Mk Mrityunjay Singh

Understanding and Optimizing the SMX Static Mixer.

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, ….

Eigenmode analysis of scalar transport in distributive mixing

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...

Numerical Study on Mixing in a Chaotic Serpentine Mixer Using a Mapping Method

We introduce a chaotic serpentine mixer (CSM), which is motivated by the three-dimensional serpentine channel [Liu et al., 2000, J. Microelectromech. Syst. 9, pp. 190–197], and demonstrate a systematic way of utilizing the mapping method [Singh et al., 2008, Microfluid Nanofluid 5, pp. 313–325] to find out an optimal set of design variables for the new mixer. The new mixer shows globally chaotic mixing even in the Stokes flow regime, while maintaining the benefits of the original design. One geometrical period of the mixer consists of two functional units, inducing two flow portraits with crossing streamlines. Each half period of the mixer consists of an “L-shaped” bend and a bypass channel. The two flow portraits may be either co-rotational or counter-rotational. As a preliminary study, first of all, mixing in the original serpentine channel has been analyzed to demonstrate the flow characteristics and to find out a critical Reynolds number showing chaotic mixing above the limit. The working principle of the newly proposed mixer is explained by the manifold of the deforming interface between two fluids. To optimize the mixer, we choose three key design variables: the sense of rotation of the two flows, the aspect ratio of the rectangular channel, and the lateral location of the bypass channel. 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 creeping flow regime. The design windows, provided as a result of the parameter study, can be used to determine a proper set of the design variables to fit with a specific application. The deforming interface of the two fluids shows that, even in a poor mixer in Stokes flow regime, as the Reynolds number increases, more efficient mixing is resulted in due to the enhanced cross-sectional vertical motion and back flows near the bends.Copyright