Parametric Study on Marangoni Instability in Two-Layer Creeping Flow

Linear stability of Newtonian fluids flowing in two layers through an infinitely long 2-D channel is carried out. Top and bottom plates of the channel are provided with constant concentrations of soluble surfactant. The current study extends the work of (Picardo et al. in J Fluid Mech 793:280–315, 2016) to investigate the effect of Peclet number and diffusivity ratio on the stability of the system. Varying the Peclet number shows non-monotonic growth in instability for two most unstable modes (M1 and M2). Neutral curves confirm that the system becomes unstable only for some range of Peclet number. The region of instability on the Peclet number space spreads with increasing Marangoni number. Upon increasing the diffusivity ratio, \(D_{r}\) , the system shows a destabilizing effect upto a certain value, beyond which the system stabilizes with an increase in \(D_{r}\) .