Abstract: Apparatus for diffusing matter between two fluids is disclosed, including a stacked configuration of alternating spacing plates and pairs of semi-permeable membranes, the spacing plates including flow passages for each of the two fluids so that they can be passed between the pairs of semi-permeable membranes and between the spacing plates and the pairs of membranes, respectively, a first and second clamping plate, and means for clamping the first and second clamping plates together with the stacked configuration pressed between them. Specifically, in the improvement for this apparatus which is disclosed, the first clamping plate includes a pair of laterally extending side walls which form that clamping plate into cup-shaped configuration, and the apparatus also includes means for engaging the side walls of the first clamping plate to the second clamping plate at a plurality of locations around the periphery of the entire apparatus in order to contain the unit under increased pressure uniformly.