Measuring surface tension coefficient of liquid by “phase standing wave” method
Authors: Sha Jin-Qiao , Yu Yi-Qing , Yang Jun-Yi , Fan Jun-Liu ,   School of Physical Science and Technology, Suzhou University of Science and Technology, Suzhou 215009, China,   School of Physical Science and Technology, Soochow University, Suzhou 215006, China
Published: September 2022

<sec>The surface tension of liquid is an important parameter to characterize the properties of liquid. The non-contact method of measuring the surface tension coefficient of liquid has the advantages of being fast, non-destructive, simple and practical. A new non-contact method of measuring the surface tension coefficient of transparent liquid based on the theory of light propagation is developed, and a special phenomenon of “self-interference” is discovered. The “Phase Standing Wave” theory is proposed to explain the phenomenon.</sec><sec>The surface wave of the liquid is excited by a frequency-adjustable vibration source (oscillator), and it propagates dynamically in the form of oscillator and cosine wave. When the white light source or laser is incident on the liquid surface obliquely, the phase distribution (cosine-like wave) generated by the light wave carrying the surface wave is first incident on the white paper which is located at the bottom of liquid, and the oscillator will also form the oscillator shadow on the white paper. The phase distribution of the light wave on the white paper spreads around dynamically in the form of cosine wave centering on the oscillator shadow. After diffuse reflection from the white paper, part of the diffuse reflection light in the observation direction carries the dynamic phase generated by the surface wave the first time back to the liquid surface and meets the surface wave again. After the light wave passes through the surface, it carries the phase generated by the surface wave the second time, that is, the superposition of two surface waves occurs in the phase of the light wave. In the phase of the light wave, the phase wave of the oscillator will propagate in the direction of the oscillator shadow, and the phase wave of the oscillator shadow will propagate in the direction of the oscillator.</sec><sec>According to the conditions of forming standing waves, two surface waves propagating in the opposite directions can form standing waves, so the phase standing waves can exist only within a relatively small range between the oscillator and the oscillator shadow. Thus the dark and bright “self-interference” with stable stripes can be observed in the far field. When white light and laser are used as light sources respectively, the fringe spacing remains unchanged, indicating that the fringe spacing is independent of the wavelength of incident light, and the light wave is only the carrier of the mechanical wave phase. The light waves with different wavelengths and coherences have no influence on the experimental measurement results.</sec><sec>The fringe spacing is measured automatically by analyzing and processing the image captured by camera. According to the dispersion relationship of surface waves, the surface tension coefficient of water is obtained automatically and accurately. The experimental setup is simple and easy to operate, the experimental phenomenon is intuitive, the stripes are clear and stable, and the anti-interference capability is strong, and can be observed in all directions. It can be widely used to measure the surface tension coefficients of other transparent liquids.</sec>