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Study of heat and mass transport on the instability of a swirling viscoelastic liquid film

  • Regular Article - Soft Matter
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Abstract

In this article, we examine the response of transport of mass and heat at the viscous gas–viscoelastic liquid interface, while the instability of the interface is defined by capillary instability. The fluids are enclosed in an annular region bounded by two rigid cylinders. The Oldroyd B-type viscoelastic fluid is considered and the outer cylinder is swirling with a uniform angular velocity. The governing mathematical equations are work out through the viscoelastic-viscous potential flow theory. The well-known normal mode procedure is utilized and a critical value of wave-number is calculated to determine the stability/instability norm for the interface. Various plots showing the effect of swirling, heat/mass transfer, etc. have been made and illustrated physically. The addition of swirl prevents the development of disturbance waves. We achieve that the transport of mass/heat at the interface reduces the amplitudes of perturbations.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical study and no experimental data].

Abbreviations

\(\rho _{o}\) :

Density of Oldroyd B viscoelastic fluid

\(\mu _{o}\) :

Viscosity of Oldroyd B viscoelastic fluid

\(\lambda _{o}\) :

Viscoelasticity of Oldroyd B viscoelastic fluid

\(\varOmega \) :

Angular velocity of outer cylinder

\(T_{o}\) :

Temperature of outer phase

\(\sigma \) :

Surface tension

\(r_{2}\) :

Radius of outer cylinder

\(\rho _{i}\) :

Density of viscous fluid

\(\mu _{i}\) :

Viscosity of viscous fluid

k :

Wave number

\(\omega \) :

Growth rate of disturbances

\(T_{i}\) :

Temperature of inner phase

R :

Radius of the interface

\(r_{1}\) :

Radius of inner cylinder

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Acknowledgements

The author M.K. A. is thankful to UGC-BSR (New-Delhi, India) (project No.F.30-442/2018 (BSR)) for start-up-grant and research funding.

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Authors and Affiliations

  1. Department of Mathematics, Babasaheb BhimraoAmbedkar University, Lucknow, India

    Mukesh Kumar Awasthi

  2. Department of Applied Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt

    G. A. Hoshoudy

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Correspondence to Mukesh Kumar Awasthi.

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Awasthi, M.K., Hoshoudy, G.A. Study of heat and mass transport on the instability of a swirling viscoelastic liquid film. Eur. Phys. J. E 44, 36 (2021). https://doi.org/10.1140/epje/s10189-021-00048-3

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