**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.