
We consider the twodimensional quasisteady Stokes flow of an incompressible Newtonian fluid occupying a timedependent simplyconnected region bounded by a free surface, the motion being driven solely by a constant surface tension acting at the free boundary. Of particular concern here are such flows that start from an initial configuration with the fluid occupying an array of touching circular disks. We show that, when there are N such disks in a general position, the evolution of the fluid region is described by a conformal map involving 2N1 timedependent parameters whose variation is governed by N Invariants and N1 first order differential equations. When N=2, or when the problem enjoys some special features of symmetry, the moving boundary of the fluid domain during the motion can be determined by solving purely algebraic equations, the solution of a single differential equation being needed only to link a particular boundary shape to a particular time. The analysis is aided by exploiting a connection with HeleShaw free boundary flows when the zerosurfacetension model is employed. If the initial configuration for the Stokes flow problem can be produced by injection (or suction) at N points into an initially empty HeleShaw cell, as can the Ndisk configuration referred to above, then so can all later configurations; the points where the fluid must be injected move, but the amount to be injected at each of the N points remains invariant. The efficacy of our solution procedure is illustrated by a number of examples, and we exploit the method to show that the free boundary in such a Stokes flow driven by surface tension alone may pass through a cusped state.

