Global Linear Instability of Flow Through a Converging–Diverging Channel

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
Mamta R. Jotkar ◽  
Gayathri Swaminathan ◽  
Kirti Chandra Sahu ◽  
Rama Govindarajan
Keyword(s):  
Reynolds Numbers ◽  
Linear Instability ◽  
Stability Study ◽  
Base Flow ◽  
Low Reynolds Numbers ◽  
Critical Reynolds Numbers ◽  
Diverging Channel ◽  
Order Of Magnitude ◽  
Flow Through ◽  
Low Reynolds

The global linear stability, where we assume no homogeneity in either of the spatial directions, of a two-dimensional laminar base flow through a spatially periodic converging–diverging channel is studied at low Reynolds numbers. A large wall-waviness amplitude is used to achieve instability at critical Reynolds numbers below ten. This is in contrast to earlier studies, which were at lower wall-waviness amplitude and had critical Reynolds numbers an order of magnitude higher. Moreover, our leading mode is a symmetry-breaking standing mode, unlike the traveling modes which are standard at higher Reynolds numbers. Eigenvalues in the spectrum lie on distinct branches, showing varied structure spanning the geometry. Our global stability study suggests that such modes can be tailored to give enhanced mixing in microchannels at low Reynolds numbers.

An Electrokinetic Micro Mixer for Lab-on-Chip Applications: Modeling, Validation, and Optimization

2011 ◽  
Author(s):  
Hendryk Bockelmann ◽  
Vincent Heuveline ◽  
Peter Ehrhard ◽  
Dominik P. J. Barz
Keyword(s):  
Electrical Potential ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Secondary Flows ◽  
Electrical Field ◽  
Lab On Chip ◽  
Low Reynolds Numbers ◽  
Micro Particle Image Velocimetry ◽  
Low Reynolds ◽  
Micro Mixer

Mixing of liquids in micro mixers at low Reynolds numbers is a challenging task since the flow regime is laminar and it is difficult to engage instabilities of the flow. In many microfluidic systems, mixing can be improved by means of electrokinetic effects. A favorable micro mixer design consists of a Y-junction, where the different liquid streams merge, and a subsequent meandering microchannel. A pressure gradient pumps the liquids to be mixed through the microchannel. An oscillating electrical field is superimposed onto the pressure-driven base flow which generates an additional electrokinetic (electro osmotic) flow. These oscillating secondary flows in conjunction with the meandering geometry are responsible for stretching and folding of the contact area of the liquids to be mixed which enhances the mass transfer rates considerably. In this contribution, we present a mathematical model which allows for the numerical simulation of flow, electrical potential, and species concentration. The model is validated by experiments relying on Micro Particle Image Velocimetry (μPIV). Consequently, this model can be used to numerically optimize the electrical field in order to achieve fast and high mixing even at low Reynolds numbers.

scholarly journals Flow through pipe orifices at low Reynolds numbers

1930 ◽  
Vol 126 (801) ◽  
pp. 231-245 ◽  
Keyword(s):  
Turbulent Flow ◽  
Discharge Coefficient ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Orifice Diameter ◽  
Vortex System ◽  
Low Reynolds Numbers ◽  
Commercial Practice ◽  
Flow Through ◽  
Low Reynolds

