Marangoni Instability Driven by Adsorption and Association of Oppositely Charged Surfactants at an Oil–Water Interface

When an aqueous buffer
solution of the cationic surfactant tetradecyltrimethylammonium
bromide near neutral pH is contacted with a solution of the fatty
acid surfactant palmitic acid in tetradecane, convective flows appear
spontaneously at the interface. This coincides with turbidity formation
in the aqueous phase, consistent with aggregation between the headgroups
of the two surfactants. Motivated by these experimental observations,
a mathematical model is developed for transport, adsorption, and fluid
flow in two immiscible contacting fluid phases, each containing a
distinct surfactant. Linear stability analysis reveals that gradients
generated by dynamic adsorption alone cannot drive instability, which
only becomes possible if there is a process by which adsorbed surfactant
is removed from the interface, as modeled by an interfacial reaction
representing formation and desorption of aggregates in the experiments.
A full numerical simulation shows that asymmetry in surfactant transport
properties can inhibit convection due to the accumulation of surfactants
on the interface.