  A pressure driven flow in contact interface between elastic solids with wavy
surfaces is studied. We consider a strong coupling between the solid and the
fluid problems, which is relevant when the fluid pressure is comparable with
the contact pressure. An approximate analytical solution is obtained for this
coupled problem. A finite-element monolithically coupled framework is used to
solve the problem numerically. A good agreement is obtained between the two
solutions within the region of the validity of the analytical one. A power-law
interface transmissivity decay is observed near the percolation. Finally, we
showed that the external pressure needed to seal the channel is an affine
function of the inlet pressure and does not depend on the outlet pressure.