Most of the experimental work in connection with the flow of fluids through diaphragm orifices in pipe lines has been directed to the establishment of the orifice as a flow meter, and has been carried out at the velocities of flow commonly encountered in commercial practice. As a result of such research the coefficients relating the volumetric discharge of incompressible fluids to the differential head across an orifice are well known over a large range of high Reynolds numbers. For a particular diameter ratio ( i. e., orifice diameter ÷ diameter of pipe line) the discharge coefficient is nearly constant under conditions of turbulent flow. Over the range from steady to turbulent flow, however, very appreciable variations occur in the value of the discharge coefficient, suggest­ing that the accompanying variations in the nature of the flow through and beyond the orifice will be no less marked. As regards the turbulent flow pattern, an investigation, in which the author collaborated, of the airflow downstream of a flat plate suggests that an orifice in a pipe will in general give rise to a vortex system, probably having some points of resemblance to the well-known Kármán street which is a feature of the two-dimensional flow past a bluff obstacle, but doubtless exhibiting interesting differences arising from the symmetrical and three-dimensional character of the flow through an orifice. At sufficiently low Reynolds numbers, on the other hand, perfect flow free from periodic vorticity will occur. The stages connecting these two extreme conditions present many points of interest not only as regards the nature of the vortex system downstream of the orifice and the conditions of flow covering its inception, but also as regards the accom­panying pressure-velocity relation during the transition.

scholarly journals Analysis of vortices in viscoelastic fluid flow through confined geometries at low Reynolds numbers

AIP Advances ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 085213
Author(s):  
Ali Zargartalebi ◽  
Mohammad Zargartalebi ◽  
Anne M. Benneker
Keyword(s):  
Fluid Flow ◽  
Viscoelastic Fluid ◽  
Reynolds Numbers ◽  
Confined Geometries ◽  
Low Reynolds Numbers ◽  
Flow Through ◽  
Low Reynolds

Investigation of drag properties for flow through and around square arrays of cylinders at low Reynolds numbers

2019 ◽  
Vol 199 ◽  
pp. 285-301 ◽  
Author(s):  
Tingting Tang ◽  
Peng Yu ◽  
Xiaowen Shan ◽  
Huisu Chen ◽  
Jian Su
Keyword(s):  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Flow Through ◽  
Low Reynolds

The base-flow and near-wake problem at very low Reynolds numbers Part 2. The Oseen approximation

1965 ◽  
Vol 23 (03) ◽  
pp. 439 ◽  
Author(s):  
H. Viviand ◽  
S. A. Berger
Keyword(s):  
Reynolds Numbers ◽  
Base Flow ◽  
Near Wake ◽  
Low Reynolds Numbers ◽  
Oseen Approximation ◽  
Low Reynolds

scholarly journals Vortex Structure and Fluid Mixing in Pulsatile Flow through Periodically Grooved Channels at Low Reynolds Numbers.

1997 ◽  
Vol 40 (3) ◽  
pp. 377-385 ◽  
Author(s):  
Tatsuo NISHIMURA ◽  
Alexandru Mihail MOREGA ◽  
Koji KUNITSUGU
Keyword(s):  
Pulsatile Flow ◽  
Vortex Structure ◽  
Reynolds Numbers ◽  
Fluid Mixing ◽  
Low Reynolds Numbers ◽  
Flow Through ◽  
Low Reynolds

Flow through collapsible tubes at low Reynolds numbers. Applicability of the waterfall model.

1980 ◽  
Vol 47 (1) ◽  
pp. 68-73 ◽  
Author(s):  
C K Lyon ◽  
J B Scott ◽  
C Y Wang
Keyword(s):  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Collapsible Tubes ◽  
Flow Through ◽  
Low Reynolds ◽  
Waterfall Model

The base-flow and near-wake problem at very low Reynolds numbers - Part 1. The Stokes approximation

1965 ◽  
Vol 23 (03) ◽  
pp. 417 ◽  
Author(s):  
H. Viviand ◽  
S.A. Berger
Keyword(s):  
Reynolds Numbers ◽  
Base Flow ◽  
Near Wake ◽  
Low Reynolds Numbers ◽  
Stokes Approximation ◽  
Low Reynolds

scholarly journals Comments on flow through collapsible tubes at low Reynolds numbers.

1981 ◽  
Vol 48 (2) ◽  
pp. 299-301 ◽  
Author(s):  
J M Downey
Keyword(s):  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Collapsible Tubes ◽  
Flow Through ◽  
Low Reynolds
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