We introduce a model of interacting singularities of Navier-Stokes, named pinçons. They follow a Hamiltonian dynamics, obtained by the condition that the velocity field around these singularities obeys locally Navier-Stokes equations. This model can be seen of a generalization of the vorton model of Novikov , that was derived for the Euler equations. When immersed in a regular field, the pinçons are further transported and sheared by the regular field, while applying a stress onto the regular field, that becomes dominant at a scale that is smaller than the Kolmogorov length. We apply this model to compute the motion of a dipole of pinçons. When the initial relative orientation of the dipole is inside the interval [0, π/2], a dipole made of pinçon of same intensity exhibits a transient collapse stage, following a scaling with dipole radius tending to 0 like (tc − t) 0.63. For long time, the dynamics of the dipole is however repulsive, with both components running away from each other to infinity.