The role of soluble surfactants in the linear stability of two-layer flow in a channel

Kalogirou, A.; Blyth, M. G.

Abstract

The linear stability of Couette-Poiseuille flow of two superposed fluid layers in a horizontal channel is considered. The lower fluid layer is populated with surfactants that appear either in the form of monomers or micelles and can also get adsorbed at the interface between the fluids. A mathematical model is formulated which combines the Navier-Stokes equations in each fluid layer, convection-diffusion equations for the concentration of monomers (at the interface and in the bulk fluid) and micelles (in the bulk), together with appropriate coupling conditions at the interface. The primary aim of this study is to investigate when the system is unstable to arbitrary wavelength perturbations, and in particular, to determine the influence of surfactant solubility and/or sorption kinetics on the instability. A linear stability analysis is performed and the growth rates are obtained by solving an eigenvalue problem for Stokes flow, both numerically for disturbances of arbitrary wavelength and analytically using long-wave approximations. It is found that the system is stable when the surfactant is sufficiently soluble in the bulk and if the fluid viscosity ratio m and thickness ratio n satisfy the condition m < n 2. On the other hand, the effect of surfactant solubility is found to be destabilising if m n 2. Both of the aforementioned results are manifested for low bulk concentrations below the critical micelle concentration; however when the equilibrium bulk concentration is sufficiently high (and above the critical micelle concentration) so that micelles are formed in the bulk fluid, the system is stable if m < n 2 in all cases examined.

Citation

Kalogirou, A., & Blyth, M. G. (2019). The role of soluble surfactants in the linear stability of two-layer flow in a channel. Journal of Fluid Mechanics, 873, 18-48. https://doi.org/10.1017/jfm.2019.392

• Journal Article Type: Article
• Acceptance Date: May 2, 2019
• Online Publication Date: Jun 18, 2019
• Publication Date: Aug 25, 2019
• Deposit Date: May 29, 2019
• Publicly Available Date: Dec 19, 2019
• Journal: Journal of Fluid Mechanics
• Print ISSN: 0022-1120
• Electronic ISSN: 1469-7645
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 873
• Pages: 18-48
• DOI: https://doi.org/10.1017/jfm.2019.392
• Keywords: Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics
• Public URL: https://nottingham-repository.worktribe.com/output/2106165
• Additional Information: License: © 2019 Cambridge University Press
• Contract Date: May 29, 2019