscous forces to the magnetic field strength and its value determines the fate of the rotor: a single, an alternating single and double, or a multiple part chain-rotor results. The type of rotor determines the mixing quality with best results in the alternating case where crossing streamlines introduce chaotic advection. Finally, an active mixing device is proposed that mimics the cilia in nature. The transverse flow induced by their motion indeed enhances mixing at the microscale.
[Show abstract][Hide abstract] ABSTRACT: Using the Mapping Method different designs of SMX motionless mixers are analyzed and optimized. The three design parameters that constitute a specific SMX design are: The number of cross-bars over the width of channel, N(x) , the number of parallel cross-bars per element, N(p) , and the angle between opposite cross-bars θ. Optimizing N(x) , somewhat surprisingly reveals that in the standard design with N(p) = 3, N(x) = 6 is the optimum using both energy efficiency as well as compactness as criteria. Increasing N(x) results in under-stretching and decreasing N(x) leads to over-stretching of the interface. Increasing N(p) makes interfacial stretching more effective by co-operating vortices. Comparing realized to optimal stretching, we find the optimum series for all possible SMX(n) designs to obey the universal design rule N(p) = (2/3) N(x) -1, for N(x) = 3, 6, 9, 12, ….
[Show abstract][Hide abstract] ABSTRACT: We conducted a numerical study on mixing in a barrier embedded micromixer with an emphasis on the effect of periodic and aperiodic
sequences of mixing protocols on mixing performance. A mapping method was employed to investigate mixing in various sequences,
enabling us to qualitatively observe the progress of mixing and also to quantify both the rate and the final state of mixing.
First, we introduce the design concept of the four mixing protocols and the route to achieve chaotic mixing of the mixer.
Then, several periodic sequences consisting of the four mixing protocols are used to investigate the mixing performance depending
on the sequence. Chaotic mixing was observed, but with different mixing rates and different final mixing states significantly
influenced by the specific sequence of mixing protocols and inertia. As for the effect of inertia, the higher the Reynolds
number the larger the rotational motion of the fluid leading to faster mixing. We found that a sequence showing the best mixing
performance at a certain Reynolds number is not always superior to other sequences in a different Reynolds number regime.
A properly chosen aperiodic sequence results in faster and more uniform mixing than periodic sequences.
Microfluidics and Nanofluidics 05/2008; 4(6):589-599. DOI:10.1007/s10404-007-0206-z · 2.53 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The mapping method is employed as an efficient toolbox to analyze, design, and optimize micromixers. A new and simplified
formulation of this technique is introduced here and applied to three micromixers: the staggered herringbone micromixer (SHM),
the barrier-embedded micromixer (BEM), and the three-dimensional serpentine channel (3D-SC). The mapping method computes a
distribution matrix that maps the color concentration distribution from inlet to outlet of a micromixer to characterize mixing
in a quantitative way. Once the necessary distribution matrices are obtained, computations are fast and numerous layouts of
the mixer are easily evaluated, resulting in an optimal design. This approach is demonstrated using the SHM and the BEM as
typical examples. Mixing analysis in the 3D-SC illustrates that also complex flows, for example in the presence of back-flows,
can be efficiently dealt with by using the new formulation of the mapping method.
Microfluidics and Nanofluidics 09/2007; 5(3):313-325. DOI:10.1007/s10404-007-0251-7 · 2.53 Impact Factor