A device (11) is provided for the concentration of a mixture of fatty material and aqueous fluid. The device (11) comprises a chamber (31) for receiving a mixture of fatty material and aqueous fluid, and a body of absorbent material (25), the chamber (31) being separated from the absorbent material (25) by a barrier member (23) having at least one opening (24), and a shutter element (21) movable from a closed position, in which said opening (24) is occluded, to an open position, in which said opening (24) permits fluid flow from the chamber (31) to the absorbent material (25). It has been found that the use of an absorbent material enables fatty material to be concentrated to the required degree in a passive, single vessel process without damage to the fatty tissue. There are also described methods for the use of the device.