Viscosity and interfacial tension of fluid are key thermophysical properties, which influence the flow, as well as heat and mass transfer of fluid, and they are crucial parameters for studying and controlling multidisciplinary processes in the field of energy, chemistry, and life sciences. The surface light scattering (SLS) method can accurately access the viscosity and interfacial tension of Newtonian fluid in the full viscosity range. It has been rigorously supported by the theory and confirmed by experiments. Since the theory is developed in the frequency domain, it is necessary to convert the collected correlation data concerning the scattered light intensity from the time domain to the frequency domain by fast Fourier transform, and therefore a high signal-to-noise ratio of the time-domain data is crucial. For the sensing interfacial properties of fluid by the SLS method, it is necessary to guarantee both measurement accuracy and speed. In order to achieve the target, it is crucial to apply a small scattering angle and then correct the instrumental broadening effect. We thus develop an algorithm for the correction of the instrumental broadening effect in the frequency domain with an assumption of Gaussian distribution broadening instrumental function. We also check the theory with a low-viscosity refrigerant R1336mzz(Z) and high-viscosity fluid ethyl myristate with SLS apparatus at the small scattering angle. This paper aims to reduce the single-point measurement time of viscosity and interfacial tension of fluid by the SLS method to 2-5 minutes and will promote the further development of SLS sensors.

The frequency-domain data evaluation scheme of SLS is addressed in this paper. Under the assumption of a Gaussian intensity distribution of the laser beam, a modified frequency-domain model is established by considering the instrument broadening effect at the small scattering angle as well as the fluctuation-dissipation theory of capillary waves in the critical damping range. The spectrum model considers a series of collected wave vectors around the pre-defined q₀. Firstly, the intensity correlation data in the time domain at the specific q₀ are obtained by the SLS apparatus, and the zero-channel data are added by evaluating the fitted normalized intensity correlation function at τ=0, and then the whole data are folded. The repeated data at the last channel are deleted, and a Fourier transform is applied to generate the frequency-domain data for subsequent fitting of the regression model. For the fitting process, an appropriate discrete component number d and integral interval variable n should be considered to represent the real wave vector distribution. Subsequently, the discrete spectrum model is fitted to the spectrum data, and the viscosity and interfacial tension are accessed with other thermophysical properties in the model as input data. In addition, the algorithm that considers multiple wave numbers simultaneously as well as the instrumental broadening effect is developed and manifests excellent performance.

Since the small angle measurement scheme is adopted in this paper, the signal-to-noise ratio is greatly improved, and the measurement time is significantly reduced to 2-5 minutes (Fig. 2). In view of the instrument broadening effect at small angles, the weighted spectrum model [Eq. (11)] with Gaussian instrumental function is adopted. By collecting the thermophysical properties of the reference fluid R1336mzz(Z) at a temperature of T=373.05 K and incident angle Θ_i of 1.0-3.2°, the discrete component number d, integral interval variable n, and mean broadening constant Δq are determined to be 10, 5, and (4507.46±223.34) m^-1, respectively (Fig. 5). The low-viscosity refrigerant R1336mzz(Z) and the high-viscosity ethyl myristate are used as two reference fluids to verify the correctness of the Gaussian modified spectrum model in two typical cases, where the capillary waves evolve as oscillatory damped modes far away from the critical oscillation point (Y'?1) and purely damped modes in the critical oscillation region (Y'→1), respectively. For low viscosity cases with Y'?1 (Fig. 6), the interfacial tension and viscosity in both the time domain and frequency domain agree well for both large and small scattering angles after the instrumental broadening correction. For high viscosity cases with Y'→1 (Fig. 7), the viscosity data obtained by the frequency-domain method considering the dissipation effect in the bulk phases underneath surface waves are sufficiently larger compared with those obtained by the time-domain based method, especially close to the near-critical oscillation region. However, the data obtained by the frequency-domain approach are in good agreement with the literature values, and the instrumental broadening correction has no influence since the frequency ω_q of surface waves tends to be zero at this time, and the spectrum broadening Δω_I is negligible as shown in Eq. (7).

To improve the accuracy and speed of SLS measurement, we have applied small scattering angles and modified the line-broadening effect simultaneously. An algorithm is theoretically developed for correcting the instrumental broadening effect in the frequency domain with the assumption of Gaussian distribution of scattering light. With the reference fluids, the integral interval variable n and discrete component number d are obtained to be 5 and 10 to represent the distribution of the wave vectors, and the mean broadening constant Δq is determined to be (4507.46 ± 223.34) m^-1 for the present SLS apparatus. We also check the theory with a low-viscosity refrigerant R1336mzz(Z) and high-viscosity fluid ethyl myristate with SLS apparatus, and the results show that the measuring speed is improved, and only 2-5 minutes for a single measurement point are required for the same accuracy as the large scattering angle scheme. This paper will facilitate the further development of SLS sensors and other applications in connection with complex interfacial property measurement.