An analytical investigation of the flow in the saturated zone of ice counterwashers

The flow of brine through the ice bed in gravitational counterwashers is investigated by analytical methods. Two types of counterwashers are considered: a drained‐top counterwasher and a flooded one. Only counterwashers of rectangular cross section and two dimensional flows are investigated. By assuming that the ice crystals move vertically upwards with a uniform velocity and that the relative flow of brine and wash water with respect to the ice bed obeys Darcy's law, the differential equations and the boundary conditions of the flow are derived. The solutions are obtained by using complex variables and conformal mapping. The solutions are presented as formulae, which make possible the rational design of counterwashers and the optimization of their dimensions and operation parameters.