In an isoolefin-diolefin rubber production process (e.g. a butyl rubber production process), the cold rubber slurry produced in the reaction vessel is transported from the reaction vessel to the flash tank during which time the cold slurry may be expressed to separate at least part of the cold liquid reaction medium from the isoolefin-diolefin rubber. The separated cold liquid reaction medium is transported off stream, for example by a mechanical filter, where it can be recycled back into the reaction vessel and/or where it can be used to cool a feed stream or streams of the reaction components. The isoolefin-diolefin rubber and the residual liquid reaction medium are transported to a flash tank for further processing. The ability to separate and recycle cold liquid reaction medium makes the process more economical. In one aspect, the slurry may be transported from the reaction vessel to the flash tank by a self-cleaning fully intermeshing co-rotating twin screw extruder, which helps overcome the problem of plugging due to rubber sticking to the surfaces of the slurry transfer apparatus.