A tangential flow separator element for separating a fluid medium for treatment into a filtrate and a retentate, said separator element comprising a monolithic rigid porous support of rectilinear structure with a single channel having a wall that is continuously covered by a separation layer, said channel being formed therein for passing a flow of the fluid medium for treatment between an inlet and an outlet for the retentate, in order to recover a filtrate from the peripheral surface of the support, the outside surface of the support presenting a profile that is constant,
- wherein the monolithic rigid porous support defines obstacles to the flow of the fluid for filtering, which obstacles extend from the inside wall of said channel, are identical in material and porous texture to the support, and present continuity of material and of porous texture with the support,
- wherein said obstacles generate variations in the flow section of the channel, and
- wherein the variations in the flow section of the channel result from a variation in at least one of the following criteria along a longitudinal axis of the channel:
- an area of a right section of the channel, a shape of the right section of the channel, and a dimension of the right section of the channel.