Unified torque scaling in counter-rotating suspension Taylor–Couette flow

Author:

Alam Meheboob1ORCID,Ghosh Manojit1ORCID

Affiliation:

1. Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bangalore 560064, Karnataka, India

Abstract

Torque measurements are reported for the Taylor–Couette flow of a neutrally buoyant non-colloidal suspension in the counter-rotation regime up to a particle volume fraction of ϕ = 0.2 . A unified scaling relation for the dimensionless torque (the pseudo-Nusselt number) of the form Nu ω 0 = ( α 0 + α 1 Ta 1 α 2 ) Ta ( 0 ) k μ r ( ϕ ) n is shown to hold over a range of Taylor numbers Ta c 1 Ta 10 6 that covers primary, secondary and tertiary bifurcating states; here, Ta 1 = Ta ( ϕ ) / Ta c 1 ( ϕ ) is the reduced Taylor number, Ta c 1 is the critical Taylor number at primary bifurcation and μ r ( ϕ ) = μ ( ϕ ) / μ ( 0 ) is the relative viscosity of the suspension. Possible effects of flow transitions and inhomogeneous distribution of particles on torque scaling are discussed. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 1)’.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

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1. Taylor–Couette and related flows on the centennial of Taylor’s seminalPhilosophical Transactionspaper: part 2;Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences;2023-03-13

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