We study convection driven by an unstable concentration difference across a horizontal permeable membrane due to a layer of brine lying over a layer of water across the membrane. The flow through the membrane changes the phenomena drastically from those in Rayleigh Benard convection; different regimes of convection across the membrane are observed [5]. By using a coarser membrane compared to that by [5], we find a new regime of convection where the Sherwood number scales linearly with the Rayleigh number. The planform plume-structure in this regime is presented. Phenomenology proposed is able to explain the flux scaling in the new regime.