Evolving shapes of dissolving objects in potential flow

If we put a dissolving object in a flow, its shape will continuously
change. Tracking of the evolving shape requires the solution of
coupled flow  and transport equation, in an evolving geometry around
the shrinking object. Two problems of this kind will be discussed.
First, we will assume that the object immersed in the flow is of an
infinite extent and we will show that in the long-time limit  such an
object attains a parabolic (in 2d) or paraboloidal shape. Next, we
will consider  the dissolution of a disk in a two-dimensional
potential flow. In the limit of large Peclet number, this problem can
be solved by taking advantage of the conformal invariance of the
model. The analytical solutions obtained in this manner will be
compared with the experimental data.