Abstract: An improved sealing sleeve for the rotating drive shaft of a gear pump or other fluid conveying system has an internal axial bore for receiving the shaft, an intermediate cavity formed in the bore and oppositely-handed helical channels extending in the bore on opposite sides of the cavity. The inward helical channels are of a hand relative to the shaft rotation for effectively pumping viscous fluid entering the annular spacing between the shaft and sleeve toward the cavity while the oppositely-handed outward helical channels effectively resist and overcome such pumped fluid flow, creating a static containment of the viscous fluid to produce a viscous seal about the shaft. Cooling fluid is conveyed through an annular passageway about the outward helical channels to solidify any viscous fluid entering the adjacent region of the outward channels to produce an outward essentially mechanical seal about the shaft.