A filtration apparatus for separating and/or enriching dissolved substances from a suspension or suspensions having at least one filter means through which flow takes place, there being arranged on the retentate side of the filter means a means for producing a shear field which produces a virtually homogeneous shear field and pressure gradient across the inflow cross-section of the filter means. The means for producing the shear field may be formed by a rotationally symmetrical rotor. There may be used as filter means matrices that are suitable for the adsorption of the dissolved substances to be separated off. There come into consideration for that purpose surface-modified membranes, for example affinity membranes. The filter apparatus may be one-tier, two-tier or multi-tier.