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For many biological systems that involve elastic structures immersed influid, small length scales mean that inertial effects are also small, and thefluid obeys the Stokes equations. One way to solve the model equationsrepresenting such systems is through the Stokeslet, the fundamental solution tothe Stokes equations, and its regularized counterpart, which treats thesingularity of the velocity at points where force is applied. In twodimensions, an additional complication arises from Stokes' paradox, whereby thevelocity from the Stokeslet is unbounded at infinity when the net hydrodynamicforce within the domain is nonzero, invalidating the solutions. Astraightforward computationally inexpensive method is presented for obtainingvalid solutions to the Stokes equations for net nonzero forcing. The approachis based on imposing a mean zero velocity condition on a large curve thatsurrounds the domain of interest. The condition is shown to be equivalent to anet-zero force condition, where the opposite forces are applied on the largecurve. The numerical method is applied to models of cellular motility andblebbing.

2D force constraints in the method of regularized Stokeslets