*3.2. Molecular Di*ff*usion and Pore Tortuosity Tests*

Hydrodynamic dispersion is a process that includes molecular diffusion and mechanical dispersion. Molecular diffusion is the process of molecular transport associated with the stochastic movement of molecules due to a concentration gradient. Mechanical dispersion is the process of mechanical mixing that takes place in porous media as a result of the movement of fluid through the pore space. When the average pore flow velocity is 0, dispersion takes the form of molecular diffusion. In this study, each sample consisted of single-grained coral sands, and there was a total of six test groups, with particle sizes ranging from 0–0.1 mm, 0.1–0.25 mm, 0.25–0.5 mm, 0.5–1 mm, and 1–2 mm, while the dry density of each sample was a fixed value: ρ*<sup>d</sup>* = 1.3 g/cm<sup>3</sup> . The tracer and sensor types were the same as those in the one-dimensional dispersion test. The test instrument was a custom-designed and built molecular diffusion device, as shown in Figure 5. There was a control partition in the middle of the device, and after the partition was lifted, the fluids in the left and right sample box compartments could flow back and forth between the compartments. The sizes of the left and right sample boxes were both 10 cm × 10 cm × 10 cm, and the left sample was saturated with NaCl solution while the right sample was saturated with fresh water. Timing and data reading were started simultaneously with the lifting of the partition.

*J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 8 of 21

**Figure 5.** Molecular diffusion and pore tortuosity test device*.*  **Figure 5.** Molecular diffusion and pore tortuosity test device.

*3.3. Molecular Diffusion and Mechanical Dispersion Tests* 

a 20 g/cm3 NaCl solution.

velocities.

Let *EN-t* and *EW-t* be the measured conductivity at time *t* on the left and right sides, respectively,

When the pore flow velocity is greater than 0, molecular diffusion and mechanical dispersion processes coexist. With an increase in average pore flow velocity, the weight of molecular diffusion versus mechanical dispersion changes. In order to further study the relationship between the weight and the flow velocity, a custom-designed molecular diffusion and mechanical dispersion test device was employed in this study, as shown in Figure 6. The device consisted of three components, namely, a dispersion body, a water supply part, and a data acquisition system. The dispersion body was made up of organic glass tubes and samples, with each tube being 8 cm in inner diameter and 80 cm in length. The samples were coral sands with particle sizes of 0.25–0.5 mm and a dry density of 1.3 g/cm3. The data acquisition system was equipped with CS655 multi-parameter sensors; the tracer was

The required coral sand samples were first prepared in the dispersion tubes. The samples were then saturated with fresh water, after which the inlet and outlet valves of the dispersion tube were shut. The NaCl solution was then injected into the tracer injection port and the injection port was shut. This was completed while simultaneously starting data acquisition, with the pore flow velocity in the device being 0. The above steps were repeated using different concentrations of NaCl solution. Next, dispersion tests with pore flow velocities greater than 0 were conducted according to the above steps, with the exception that the inlet and outlet valves of the dispersion tube were reopened after the injection of the tracer to allow the pore fluid at a certain flow velocity to pass through the samples. The pore flow velocity was controlled by adjusting the output power of the water pump. By repeating the above test procedure, dispersion tests were performed at several different pore flow

Let *EN-t* and *EW-t* be the measured conductivity at time *t* on the left and right sides, respectively, and *EM-t* = (*EN-t* + *EW-t*)/2 be the mean value of the two measured conductivities at time *t*.
