Solutal Marangoni instability in layered two-phase flows

TL;DR

This paper investigates the linear stability of layered two-phase flows with soluble surfactants, revealing how Marangoni effects induce instabilities under certain conditions, with implications for microfluidic and thermocapillary applications.

Contribution

It provides a detailed analysis of solutal Marangoni instabilities in layered flows, identifying conditions for long and short wave modes and their interactions with viscosity-induced instabilities.

Findings

Marangoni stresses destabilize flow with concentration gradients.

Long wave instability depends on viscosity, thickness ratios, and mass transfer direction.

Short wave instability can occur even with non-deforming interfaces.

Abstract

In this paper, the instability of layered two-phase flows caused by the presence of a soluble surfactant (or a surface active solute) is studied. The fluids have different viscosities, but are density matched to focus on Marangoni effects. The fluids flow between two flat plates, which are maintained at different solute concentrations. This establishes a constant flux of solute from one fluid to the other in the base state. A linear stability analysis is performed, using a combination of asymptotic and numerical methods. In the creeping flow regime, Marangoni stresses destabilize the flow, provided a concentration gradient is maintained across the fluids. One long wave and two short wave Marangoni instability modes arise, in different regions of parameter space. A well-defined condition for the long wave instability is determined in terms of the viscosity and thickness ratios of the fluids, and the direction of mass transfer. Energy budget calculations show that the Marangoni stresses that drive long and short wave instabilities have distinct origins. The former is caused by interface deformation while the latter is associated with convection by the disturbance flow. Consequently, even when the interface is non-deforming (in the large interfacial tension limit), the flow can become unstable to short wave disturbances. On increasing $Re$, the viscosity-induced interfacial instability comes into play. This mode is shown to either suppress or enhance the Marangoni instability, depending on the viscosity and thickness ratios. This analysis is relevant to applications such as solvent extraction in microchannels, in which a surface-active solute is transferred between fluids in parallel stratified flow. It is also applicable to the thermocapillary problem of layered flow between heated plates.