An apparatus for slicing products, the apparatus comprising an annular-shaped cutting head (50,150) comprising: an axis defining an axial direction; knife assemblies located at a circumference of the cutting head (50,150), each knife assembly comprising a flat knife and means for securing the knife to the cutting head (50,150), each of the knives extending radially inward and in a first circumferential direction of the cutting head (50,150) to define a gate opening and produce product slices with parallel cuts and a uniform thickness; and arcuate interior surfaces each located in the first circumferential direction relative to a corresponding one of the knife assemblies such that each of the interior surfaces defines a trailing edge (84,184) that leads one of the knife assemblies and defines therewith the gate opening with the knife that trails the interior surface, and such that each of the interior surfaces defines a leading edge that trails a different one of the knife assemblies, each of the interior surfaces having a plurality of continuous flow paths (72,74,172,274,374,474,574,674,774) defined therein that extend across at least a majority of the interior surface from adjacent a leading edge thereof and continuing through the trailing edge (84,184) thereof and are fluidically connected to one of the gate openings between the interior surface and the knife that trails the interior surface; wherein each of the continuous flow paths (72,74,172,274,374,474,574,674,774) of each of the interior surfaces comprises first and second channels (74,274,674,774;72,172) recessed in, respectively, a shoe member (62,262,362,462,562,662,762) that defines the leading edge of the interior surface and a gate member (68,168) that defines the trailing edge (84,184) of the interior surface, each of the second channels (72,172) being individually aligned with a corresponding one of the first channels (74,274,674,774), characterised in that the first channels (74,274,674,774) have smaller cross-sectional areas and/or different cross-sectional shapes than the second channels (72,172) aligned with the first channels (74,274,674,774). an axis defining an axial direction; knife assemblies located at a circumference of the cutting head (50,150), each knife assembly comprising a flat knife and means for securing the knife to the cutting head (50,150), each of the knives extending radially inward and in a first circumferential direction of the cutting head (50,150) to define a gate opening and produce product slices with parallel cuts and a uniform thickness; and arcuate interior surfaces each located in the first circumferential direction relative to a corresponding one of the knife assemblies such that each of the interior surfaces defines a trailing edge (84,184) that leads one of the knife assemblies and defines therewith the gate opening with the knife that trails the interior surface, and such that each of the interior surfaces defines a leading edge that trails a different one of the knife assemblies, each of the interior surfaces having a plurality of continuous flow paths (72,74,172,274,374,474,574,674,774) defined therein that extend across at least a majority of the interior surface from adjacent a leading edge thereof and continuing through the trailing edge (84,184) thereof and are fluidically connected to one of the gate openings between the interior surface and the knife that trails the interior surface; wherein each of the continuous flow paths (72,74,172,274,374,474,574,674,774) of each of the interior surfaces comprises first and second channels (74,274,674,774;72,172) recessed in, respectively, a shoe member (62,262,362,462,562,662,762) that defines the leading edge of the interior surface and a gate member (68,168) that defines the trailing edge (84,184) of the interior surface, each of the second channels (72,172) being individually aligned with a corresponding one of the first channels (74,274,674,774), characterised in that the first channels (74,274,674,774) have smaller cross-sectional areas and/or different cross-sectional shapes than the second channels (72,172) aligned with the first channels (74,274,674,774).