A pump assembly for generating and dispensing of particles of a solid material with or without dispensing of a fluid. The pump assembly preferably includes a fluid pump which in a cycle of operation draws the fluid through a fluid inlet and dispenses the fluid out a fluid outlet. The pump assembly carries a block of the solid material coalesced together and a rasp member, which during the cycle of operation, moves relative the rasp in engagement with the block whereby the rasp member disengages particles of the solid material from the block which particles drop under gravity downwardly adjacent the fluid outlet, for example, onto a user's hand as in the case that the fluid is a hand cleaning fluid and the solid is a solid soap.