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Mechanism of instability in non-uniform dusty channel flow

Published online by Cambridge University Press:  23 October 2024

Anup Kumar  and
Rama Govindarajan Open the ORCID record for Rama Govindarajan [Opens in a new window]
Anup Kumar
Affiliation:
International Centre for Theoretical Sciences, Bengaluru 560089, India
Rama Govindarajan*
Affiliation:
International Centre for Theoretical Sciences, Bengaluru 560089, India
*
†Email address for correspondence: [email protected]
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Abstract

Particles in pressure-driven channel flow are often inhomogeneously distributed. Two modes of low-Reynolds-number instability, absent in Poiseuille flow of clean fluid, are created by inhomogeneous particle loading, and their mechanism is worked out here. Two distinct classes of behaviour are seen: when the critical layer of the dominant perturbation overlaps with variations in particle concentration, the new instabilities arise, which we term overlap modes. But when the layers are distinct, only the traditional Tollmien–Schlichting mode of instability occurs. We derive the dominant critical-layer balance equations in this flow along the lines done classically for clean fluid. These reveal how concentration variations within the critical layer cause the two particle-driven instabilities. As a result of these variations, disturbance kinetic energy production is qualitatively and majorly altered. Surprisingly, the two overlap modes, although completely different in the symmetry of the eigenstructure and regime of exponential growth, show practically identical energy budgets, highlighting the relevance of variations within the critical layer. The wall layer is shown to be unimportant. We derive a minimal composite theory comprising all terms in the complete equation which are dominant somewhere in the flow, and show that it contains the essential physics. When particles are infinitely dense relative to the fluid, the volume fraction is negligible. But for finite density ratios, the volume fraction of particles causes a profile of effective viscosity. This is shown to be uniformly stabilizing in the present flow. Gravity is neglected here, and will be important to study in the future. So will the transient growth of perturbations due to non-normality of the stability operator, in a quest for the mechanism of transition to turbulence.

JFM classification

Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 997 , 25 October 2024 , A77
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Copyright
© The Author(s), 2024. Published by Cambridge University Press.

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