  In this paper, we formulate, analyse and implement the discrete formulation
of the Brinkman problem with mixed boundary conditions, including slip boundary
condition, using the Nitsche's technique for virtual element methods. The
divergence conforming virtual element spaces for the velocity function and
piecewise polynomials for pressure are approached for the discrete scheme. We
derive a robust stability analysis of the Nitsche stabilized discrete scheme
for this model problem. We establish an optimal and vigorous a priori error
estimates of the discrete scheme with constants independent of the viscosity.
Moreover, a set of numerical tests demonstrates the robustness with respect to
the physical parameters and verifies the derived convergence results.
