We present the design procedure for switchable acoustic demultiplexers based on a fluid-fluid phononic crystal (PnC) platform. It consists of a T-shaped PnC waveguide coupled to two output waveguide ports through two dissimilar point-defect cavities. The PnC platform consists of a periodic array of infinitely long rods of water (inclusions) embedded in mercury background. The waveguides are made by the removal of a row or a column of inclusions from the PnC, while the fluid in one of the two dissimilar cavities is methyl nonafluorobutyl ether (MNE) and in the other is ethyl nonafluorobutyl ether (ENE). The difference in the sound velocity in MNE and ENE provides an adequate difference in the dissimilar cavities resonant modes, required for the demultiplexing functionality of the designed structure. The different dependences of the sound velocities in these two fluids on temperature have also enabled the switching of the multiplexed channel, simply by appropriately changing the cavities temperature.