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Coupled bulk and interfacial transport of surfactants governs the settling of a drop towards a wall

Published online by Cambridge University Press:  24 May 2024

Sayali N. Jadhav ,
Shubhadeep Mandal  and
Uddipta Ghosh Open the ORCID record for Uddipta Ghosh [Opens in a new window]
Sayali N. Jadhav
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Gandhinagar, Gujarat 382055, India
Shubhadeep Mandal
Affiliation:
Department of Mechanical Engineering, Indian Institute of Science, Bengaluru, Karnataka 560012, India
Uddipta Ghosh*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Gandhinagar, Gujarat 382055, India
*
†Email address for correspondence: uddipta.ghosh@iitgn.ac.in
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Abstract

Surfactant-like impurities are omnipresent in multiphase emulsions and may substantially affect the motion of small droplets by altering their interfacial properties. Usually these surfactants are soluble in the bulk and undergo adsorption–desorption onto the interface which modifies their surface concentration and hence their overall influence on droplet motion. Yet, the impact of the bulk solubility and transport of surfactants on droplet dynamics, especially in the presence of bounding walls, remains poorly understood. As such, in this article, we assess the impact of bulk soluble surfactants on the settling of a spherical drop towards a plane wall. We consider coupled bulk and interfacial transport of surfactants, mediated by adsorption–desorption processes and construct a semi-analytical framework for arbitrary values of ‘bulk interaction parameter’, which dictates the strength of adsorption–desorption kinetics compared with bulk diffusion. Our results indicate that while mass exchange between the bulk and the interface can remobilize the drop, a finite bulk diffusion rate restricts this process and therefore slows down the drop. This also results in bulk concentration depletion near the south pole and accumulation near the north pole, the extent of which becomes strongly asymmetric with an enhanced intensity of depletion, as the drop approaches the wall. Presence of the wall and bulk solubility are found to aid each other towards remobilizing the drop by aptly modifying the interfacial concentration. Our results may provide fundamental insights into the kinetics of surfactant-laden drops, with potential applications in food and pharmaceutical industries, separation processes, etc.

JFM classification

Drops and Bubbles: Drops and Bubbles Low-Reynolds-number flows: Low-Reynolds-number flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 987 , 25 May 2024 , A41
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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