Chemistry Reference
In-Depth Information
present, the dilation of the ring major diameter is altered, as is the trajec-
tory subsequent to surface interaction. The solid boundary demonstrates
the behaviour of a no-slip interface (Fig. 5d), and the viscoelastic surface
condition, obtained by spreading a surfactant film on the water surface,
represents an intermediate-slip interface (Fig. 5c). A surfactant-covered
surface constitutes an intermediate-slip condition because of the Maran-
goni effect. This effect arises from gradients in surfactant concentration
that lead to gradients in surface tension, which then give rise to surface
stresses and surface flows. Owing to Marangoni stresses, a surfactant sur-
face can support a finite surface shear, whereas a free surface in the ab-
sence of any adsorbed film cannot. These Marangoni stresses develop as a
result of the vortex-induced surface velocities, which act to redistribute
surfactant and compress the film as the ring interacts with the surface.
Such compression results in spatial gradients of the surface tension that
seek to equilibrate and produce a surface flow field by themselves. These
opposing flows in the surface viscous boundary layer can have strong im-
plications for the bulk flow. Vorticity, opposite in sign to that of the pri-
mary vortex cell, can be generated in this near-surface layer. In all the
cases studied, save for the clean case, coherent secondary and tertiary vor-
tex rings were formed as a result of this newly generated vorticity. In Fig.
5c, a second vortex outside the primary cell can be seen forming very near
the interface, and in Fig. 5d, two additional vortex rings are observed de-
veloping as a result of the wall interaction. Thus, a surface with an ad-
sorbed surfactant can act intermediate between a free-slip boundary and a
no-slip boundary. The ability of a surfactant surface to hydrodynamically
resemble a solid boundary is widely evidenced in studies of airҟ/water gas
exchange. For mass transfer at a smooth solid boundary, the gas-transfer
velocity is found to follow a -2/3 exponential Schmidt-number dependence
(Deacon 1977). It has been observed (e.g., Jähne et al. 1984) that film-
covered free surfaces, which inhibit formation of small-scale waves, tend
to follow the same -2/3 dependence rather than a -1/2 dependence that is
expected for an ideal free surface.
In order to elucidate the affects of a surfactant on the near-surface flow
further, the temporal evolution of the radial component of the near-surface
velocity as the vortex ring approaches the surface is plotted in Figs. 6a, b.
Velocity measurements were carried out using the non-invasive full-field
flow measurement technique known as digital particle image velocimetry
(DPIV). In addition to a general attenuation of the tangential velocity, we
observe the quasi-no-slip condition occurring outside of the vortex core for
the microlayer situation. This is a direct consequence of surfactant-induced
Marangoni forces that develop at the interface. These vortex ring experi-
ments illustrate the degree to which surface films can modify near-surface
