We developed a microfluidic system for vibrational polariton studies, which consists of two microfluidic chips: one for solution mixing and another for tuning an infrared cavity made of a pair of gold mirrors and a PDMS (polydimethylsiloxane) spacer. We show that the cavity of the system can be accurately tuned with either piezoelectric actuators or microflow-induced pressure to result in resonant coupling between a cavity mode and a variational mode of the solution molecules. Acrylonitrile solutions were chosen to prove the concept of vabriational strong coupling (VSC) of a CN stretching mode with light inside the cavity. We also show that the Rabi splitting energy is linearly proportional to the square root of molecular concentration, thereby proving the relevance and reliability of the system for VSC studies.