Jimbo mentioned the continued use of Archimedean screws in sewage works and other places where pumps must deal with a hign solids content.
A later pump well-adapted to pumping liquids with a significant solid content was the pulsometer pump. In the later C19 and very early C20, pulsometer pumps, invented 1872, were well regarded for low-lifts (30 to 40 feet) where pumps had to cope with 'thick and dirty water' and on this account were recommended for use as pilot pumps in sinking and in coal washeries. Their main stated disadvantage was their large use of steam. [W.E.Lishman 'Pumping', pp. 169-192 in vol.3 & pp.193-253 in vol. 4, in W.S.Boulton (ed) 'Practical Coal Mining', London: Gresham, n.d. (c1910), 6 vols, esp. vol.4 pp.228-9] In mining applications I imagine they rapidly were superseded by electric pumps in the opening decades of C20, saving transmitting steam down to shaft bottom.
Besides Archmedean screws and pulsometer pumps, what other designs of pumps were good at coping with high solid contents?