  Gopal and Trefethen recently introduced "lightning solvers" for the 2D
Laplace and Helmholtz equations, based on rational functions with poles
exponentially clustered near singular corners. Making use of the Goursat
representation in terms of analytic functions, we extend these methods to the
biharmonic equation, specifically to 2D Stokes flow. Solutions to model
problems are computed to 10-digit accuracy in less than a second of laptop
time. As an illustration of the high accuracy, we resolve two or more
counter-rotating Moffatt eddies near a singular corner.
