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Electric field mediated von Kármán vortices in stratified microflows: transition from linear instabilities to coherent mixing

Published online by Cambridge University Press:  18 February 2019

Satarupa Dutta Open the ORCID record for Satarupa Dutta [Opens in a new window] ,
Abir Ghosh ,
Partho Sarathi Gooh Pattader  and
Dipankar Bandyopadhyay Open the ORCID record for Dipankar Bandyopadhyay [Opens in a new window]
Satarupa Dutta
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Guwahati, Assam 781039, India
Abir Ghosh
Affiliation:
Centre for Nanotechnology, Indian Institute of Technology Guwahati, Assam 781039, India
Partho Sarathi Gooh Pattader
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Guwahati, Assam 781039, India Centre for Nanotechnology, Indian Institute of Technology Guwahati, Assam 781039, India
Dipankar Bandyopadhyay*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Guwahati, Assam 781039, India Centre for Nanotechnology, Indian Institute of Technology Guwahati, Assam 781039, India
*
†Email address for correspondence: dipban@iitg.ac.in
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Abstract

Application of an electric field across the pressure-driven stratified flow of a pair of miscible fluids inside a microchannel manifests interesting electrohydrodynamic (EHD) instabilities. Experiments uncover distinctive instability regimes with an increase in electric field Rayleigh number ($Ra^{\unicode[STIX]{x1D713}}$) – a linear-onset regime, a time-periodic nonlinear regime analogous to the von Kármán vortex street in the downstream and a regime with coherent flow patterns. The experiments also reveal that such linear and nonlinear instabilities can be stimulated non-invasively in a microchannel to mix or de-mix fluids simply by turning the electric field on or off, indicating the suitability of the process for on-demand micromixing. The characteristics of these instabilities have been theoretically investigated with the help of an Orr–Sommerfeld framework, which discloses the possibility of five distinctive finite-wavenumber modes for the instability. The EHD stresses originating due to the application of electric field stimulate a pair of shorter-wavelength electric field modes beyond a critical value of $Ra^{\unicode[STIX]{x1D713}}$. Increase in the levels of charge injection and EHD stresses lower the critical $Ra^{\unicode[STIX]{x1D713}}$ of these modes. The relatively longer-wavelength viscous mode is found to appear when the viscosity stratification between the fluid layers is high. Beyond a threshold Schmidt number ($Sc$), a diffusive mode is also found to appear near the mixed interfacial region. A thinner interface between the fluids at a higher $Sc$ helps this mode to behave as the interfacial mode of immiscible fluids. Contrast of ionic mobility in the fluids leads to the appearance of the K-mode of instability at much shorter wavelengths. The reported phenomena can be of significance in the domains of microscale mixing, pumping, heat exchange, mass transfer and reaction engineering.

JFM classification

Instability: Absolute/convective instability Mixing: Chaotic advection Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 169 - 211
Copyright
© 2019 Cambridge University Press 

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Dutta et al. supplementary material 1

Experimental video depicting linear regime I of instability developed in a benzenesilicone oil stratified flow through a 420 μm diameter channel, upon application of 0 – 300 V DC voltage through 420 μm diameter copper wire electrodes. The arrow indicates the direction of flow.

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Video 3.5 MB

Dutta et al. supplementary material 2

Experimental video depicting non-linear regime II of instability developed in a benzene-silicone oil stratified flow through a 420 μm diameter channel, upon application of 300 – 600 V DC voltage through 420 μm diameter copper wire electrodes. The arrow indicates the direction of flow.

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Video 7.6 MB

Dutta et al. supplementary material 3

Experimental video depicting non-linear regime III of instability developed in a benzene-silicone oil stratified flow through a 420 μm diameter channel, upon application of 600 – 900 V DC voltage through 420 μm diameter copper wire electrodes. The arrow indicates the direction of flow.

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Video 5.6 MB

Dutta et al. supplementary material 4

Experimental video depicting non-linear chaotic regime IV of instability developed in a benzene-silicone oil stratified flow through a 420 μm diameter channel, upon application of 900 – 1000 V DC voltage through 420 μm diameter copper wire electrodes. The arrow indicates the direction of flow.

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Video 16.8 MB

Dutta et al. supplementary material 5

Experimental video depicting response of benzene-silicone oil stratified flow through a 420 μm diameter channel, upon application of 0 – 500 V DC voltage through multiple copper wire electrodes of 420 μm diameter. The arrow indicates the direction of flow.

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Video 11.5 MB

Dutta et al. supplementary material 6

CFD simulation video (corresponding to figure 19) depicting response of benzenesilicone oil stratified flow through a 420 μm diameter channel, upon application of 300 V DC voltage through copper wire electrodes of 420 μm diameter. The arrow indicates the direction of flow.

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Video 690.8 KB

Dutta et al. supplementary material 7

CFD simulation depicting response of benzene-oleic acid stratified flow through a 420 μm diameter channel, upon application of 300 V DC voltage through copper wire electrodes of 420 μm diameter. The arrow indicates the direction of flow. The parameters used for the simulation are Sc = 500, KL=-4, EL=-0.15, and Re = 0.5.

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Video 743.4 KB

Dutton et al. supplementary movie 8

CFD simulation depicting response of benzene-silicone oil stratified flow through a 420 μm diameter channel, upon application of 500 V DC voltage through copper wire electrodes of 420 μm diameter. The arrow indicates the direction of flow. The parameters used for the simulation are Sc = 500, KL=-0, EL=-0.15, and Re = 0.5.

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Video 552.4 KB