Consider a Brownian particle in a deterministic time-independent incompressible flow in a bounded domain. We are interested how flow affects the expected exit time, the time the particle needs to reach the boundary of the domain. In particular, whether the presence of the flow decreases the maximum of this expected exit time. One would expect that any stirring improves mixing, thus decreasing the expected exit time. We will show that generally it is not true in two dimensions. This is a joint work with G.Iyer, L.Ryzhik, and A.Zlatos.