  Fluid mechanics can be formulated on dynamical surfaces of arbitrary
co-dimension embedded in a background space-time. This has been the main object
of study of the blackfold approach in which the emphasis has primarily been on
stationary fluid configurations. Motivated by this approach we show under
certain conditions that a given stationary fluid configuration living on a
dynamical surface of vanishing thickness and satisfying locally the first law
of thermodynamics will behave like an elastic brane when the surface is subject
to small deformations. These results, which are independent of the number of
space-time dimensions and of the fluid arising from a gravitational dual,
reveal the (electro)elastic character of (charged) black branes when
considering extrinsic perturbations.
