We present here a "proof of concepts" experiment that has been realized to show that time-dependent phenomena can be successfully studied in the terahertz region in a non pump-probe configuration. We have built-up an original analytical setup that has allowed following the evaporation of a deuterated water droplet cast on a CVD diamond substrate simultaneously in the near-middle infrared region and in the terahertz range. We have used a synchrotron light source in the terahertz region and a conventional thermal source in the infrared range. The results demonstrate that it is possible to study time-dependent phenomena simultaneously in the middle and terahertz ranges monitoring the entire chemical-physical process that occurs in the time domain of minutes.