Measurement and computation of hydrodynamic coupling at an air/water interface with an insoluble monolayer

The coupling between a bulk vortical flow and a surfactant-influenced air/w ater interface has been examined in a canonical flow geometry through exper iments and computations. The flow in an annular region bounded by stationar y inner and outer cylinders is driven by the constant rotation of the floor and the free surface is initially covered by a uniformly distributed insol uble monolayer. When driven slowly, this geometry is referred to as the dee p-channel surface viscometer and the flow is essentially azimuthal. The onl y interfacial property that affects the flow in this regime is the surface shear viscosity, mu (s), which is uniform on the surface due to the vanishi ngly small concentration gradient. However, when operated at higher Reynold s number, secondary flow drives the surfactant film towards the inner cylin der until the Marangoni stress balances the shear stress on the bulk fluid. In general, the flow can be influenced by the surface tension, sigma, and the surface dilatational viscosity, kappa (s), as well as mu (s). However, because of the small capillary number of the present flow, the effects of s urface tension gradients dominate the surface viscosities in the radial str ess balance, and the effect of mu (s) can only come through the azimuthal s tress. Vitamin K, was chosen for this study since it forms a well-behaved i nsoluble monolayer on water and ps is essentially zero in the range of conc entration on the surface, c, encountered. Thus the effect of Marangoni elas ticity on the interfacial stress could be isolated. The flow near the inter face was measured in an optical channel using digital particle image veloci metry. Steady axisymmetric flow was observed at the nominal Reynolds number of 8500. A numerical model has been developed using the axisymmetric Navie r-Stokes equations to examine the details of the coupling between the bulk and the interface. The nonlinear equation of state, sigma (c), for the vita min K-1 monolayer was measured and utilized in the computations. Agreement was demonstrated between the measurements and computations, but the flow is critically dependent on the nonlinear equation of state.