This paper reports the results of a numerical investigation of the
transient evolution of
the flow around a spherical bubble rising in a liquid contaminated by a
weakly soluble
surfactant. For that purpose the full Navier–Stokes equations are solved
together with
the bulk and interfacial surfactant concentration equations, using values of the
physical-chemical constants of a typical surfactant characterized by a simple surface
kinetics. The whole system is strongly coupled by nonlinear boundary conditions
linking the diffusion flux and the interfacial shear stress to the interfacial
surfactant
concentration and its gradient. The influence of surfactant characteristics is
studied by
varying arbitrarily some physical-chemical parameters. In all cases, starting
from the
flow around a clean bubble, the results describe the temporal evolution of the
relevant scalar and dynamic interfacial quantities as well as the changes in the
flow structure
and the increase of the drag coefficient. Since surface diffusion is extremely weak
compared to advection, part of the bubble (and in certain cases all the interface)
tends
to become stagnant. This results in a dramatic increase of the drag which in several
cases reaches the value corresponding to a rigid sphere. The present results
confirm the
validity of the well-known stagnant-cap model for describing the flow around a bubble
contaminated by slightly soluble surfactants. They also show that a simple relation
between the cap angle and the bulk concentration cannot generally be obtained
because diffusion from the bulk plays a significant role.