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Thermocapillary dynamics of a surfactant-laden droplet with internal thermal singularity

Published online by Cambridge University Press:  18 October 2023

Arindam Basak Open the ORCID record for Arindam Basak [Opens in a new window] ,
Rajaram Lakkaraju Open the ORCID record for Rajaram Lakkaraju [Opens in a new window]  and
G.P. Raja Sekhar Open the ORCID record for G.P. Raja Sekhar [Opens in a new window]
Arindam Basak
Affiliation:
Department of Mathematics, Indian Institute of Technology Kharagpur, West Bengal 721302, India
Rajaram Lakkaraju
Affiliation:
TuRbulent Interfaces and Dispersion Group, Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India
G.P. Raja Sekhar*
Affiliation:
Department of Mathematics, Indian Institute of Technology Kharagpur, West Bengal 721302, India
*
†Email address for correspondence: rajas@iitkgp.ac.in
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Abstract

Thermocapillary droplets with internal thermal singularities have potential applications in drug delivery and cell analysis. Inspired by the work of Pak et al. (J. Fluid Mech., vol. 753, 2014, pp. 535–552), which was investigated for a surfactant-laden non-deformable droplet in an isothermal Poiseuille flow, we have explored the droplet dynamics by taking account of additional internal thermal singularities, namely monopole and dipole. A generalized mathematical model is developed, which is solved by using the solenoidal decomposition to describe the flow field in any arbitrary Stokes flow, and results are shown extensively for the case of a non-isothermal Poiseuille flow. Under small Péclet number ($Pe_s$) limit, the droplet with an off-centred monopole or a dipole oriented along the flow direction shows cross-stream migration at $O(Pe_s^2)$. However, a dipole oriented perpendicular to the flow direction results in an $O(1)$ effect due to thermocapillarity, and from $O(Pe_s)$ onwards, we observe the combined impact of thermocapillary and surfactant-induced Marangoni stresses. As a surprise, we see cross-stream migration of the droplet from the Poiseuille flow centreline in a non-isothermal field, in contrast to existing findings which rule out any cross-stream migration. We show the trade-off between thermal Marangoni number ($Ma_T$) and surfactant Marangoni number ($Ma_\varGamma$). Our findings on droplet dynamics inspire new possibilities for microfluidics-based design.

JFM classification

Drops and Bubbles: Thermocapillarity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 973 , 25 October 2023 , A24
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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