A separating device comprising support plates and cut diaphragm sections of a semi-permeable material, for a first and second fluid flowing on opposite sides of said diaphragm sections in separate flow paths, wherein said support plates are sealed from the outside of said device and additionally sealed to assure the separate flow of the first and second fluid by a sealing means, the support plates are provided with cutoff channel grooves, said cutoff channel grooves of adjacent facing support plates form conduits into which sealling material in a flowable state is injected, the sealing material is injected into said conduits through perforations in said support plates, said perforations communicate with said conduits and other perforations in other adjacent facing support plates, and the sealing material is allowed to solidify in said perforations and said conduits thus forming said sealing means.