  Two-dimensional Stokes flow with injection and suction is investigated
through a second-order, perturbative mode-coupling approach. We examine the
time-dependent disturbance of an initially circular interface separating two
viscous fluids, and derive a system of nonlinear differential equations
describing the evolution of the interfacial perturbation amplitudes. Linear
stability analysis reveals that an injection-induced expanding interface is
stable, while a contracting motion driven by suction is unstable. Curiously, at
the linear level this suction instability is independent of the viscosity
contrast between the fluids. However, second-order results tell a different
story, and show that the viscosity contrast plays a key role in determining the
shape of the emerging interfacial patterns. By focusing on the onset of
nonlinear effects, we have been able to extract valuable information about the
most fundamental features of the pattern-forming structures for arbitrary
values of viscosity contrast and surface tension.
