Linear instability driven by an electric field in two-layer channel flow of Newtonian and Herschel–Bulkley fluids

We investigate the linear stability characteristics of a pressure-driven two-layer channel flow of immiscible Newtonian and Herschel–Bulkley fluids subjected to an applied electric field normal to the flow. The linear stability equations are derived and solved using an accurate spectral Chebyshev co...

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Veröffentlicht in:Journal of non-Newtonian fluid mechanics 2020-11, Vol.285, p.104400, Article 104400
Hauptverfasser: Gautam, K., Narayana, P.A.L., Sahu, Kirti Chandra
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description We investigate the linear stability characteristics of a pressure-driven two-layer channel flow of immiscible Newtonian and Herschel–Bulkley fluids subjected to an applied electric field normal to the flow. The linear stability equations are derived and solved using an accurate spectral Chebyshev collocation method. It is found that the electric field can stabilise or destabilise the flow depending on the electrical properties of the fluids. We also observe that increasing the electric permittivity ratio and decreasing the electrical conductivity ratio, while keeping the rest of the parameters constant, enhances the growth rate of the disturbances. The “Reynolds stress” of the Newtonian layer and the work done by the velocity and stress disturbances tangential to the interface are found to be the mechanism of the instability observed due to the applied electric field. A parametric study is also conducted by varying the thickness of the bottom layer, Bingham number and flow index of the Herschel–Bulkley fluid. Increasing Bingham number is found to be stabilising or destabilising depending on the thickness of the non-Newtonian layer and the maximum disturbance growth occurs at an optimum value of non-Newtonian layer thicknesses. Increasing the shear-thinning and shear-thickening nature is shown to destabilise the flow. Our study is relevant in many microfluidic and electronic cooling applications. •Linear stability characteristics of two-layer channel flow under electric field is studied.•The bottom layer is non-Newtonian fluid characterised by the Herschel–Bulkley model.•It is found that the electric field stabilises or destabilises the flow depending on the electrical properties.•An energy budget analysis is conducted to understand the mechanism of the instability observed.•This study finds its applications in microfluidic and electronic cooling systems.
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The linear stability equations are derived and solved using an accurate spectral Chebyshev collocation method. It is found that the electric field can stabilise or destabilise the flow depending on the electrical properties of the fluids. We also observe that increasing the electric permittivity ratio and decreasing the electrical conductivity ratio, while keeping the rest of the parameters constant, enhances the growth rate of the disturbances. The “Reynolds stress” of the Newtonian layer and the work done by the velocity and stress disturbances tangential to the interface are found to be the mechanism of the instability observed due to the applied electric field. A parametric study is also conducted by varying the thickness of the bottom layer, Bingham number and flow index of the Herschel–Bulkley fluid. Increasing Bingham number is found to be stabilising or destabilising depending on the thickness of the non-Newtonian layer and the maximum disturbance growth occurs at an optimum value of non-Newtonian layer thicknesses. Increasing the shear-thinning and shear-thickening nature is shown to destabilise the flow. Our study is relevant in many microfluidic and electronic cooling applications. •Linear stability characteristics of two-layer channel flow under electric field is studied.•The bottom layer is non-Newtonian fluid characterised by the Herschel–Bulkley model.•It is found that the electric field stabilises or destabilises the flow depending on the electrical properties.•An energy budget analysis is conducted to understand the mechanism of the instability observed.•This study finds its applications in microfluidic and electronic cooling systems.</description><identifier>ISSN: 0377-0257</identifier><identifier>EISSN: 1873-2631</identifier><identifier>DOI: 10.1016/j.jnnfm.2020.104400</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Channel flow ; Chebyshev approximation ; Collocation methods ; Disturbances ; Electric field ; Electric fields ; Electrical properties ; Electrical resistivity ; Flow stability ; Fluid flow ; Herschel–Bulkley fluid ; Interface ; Interface stability ; Linear instability ; Microfluidics ; Reynolds stress ; Shear thickening (liquids) ; Shear thinning (liquids) ; Thickening ; Thickness</subject><ispartof>Journal of non-Newtonian fluid mechanics, 2020-11, Vol.285, p.104400, Article 104400</ispartof><rights>2020 Elsevier B.V.</rights><rights>Copyright Elsevier BV Nov 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c331t-2e86360b523073deb9a1742bb969e7188836ca7c51cd31eaf401284e964cd72a3</citedby><cites>FETCH-LOGICAL-c331t-2e86360b523073deb9a1742bb969e7188836ca7c51cd31eaf401284e964cd72a3</cites><orcidid>0000-0002-7286-5244 ; 0000-0002-1960-0247 ; 0000-0002-7357-1141</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0377025720301579$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Gautam, K.</creatorcontrib><creatorcontrib>Narayana, P.A.L.</creatorcontrib><creatorcontrib>Sahu, Kirti Chandra</creatorcontrib><title>Linear instability driven by an electric field in two-layer channel flow of Newtonian and Herschel–Bulkley fluids</title><title>Journal of non-Newtonian fluid mechanics</title><description>We investigate the linear stability characteristics of a pressure-driven two-layer channel flow of immiscible Newtonian and Herschel–Bulkley fluids subjected to an applied electric field normal to the flow. 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subjects Channel flow
Chebyshev approximation
Collocation methods
Disturbances
Electric field
Electric fields
Electrical properties
Electrical resistivity
Flow stability
Fluid flow
Herschel–Bulkley fluid
Interface
Interface stability
Linear instability
Microfluidics
Reynolds stress
Shear thickening (liquids)
Shear thinning (liquids)
Thickening
Thickness
title Linear instability driven by an electric field in two-layer channel flow of Newtonian and Herschel–Bulkley fluids
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