Abstract:
Chaotic mixing in a curved-square channel flow is studied experimentally and numerically. Two walls of the channel (inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction toward the exit of the channel. This flow is a kind of Taylor-Dean flows. There are two parameters dominating the flow, the Dean number De (∝ the pressure gradient or the Reynolds number) and the Taylor number Tr (∝ the angular velocity of the wall rotation). In the present paper, we analyze the physical mechanism of chaotic mixing in the Taylor-Dean flow by comparing experimental and numerical results. We produced a micromixer model of the curved channel several centimeters long with square cross section of a few millimeters side. The secondary flow was measured using laser induced fluorescence (LIF) method to examine secondary flow characteristics. We also performed three-dimensional numerical simulations for the exactly same configuration as the experimental system to study the mechanism of chaotic mixing. It is found that good mixing performance is achieved for the case of De ≤ 0.1Tr, and that mixing efficiency changes according to the difference in inflow conditions. The flow is studied both experimentally and numerically, and both results agree with each other very well.

Abstract:
In this study a biophysical passive micromixer with channel anamorphosis in a space of 370 mm, which is shorter than traditional passive micromixers, could be created by mimicing features of vascular flow networks and executed with Reynolds numbers ranging from 1 to 90. Split and recombination (SAR) was the main mixing method for enhancing the convection effect and promoting the mixing performance in the biophysical channel. The 2D numerical results reveal that good mixing efficiency of the mixer was possible, with εmixing = 0.876 at Reynolds number ration Rer = 0.85. Generally speaking, increasing the Reynolds number will enhance the mixing. In addition, the sidewall effect will influence the mixing performance and an optimal mixing performance with εmixing = 0.803 will occur at an aspect ratio of AR = 2. These findings will be useful for enhancing mixing performance for passive micromixers.

Abstract:
We consider a Taylor-Dean-type flow of an electrically conducting liquid in an annulus between two infinitely long perfectly conducting cylinders subject to a generally helical magnetic field. The cylinders are electrically connected through a remote, perfectly conducting endcap, which allows a radial electric current to pass through the liquid. The radial current interacting with the axial component of magnetic field gives rise to the azimuthal electromagnetic force, which destabilizes the base flow by making its angular momentum decrease radially outwards. This instability, which we refer to as the pseudo--magnetorotational instability (MRI), looks like an MRI although its mechanism is basically centrifugal. In a helical magnetic field, the radial current interacting with the azimuthal component of the field gives rise to an axial electromagnetic force, which drives a longitudinal circulation. First, this circulation advects the Taylor vortices generated by the centrifugal instability, which results in a traveling wave as in the helical MRI (HMRI). However, the direction of travel of this wave is opposite to that of the true HMRI. Second, at sufficiently strong differential rotation, the longitudinal flow becomes hydrodynamically unstable itself. For electrically connected cylinders in a helical magnetic field, hydrodynamic instability is possible at any sufficiently strong differential rotation. In this case, there is no hydrodynamic stability limit defined in the terms of the critical ratio of rotation rates of inner and outer cylinders that would allow one to distinguish a hydrodynamic instability from the HMRI. These effects can critically interfere with experimental as well as numerical determination of MRI.

Abstract:
A novel parallel laminar micromixer with a two-dimensional staggered Dean Vortex micromixer is optimized and fabricated in our study. Dean vortices induced by centrifugal forces in curved rectangular channels cause fluids to produce secondary flows. The split-and-recombination (SAR) structures of the flow channels and the impinging effects result in the reduction of the diffusion distance of two fluids. Three different designs of a curved channel micromixer are introduced to evaluate the mixing performance of the designed micromixer. Mixing performances are demonstrated by means of a pH indicator using an optical microscope and fluorescent particles via a confocal microscope at different flow rates corresponding to Reynolds numbers ( Re) ranging from 0.5 to 50. The comparison between the experimental data and numerical results shows a very reasonable agreement. At a Re of 50, the mixing length at the sixth segment, corresponding to the downstream distance of 21.0 mm, can be achieved in a distance 4 times shorter than when the Re equals 1. An optimization of this micromixer is performed with two geometric parameters. These are the angle between the lines from the center to two intersections of two consecutive curved channels, θ, and the angle between two lines of the centers of three consecutive curved channels, φ. It can be found that the maximal mixing index is related to the maximal value of the sum of θ and φ, which is equal to 139.82°.

