# 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
#### 2.1.1 Experiments and Studies on the Permeability of Media to Viscous Fluids
They fabricated their own experimental setup, which is schematically shown in Figure 2. The study focused on the permeability of thin PDMS membranes under convective conditions, and the experimental conclusions pointed out that macroscopic deformation can significantly affect the microstructure of soft materials and their transport properties. [PERSON], et al. [29] investigated the effect of polydimethylsiloxane (PDMS) cross-linking on the permeation properties of polyacrylonitrile (PAN)/PDMS nanofiltration (NF) composite membranes and found results that were inconsistent with the results of the swelling of the dense, This may be due to the lower pore intrusion rate of the composite film prepared at 10/2 compared to 10/1, or due to the heterogeneity of the silicone network. [PERSON] ML, ([PERSON], [PERSON]) et al. [30] investigated the change in permeability in a viscous material, natural gas-containing hydrate sediments, by a series of experiments, using different initial water saturations to reach hydrate saturations of up to 45% and measuring the corresponding fluid permeability during steady-state flow, which gradually decreases as the hydrate saturation increases. [PERSON] et al. [31] studied the spherical flow of Newtonian fluids in porous media based on fractal theory and technology. Three-dimensional spherical porous media percolation is widely found in hydrocarbon reservoirs. When only a small part of the reservoir is opened, the flow area has spherical radial flow, that is, the fluid flows from the center of the outward wellbore. The fractal permeability model of spherical porous media percolation is shown in Figure 3. The experiment reveals the physical mechanism affecting the spherical permeability and verifies the correctness of the fractal model of spherical permeability. [PERSON] et al. [32] conducted an experimental study of the effect of different fluids and clay minerals on the permeability of rocks; the conclusions of their study showed that the nature of the viscous fluid itself has an influence on the macroscopic permeability of the permeable material, and the physical and chemical relationship between the fluid and the permeable material should also be considered along with the liquid permeability. The experimental device of media permeability to liquid designed by their research is shown in Figure 4. The experimental device provides a new experimental method for studying the permeability of viscous liquid. Figure 3: Seepage radius diagram of spherical porous media. In the figure, r is the radial distance from a point in the reservoir to the center of the well, and \(r_{0}\) is the radius of the well. The results show that the spherical permeability increases with the increase in pore surface integral shape dimension and porosity. It decreases with the increase in tortuosity fractal dimension and with increasing radial distance [31]. Figure 2: The section diagram of the experimental device which used alcohol and air to explore the permeability of thin PDMS film under convective conditions. The glass channel under the device is 5 mm wide, 0.5 mm deep, and 45 mm long, and a PDMS film with a thickness of 60–200 \(\upmu\)m is attached to the lower plate surface to form a closed channel. The two pipelines importing ethanol solution and air are fixed by thick PDMS blocks. The valve of the ethanol pipeline on the left controls the input and exit of ethanol, and the air pipeline on the right is connected with the pressure control pump to adjust the pressure in the channel. Finally, the position of the semilunar surface of the PDMS membrane over time is recorded by a high-speed camera during the experiment. [PERSON] et al. [33] analyzed the complex fluid model of a tight reservoir and its applicability, using glycerol and methane gas for the pore structure of the tight reservoir at a micro- and nano-scale, and analyzed the theoretical basis and scope of application of the complex fluid model of the tight reservoir in detail.