*2.1. Marangoni Effect*

In a gas–liquid mass transfer process, the interface condition is important. Interfacial tension, molecular structure of the interface, intermolecular forces of combining gas and liquid molecules, and interface turbulence all have an important impact on the gas–liquid mass transfer process [29]. During gas–liquid mass transfer, the interfacial convection phenomenon is caused by the change in some physical properties of the liquid such as surface tension and density due to the mass transfer at the interface, which may lead to convective movement of the interfacial fluid [29–31]. Researchers attribute this to the Marangoni effect or Rayleigh effect caused by transmission, which in turn strengthens the transmission process [30,32]. During interphase mass transfer, when the temperature or concentration in different areas on the surface are different, a surface tension gradient is generated, resulting in the movement of liquid on the surface layer and liquid under the interface. This interfacial convection phenomenon is known as the Marangoni effect. The Marangoni effect not only has various geometric patterns on the flow structure, but also enhances the heat and mass transfer processes. Marangoni convection can be characterized by the dimensionless number Ma, which is expressed as follows:

$$\mathbf{Ma} = \frac{\mathbf{d}\Delta\sigma}{\mathbf{D}\mu} \tag{1}$$

where d is the characteristic length (m); Δσ is the difference in surface tension between the surface fluid and the main fluid (N m−1); D is the diffusion coefficient of the solute in the fluid (m<sup>2</sup> s−1); and μ is the viscosity of the fluid (Pa s). In Equation (1), when Ma > 0 and exceeds a certain critical value, the surface tension gradient generated by the interface will cause Marangoni convection. In gas–liquid and liquid–liquid liquefaction processes, due to the changes in the physical and chemical properties of the system [33,34], the heat and mass transfer processes cause interfacial instability, and the surface tension is a function of concentration and temperature, which causes the temperature and concentration gradient of the interface to lead to the surface tension gradient of the interface, resulting in Marangoni convection.
