An apparatus for separating a first fluid from a mixture of fluids in a container, the first fluid being substantially immiscible with respect to one or more other fluids in the mixture comprises an endless strip of material having an affinity for the first fluid, a pair of advancing members for advancing successive portions of the strip into and out of contact with the first fluid and a means for maintaining the successive portions of the strip in contact with the first fluid as the successive portions of the strip are sequentially advanced. The pair of advancing members have cooperating surfaces that positively engage the strip with sufficient force so that movement of the advancing members relative to one another sequentially advances successive portions of the strip. A guiding element directs the strip away from engagement with the cooperating surface of one of the advancing members at the location where the strip is released from positive engagement with the advancing members.