An inverted up-flow separator for the separation and recovery of target minerals, selected from the group consisting of fine and ultra-fine minerals, from a feed including particulate matter which comprises target mineral particles and gangue particles, the inverted up-flow separator including: (a) at least one working fluid inlet ; an upper column ; a feed inlet , for a feed including particulate matter which comprises target mineral particles and gangue particles, into the upper column ; a lower column ; a recovered product outlet ; the upper column and lower column being in fluid flow communication with each other; a connecting member , connecting the upper column and lower column ; and wherein: (b) the feed inlet has a feed outlet , the position at which the feed outlet terminates, in the inverted up-flow separator , being adjustable to optimise the discharge of feed in the inverted up-flow separator , (c) the upper column has a greater diameter than a diameter of the lower column ; and (d) the upper column and lower column are configured and dimensioned such that upon introduction of an up-flow working fluid into the lower column , through the at least one working fluid inlet , the particulate matter in the inverted up-flow separator , when filled with fluid, is fluidised thereby imparting a first up-flow velocity (V 1 ) to the particulate matter in the lower column and a second up-flow velocity (V 2 ) to the particulate matter in the upper column , wherein the first up-flow velocity (V 1 ) is greater than the second up-flow velocity (V 2 ) and wherein the ratio of the first up-flow velocity (V 1 ) imparted to the particulate matter in the lower column to the second up-flow velocity (V 2 ) imparted to the particulate matter in the upper column is between 1:0.6 to 1:0.8. (a) at least one working fluid inlet ; an upper column ; a feed inlet , for a feed including particulate matter which comprises target mineral particles and gangue particles, into the upper column ; a lower column ; a recovered product outlet ; the upper column and lower column being in fluid flow communication with each other; a connecting member , connecting the upper column and lower column ; and wherein: (b) the feed inlet has a feed outlet , the position at which the feed outlet terminates, in the inverted up-flow separator , being adjustable to optimise the discharge of feed in the inverted up-flow separator , (c) the upper column has a greater diameter than a diameter of the lower column ; and (d) the upper column and lower column are configured and dimensioned such that upon introduction of an up-flow working fluid into the lower column , through the at least one working fluid inlet , the particulate matter in the inverted up-flow separator , when filled with fluid, is fluidised thereby imparting a first up-flow velocity (V 1 ) to the particulate matter in the lower column and a second up-flow velocity (V 2 ) to the particulate matter in the upper column , wherein the first up-flow velocity (V 1 ) is greater than the second up-flow velocity (V 2 ) and wherein the ratio of the first up-flow velocity (V 1 ) imparted to the particulate matter in the lower column to the second up-flow velocity (V 2 ) imparted to the particulate matter in the upper column is between 1:0.6 to 1:0.8. <EOS>