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Fiber-optic sensors provide remote access, are readily embedded within structures, and can operate in harsh environments. Nevertheless, fiber-optic sensing of liquids has been largely restricted to measurements of refractive index and absorption spectroscopy. The temporal dynamics of fluid evaporation have potential applications in monitoring the quality of water, identification of fuel dilutions, mobile point-of-care diagnostics, climatography and more. In this work, the fiber-optic monitoring of fluids evaporation is proposed and demonstrated. Sub-nano-liter volumes of a liquid are applied to inline fiber-optic micro-cavities. As the liquid evaporates, light is refracted out of the cavity at the receding index boundary between the fluid and the ambient surroundings. A sharp transient attenuation in the transmission of light through the cavity, by as much as 50 dB and on a sub-second time scale, is observed. Numerical models for the transmission dynamics in terms of ray-tracing and wavefront propagation are provided. Experiments show that the temporal transmission profile can distinguish between different liquids.