It is true that here we a mixed state, which complicates a bit. In the mixed state, the magnetic flux penetrates the sample in the form of a vortex that carries unit flux quanta. These vortices repel each other and minimize their free energy by forming a triangular lattice (that is called a vortex lattice ). Since the vortex density is uniform, the repulsive interactions between each vortex and all of its neighbors are canceled. From Maxwell's equation it follows that when the vortexes form a regular triangular lattice, no macroscopic currents flow within the superconductor.
Let us now consider what happens when the current in a mixed state is passed through a superconductor. A non-zero current (J) requires a non-zero CurlB, and this requires a gradient in vortex density. The repulsive interaction with vortices on both sides no longer cancels out because the density gradient implies unequal distances between them. Each vortex thus experiences a net force that is proportional to both the density of the vortices and its gradient;
This force on each vortex, which corresponds to a Lorentz force, causes the vortices to move. The vortex motion creates an electric field parallel to J, creating a resistance known as flow-flow resistance. thus the material is no longer superconductive.