  The dynamics of passive Brownian tracer particles in steady two-dimensional
potential flows between sources and sinks is investigated. The first-passage
probability, $p(t)$, exhibits power-law decay with a velocity-dependent
exponent in radial flow and an order-dependent exponent in multipolar flows.
For the latter, there also occur diffusive ``echo'' shoulders and exponential
decays associated with stagnation points in the flow. For spatially extended
dipole sinks, the spatial distribution of the collected tracer is independent
of the overall magnitude of the flow field.
