A lateral-flow assay device includes a substrate having a sample addition zone and a wash addition zone downstream thereof along a fluid flow path through which a sample flows. The fluid flow path is configured to receive a wash fluid in the wash addition zone. A hydrophilic surface is arranged in the wash addition zone. Flow constriction(s) are spaced apart from the fluid flow path and arranged to define, with the hydrophilic surface, a reservoir configured to retain the wash fluid by formation of a meniscus between the hydrophilic surface and the flow constriction(s). The fluid flow path draws the wash fluid from the reservoir by capillary pressure. Apparatus for analyzing a fluidic sample and methods of displacing a fluidic sample in a fluid flow path of an assay device are also described.