Surfactant Effects in Interfacial Fluid Dynamics

Ashley James

Department of Aerospace Engineering and Mechanics

University of Minnesota

 

Surfactants are substances that preferentially accumulate at interfaces between two fluids, altering the local surface tension. Non-uniform distribution of surfactant on an interface induces a Marangoni force tangential to the interface, in addition to the usual normal surface tension force. This Marangoni force tends to make the surfactant distribution uniform, as does diffusion of surfactant along the interface. External imposition of a tangential flow of sufficient strength can counteract this tendency toward uniformity by dragging the surfactant toward a single location on the interface. In regions of high surfactant concentration the surface tension is low, so the interface offers less resistance to deformation and can become highly curved. This work is primarily focused on applications involving the formation of such regions and the subsequent pinch-off of very small droplets or bubbles.

A numerical method to simulate interfacial surfactant mechanics within a volume of fluid method has been developed. Two important features of this new method are that it conserves surfactant mass exactly and the form of the equation of state is not restricted, i.e. the relation between surfactant concentration and surface tension can be linear or nonlinear. To conserve surfactant, the surfactant mass and the interfacial surface area are tracked as the interface evolves, and then the surfactant concentration is reconstructed. The algorithm is coupled to an incompressible Navier-Stokes solver that uses a continuum method to incorporate both the normal and tangential components of the surface tension force into the momentum equation.

Numerical simulations demonstrate the effect of surfactant on the dynamics of several problems by comparison to surfactant-free simulations. First, the buoyant rise of a bubble is examined. Next, the evolution of a drop in an extensional flow is studied. Finally, the motion of a drop through a constriction is investigated. In each of these problems surfactant accumulation allows high interface curvature and the formation of small secondary drops or bubbles.