It is well known that brine drainage from growing sea ice has a controlling influence on its mechanical, electromagnetic, biological and transport properties, and hence upon the buoyancy forcing and ecology in the polar oceans. When the ice has exceeded a critical thickness the drainage process is dominated by brine channels: liquid conduits extending through the ice. We describe a theoretical model for the drainage process using mushy layer theory which demonstrates that the brine channel spacing is governed by a selection mechanism that maximizes the rate of removal of stored potential energy, and hence the brine flux from the system. The fluid transport through the sea ice and hence the scaling laws for brine fluxes and brine channel spacings are predicted. Importantly, the resulting brine flux scaling is consistent with experimental data for growth from a fixed temperature surface, allowing all parameters in the scaling law to be determined. This provides an experimentally tested first principles derivation of a parameterization for brine fluxes from growing sea ice.