Biomimetic adhesive compositions can be used in various aspects of subterranean treatment operations. Methods for treating a subterranean formation can comprise: providing an adhesive composition that comprises a first polymer comprising a plurality of monomers that comprise a phenolic moiety, a biopolymer that is crosslinkable with the first polymer, a crosslinking agent, and an oxidizing agent; introducing the adhesive composition into a subterranean formation; and forming a coacervate-bound surface in the subterranean formation by crosslinking the first polymer.