Abstract:
Investigations of counter-rotating Taylor-Couette flow (TCF) in the narrow gap limit are conducted in a very large aspect ratio apparatus. The phase diagram is presented and compared to that obtained by Andereck et al. The spiral turbulence regime is studied by varying both internal and external Reynolds numbers. Spiral turbulence is shown to emerge from the fully turbulent regime via a continuous transition appearing first as a modulated turbulent state, which eventually relaxes locally to the laminar flow. The connection with the intermittent regimes of the plane Couette flow (pCf) is discussed.

Abstract:
Taylor vortex flow is one of the important vortex flows that have been studied since its classic study made by G. I. Taylor in 1923. State of the flow between inner and outer cylinders of a rotating co-axial cylinder transits from Couette flow to Taylor vortex flow and to wavy Taylor vortex flow as the increase of Reynolds number. This study has identified the critical Reynolds number when the flow changes from Taylor vortex flow to wavy Taylor vortex flow. The numerical analysis making use of the attractor in the chaos theory has been used in this identification of the critical Reynolds number. The calculated critical Reynolds numbers of each flow mode are almost identical to the values obtained by the visualization experiment at small aspect ratios. In the region where the aspect ratio is larger than the ratio at the peak critical Reynolds number, the distribution of the Reynolds number is qualitatively similar between the calculated and experimental values.

Abstract:
The micromixer, which has a rotor with a curved channel, is studied experimentally. The secondary flow in a curved channel of rectangular cross-section is investigated using PIV (Particle Image Velocimetry) and LIF (Laser Induced Fluorescence) methods. Two walls of the channel (the inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction of the exit of the channel. The non-dimensional channel curvature δ=a/R is taken to be about 0.1, where 2a is the width of the channel, R the curvature radius of the channel. Other non-dimensional parameters concerned are the Dean number De=Reδ^{1/2}, the Reynolds number Re=qd_{h}/v, where q is the mean flow velocity in the channel axis direction, ν the kinematic viscosity, dh the hydraulic diameter of the channel, and the Taylor number Tr=2(2δ)^{1/2}Ωa^{2}/(δv), where Ω is the angular velocity of the rotor. Photographs of the flow in a cross-section at 180° downstream from the curved channel entrance are taken by changing the flux (De) at a constant rotational speed (Tr) of the channel walls. It is found that good mixing performance is obtained in the case of De≤0.1|Tr| and for that case secondary flows show chaotic behaviors. And then we have confirmed the occurrence of reversal of the mean axial flow.

Abstract:
We study magnetic effects induced by rigidly rotating plates enclosing a cylindrical MHD Taylor-Couette flow at the finite aspect ratio $H/D=10$. The fluid confined between the cylinders is assumed to be liquid metal characterized by small magnetic Prandtl number, the cylinders are perfectly conducting, an axial magnetic field is imposed $\Ha \approx 10$, the rotation rates correspond to $\Rey$ of order $10^2-10^3$. We show that the end-plates introduce, besides the well known Ekman circulation, similar magnetic effects which arise for infinite, rotating plates, horizontally unbounded by any walls. In particular there exists the Hartmann current which penetrates the fluid, turns into the radial direction and together with the applied magnetic field gives rise to a force. Consequently the flow can be compared with a Taylor-Dean flow driven by an azimuthal pressure gradient. We analyze stability of such flows and show that the currents induced by the plates can give rise to instability for the considered parameters. When designing an MHD Taylor-Couette experiment, a special care must be taken concerning the vertical magnetic boundaries so they do not significantly alter the rotational profile.

Abstract:
The popular show Supernatural, in particular the character of Dean Winchester, provides an interesting examination of freedom of choice. In fact Supernatural proves itself amenable to an existentialist reading of law, in particular the existentialism of Jean Paul Sartre. After a brief introduction to the show, the elements of Sartre’s existentialism I will be developing in this paper include freedom, choice and authenticity. These elements combine to demonstrate the existentialist law favoured by Dean, whereby Dean’s scepticism of God allows for an authenticity that furthers his own autonomy. The patterning trope of two brothers is essential to Dean developing his own law and morality separate from the divine one that is imposed on him throughout the show, with natural law showcasing that there is more than one kind of existentialist law to choose from.

Abstract:
A novel design for vortex modulation of a passive chaotic micromixer, named a circulation-disturbance micromixer (CDM), has been achieved and analyzed experimentally and numerically. The systematic numerical analyses - topological flow characteristics and particle tracking method - have been developed, that enable visualization of detailed mixing patterns. To display the cross section of mixing region of flows in our CDM, the biotin-streptavidin binding is detected through the fluorescence resonance energy transfer (FRET) pair of fluorescent proteins - R-phycoerythrin (RPE) and cross-linked allophycocyanin (clAPC). We expect the diagnosis technique using FRET will be successfully applied to biochemical analysis in microfluidic system.