Mrityunjay K. Singh

Technische Universiteit Eindhoven, Eindhoven, North Brabant, Netherlands

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Publications (11)23.85 Total impact

  • Han E.H. Meijer, Mrityunjay K. Singh, Patrick D. Anderson
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    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.
    Progress in Polymer Science. 10/2012; 37(10):1333–1349.
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    Macromolecular Materials and Engineering 02/2011; 296(3‐4):373 - 379. · 2.34 Impact Factor
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    ABSTRACT: Various designs of the so called Low-Pressure Drop (LPD) static mixer are analyzed for their mixing performance using the mapping method. The two types of LPD designs, the RR and RL type, show essentially different mixing patterns. The RL design provides globally chaotic mixing, whereas the RR design always yields unmixed regions separated by KAM boundaries from mixed regions. The crossing angle between the elliptical plates of the LPD is the key design parameter to decide the performance of various designs. Four different crossing angles from 90° to 160° are used for both the RR and RL designs. Mixing performance is computed as a function of the energy to mix, reflected in overall pressure drop for all designs. Optimization using the flux-weighted intensity of segregation versus pressure drop proves the existence of the best mixer with an optimized crossing angle. The optimized angle proves to be indeed the LLPD design used in practice: the RL-120 with θ = 120°, although RL-140 θ = 140° performs as good. Shear thinning shows minor effects on the mixing profiles, and the main optimization conclusions remain unaltered. © 2009 American Institute of Chemical Engineers AIChE J, 2009
    AIChE Journal 08/2009; 55(9):2208 - 2216. · 2.49 Impact Factor
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    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.
    Macromolecular Symposia 04/2009; 279(1):201 - 209.
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    Mrityunjay K Singh, Patrick D Anderson, Han E H Meijer
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    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, ….
    Macromolecular Rapid Communications 02/2009; 30(4-5):362-76. · 4.93 Impact Factor
  • Macromolecular Symposia - MACROMOL SYMPOSIA. 01/2009; 279(1).
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    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 01/2009; 21(9). · 1.94 Impact Factor
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    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 application.
    Microfluidics and Nanofluidics 01/2009; 7(6):783-794. · 3.22 Impact Factor
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    ABSTRACT: Using the mapping method an efficient methodology is developed for mixing analysis in the rotated arc mixer (RAM). The large parameter space of the RAM leads to numerous situations to be analyzed to achieve best mixing, and hence, it is indeed a challenging task to fully optimize the RAM. Two flow models are used to study mixing: one based on the full three-dimensional (3-D) flow field, and a second one based on a simplified 2.5-D model, where an analytical solution is used for transverse velocity components in combination with a Poiseuille profile for the axial velocity component. Detailed 3-D velocity field analyses reveal locally significant deviations from the Poiseuille profile e.g., presence of back-flow, but only minimal differences in mixing performance is found using both flow models (3- and 2.5-D) in the RAM designs that are candidates for accomplishing chaotic mixing. Despite the computational advantage of the 2.5-D approach over the 3-D approach, it is still cumbersome to analyze mixing for large number of designs using techniques based on particle tracking, e.g., Poincaré sections, dye traces, stretching distributions. Therefore, in this respect the mapping method provides an engineering tool able to tackle this optimization problem in an efficient way. On the basis of mixing evaluations, both in qualitative and quantitative sense, for the whole range of parameter space, the optimum set of design and kinematical parameters in the RAM is obtained to accomplish the best mixing. © 2008 American Institute of Chemical Engineers AIChE J, 2008
    AIChE Journal 10/2008; 54(11):2809 - 2822. · 2.49 Impact Factor
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    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. · 3.22 Impact Factor
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    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 5(3):313-325. · 3.22 Impact Factor