Liquid concentration sensing via weakly coupled point defects in a phononic crystal

Abstract

A pair of weakly coupled point defects in a liquid–solid phononic crystal are employed for liquid concentration sensing. An exemplary case of methanol in ethanol is investigated. As the physical and chemical properties of the two constituents are very similar, sensing is a rather difficult task by other analytical means. The defects are formed by thin-walled polyethylene tubing filled with either the reference liquid (ethanol) or the mixture in a square phononic crystal composed of cylindrical steel rods in water. Finite-element method simulations for the dual defect system, which has a small form factor comparable to the acoustic wavelength in water, revealed that two sharp transmission peaks corresponding to the even and odd modes arising from symmetry lifting due to weak defect interaction behave in different manners as the methanol concentration is varied. Specifically, the even mode frequency exhibits a linear dependence on the concentration, whereas the odd mode is associated with a quadratic shift. Besides, a simple coupled mass-spring model is employed to analyze the observed peak behavior as a function of methanol concentration in ethanol. Accordingly, when the acoustic properties of the two liquids in a binary mixture vary in a parallel manner with temperature, the ratio of the resonance frequencies depends only on the concentration, thus offering a sensing scheme immune to temperature fluctuations. Furthermore, it is shown for a number of water-miscible liquids that the even and odd mode frequencies are representative of the dominant contents of the reference and the sample cells.