# 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
#### 2.1.3 Experiments and Studies on the Flat-Plate Gap Method  
The flat-plate gap method for viscous fluids is an important experimental method for investigating the properties of viscous fluids flowing between two parallel solid surfaces. This traditional experiment not only reveals the behavior of the fluid at the microscopic scale but also measures important parameters such as its rheological properties and viscosity [58]. In the experiments of the flat-plate gap method for viscous fluids, it is first necessary to prepare two parallel solid surfaces, usually flat plates or pipe walls. The flatness of these surfaces has an important effect on the experimental results, so high-precision experimental equipment is usually used [59; 60]. Next, an appropriate sample of viscous fluid is selected for the experiment. The choice of viscous fluid can be determined according to the specific purpose and requirements of the experiment [61], e.g., fluid samples with different viscosities and different rheological properties can be selected. While the experiment is in progress, a small gap, usually between a few micrometers and a few millimeters, is set between two flat plates. The size of this gap will directly affect the flow characteristics of the fluid therein. The fluid can be guided to flow in the gap by applying some pressure or by applying an electric field (for galvanic fluids) [62; 63]. During the experiments, the flow data of the fluid in the gap are obtained by means of appropriate measuring devices such as pressure transducers, flowmeters, or laser measuring devices. The commonly measured parameters include the flow velocity distribution, shear stress distribution, and pressure distribution of the fluid [64; 65; 66]. The measurement of these data is important for inferring the viscosity, flow resistance, and flow behavior of viscous fluids in confined spaces, but this experimental method has the problems that the control of experimental conditions requires high-precision equipment and operating techniques, and the stability of experimental environments is highly required. Therefore, [PERSON], H, et al. [67] investigated the laminar, turbulent, and transitional flow regimes of a viscous fluid in a narrow gap between two substrates with a parallel distance of 2 mm and obtained the static and stagnant pressure ratio distributions along the axis of the channel using both optical and gas-dynamics methods. [PERSON], AH, et al. [68] developed a mathematical model to investigate the flow behavior of viscous fluid in a narrow gap between two rectangular elastomeric plates with a distance of 2 mm. The model is based on low-Reynolds-number fluid dynamics and linear plate theory, and it is concluded that the outflow volume of a viscous fluid increases linearly with increasing pressure. [PERSON], JR, et al. [69] investigated the combined effect of the properties of viscous liquids subjected to pressure as well as non-Newtonian coupled stresses by developing a mathematical model of piezoelectric-viscous dependence and non-Newtonian coupled stresses in a wide parallel rectangular-plate extruded membrane based on [PERSON] microcontinuum medium theory and incorporating factors related to the variation in viscosity with pressure. [PERSON], [PERSON], et al. [70] designed a set of mathematical models based on the Cartesian coordinate system for the effects of piezo-viscous dependence and non-Newtonian coupling stress on the performance of cylindrical-perforated-plate extrusion-film bearings. The digital model is shown in Figure 7.  
[PERSON], JA, et al. [71] studied the diffusive motion patterns between a thin film of viscous fluid and a thin elastomeric sheet on a plate by extrusion using a permeable horizontal plate and showed that an air gap forms underneath the viscous fluid as it is extruded through the plate until the fluid re-flows onto the plate. For very light or stiff elastic sheets, the air gap contacts may extend well beyond the fluid discharge zone. [PERSON], AD, et al.