# Research Progress and Engineering Applications of Viscous Fluid Mechanics
## 2 Advances in the Study of the State of Motion of Viscous Fluids
### Experimentation and Research
#### 2.1.4 Experiments and Studies on the Oscillation Method  
The viscosity of a fluid is measured or its state of motion is studied using an oscillating-disk- or oscillating-cylinder-type geometry or by external shock conduction, which is inferred from the frequency of the oscillations and the response of the oscillator. The basic principle is to use external excitation to cause oscillations within or on the surface of the fluid and to reveal the fluid's hydrodynamic behavior and oscillatory modes by observing and analyzing the oscillatory phenomena [73; 74]. This method is commonly used to study polymer solutions or complex liquid systems containing additives [75]. As a research tool, the viscous liquid oscillation method, although it has an important role in fluid dynamics and engineering applications, has some potential problems and challenges, which include complex fluid behavior and nonlinear effects, difficulties in ensuring the control and stability of the experimental conditions, the large amount of resultant data requiring complex data processing algorithms and technical support, and the lack of a precise interpretation for the phenomena of liquid oscillations that have been observed and recorded, which makes the exact interpretation and physical significance of the different oscillation modes difficult to analyze [76; 77; 78]. The results of oscillations of single geometries in the experiments of the oscillation law of viscous fluids often do not allow a clear determination of the exercises between the two. [PERSON], AN, et al. [79] studied the low-amplitude and high-frequency oscillations induced by the reciprocating motion of ellipsoidal cylinders with different axial ratios in viscous fluids based on the law of harmonics, and the limits of the asymptotic theory were determined through the observation of oscillations of the surface of the liquid, which is more diverse than the study of the oscillatory behavior of individual geometries in viscous liquids. In addition to the study of viscous liquids using geometries probed into the liquid to produce displacements or oscillations, the use of acoustic waves to impart oscillations to the liquid is a very worthwhile research method. In view of this problem, [PERSON], [PERSON] et al. [80] implemented non-contact positioning suspension of viscous liquids such as silicone oil and propanol based on acoustic suspension, and placed them under the same ambient pressure to measure the surface tension and viscosity of each liquid. The construction diagram of the experimental device is shown in Figure 9.  
[PERSON], [PERSON], et al. [81], based on the transient deformation induced by oscillation, built an experimental setup and predicted and analyzed the small-amplitude axisymmetric-shape oscillations of a viscoelastic droplet suspended in a gas and improved the Jeffreys model to obtain a new characteristic equation for the complex frequency, which quantifies the effects of the two time scales, stress relaxation and deformation delay time, on the oscillatory behavior of the droplet. Due to the traditional experimental research method of building physical platforms having many inconveniences, such as the stability being difficult to control and the experimental results being difficult to obtain, many researchers use computer technology to digitize the physical environment of the object of study in order to control the variables, and the digital simulation makes it easy to extract the results. [PERSON], [PERSON], et al. [82] took into account the emergence of severe precession and frequency shifts in experiments in the measurement of the surface tension of liquid introducing non-negligible measurement errors in the determination, so the effects of the oscillation amplitude of viscous droplets and the viscous effect on the droplet oscillation were investigated by three-dimensional modeling simulation. The modeling and simulation are shown in Figures 10 and 11. Figure 10: Schematic diagram of an oscillating droplet.