A mathematical model describing the residence time for a liquid component in a gas-liquid-solid monolith reactor has been developed. When travelling in a slug flow pattern, the liquid exhibits alternating regions of upflow in well mixed liquid slugs and downflow along the walls of the monolith channel. The model was developed for flow in a single square capillary and indicates a mixing pattern that resembles well-mixed behaviour. Theoretical calculations are compared with experimental results. The model can be extended to the monolith froth reactor by a statistical analysis of flow within the channels of the monolith. Because the monolith reactor represents a distribution of flow patterns, it exhibits greater axial mixing and higher average residence times than would be expected based on the single channel analysis.