Numerical Simulation Of The Interphase Mass Transfer Of A Deformable Drop/Bubble And The Marangoni Effect

On the interphase boundary accompanied with heat or mass transfer processes, the inhomogeneous distribution of temperature or solute concentration (or inhomogeneous distribution of surfactant) will lead to interfacial tension gradient followed by unsteady flow near the interface. Such interfacial instability is referred as Marangoni effect. The effect occurs at the boundary layer of heat or mass transfer processes, which significantly influences heat or mass transfer rates. In industry, especially in the multiphase contactor or reactor, the production efficiency often depends on the interphase mass transfer rate of the solute or reactant through the surface of a droplet or a bubble. For example, this can be involved in heat or mass transfer processes in adsorption, rectification or extraction as well as chemical reaction processes in stirred tanks or micro-reactors. Therefore, the systematical exploration of interphase heat or mass transfer and Marangoni effect will be very helpful in the transport mechanism, especially in improvement of interphase mass transfer theory. In another hand, it will contribute to build universal empirical correlations for heat or mass transfer coefficients, which are very important to the design and scale-up of separation equipment and reactors.Marangoni effect is caused by extensive coupling of multiphase flow with interphase heat or mass transfer originated from very complicated mechanisms. To simplify this issue, in this thesis, it is assumed that in a constant temperature system, a droplet or bubble moves unsteadily companied with the mass transfer process in another infinite continuous phase of an immiscible liquid. Initially, the droplet or bubble is spherical. Based on this simplified model, a numerical calculation method was improved in the level set method framework to calculate the two-phase flow and interphase mass transfer, and the numerical simulation was performed and programmed with Fortran language. The program can be not only applied to gas-liquid or liquid-liquid systems irrespective of mass transfer resistance distribution, but suitable for describing non-Newtonian fluid systems by addition of the corresponding user-defined module.Taking advantage of this program, the dissolution process of a CO2 bubble in a CMC solution was simulated. This process was the continuous phase resistance control. CMC was a non-Newtonian fluid, and the Carreau model was employed to demonstrate the rheological characteristic. The volume-changing method was incorporated to follow the volume variation of a bubble during solution. It was found that the predicted results were coincided with the experimental data. Because of the motion of the bubble, the viscosity distribution in the continuous phase was variable, and the dissolved gas concentration in the wake demonstrated different patterns.The concentration transformation method could deal with the discontinuous boundary conditions of the interphase mass transfer process. With the level set method, the interphase mass transfer could be calculated via a "one-fluid" algorithm. However, the concentration gradient was high in the interface, especially with large interfacial deformation, leading to serious numerical diffusion. Therefore, a semi-Lagrangian advection scheme was used to alleviate the numerical diffusion so is to increase the accuracy of prediction in mass transfer in real systems. The new algorithm was employed to realize 2D numerical reconstruction in the interphase mass transfer process accompanied with solute-induced Marangoni effect. The mass transfer coefficient accompanied with Marangoni effect was accurately predicted. Besides, the influence of local vortex with sub-particle scale on the mass transfer rate was also analyzed.In fact, Marangoni effect develops in a 3D space. Thus, the movement of a droplet in the continuous phase was not in axial symmetry, with additional vibrating and lateral migration. To simplify the issue, in this thesis, a three-dimensional spherical drop was simulated without droplet deformation to investigate the 3D evolution of the solute-induced Marangoni effect. In this simulation, the local grid adjacent to the interface was refined to 10 μm to capture the instability detail. The calculated results showed the Marangoni effect in three-dimensional space developed after the internal circulation formation with a non-axisymmetric configuration and circumferential flow.In a single droplet, the space is very narrow, so the Marangoni convection is limited by the space. Moreover, the droplet deformation influences greatly on the Marangoni convection. Therefore, the 2D algorithm was extended to a 3D system with the level set method to simulate the 3D movement of a deformable drop and the solute-induced Marangoni effect. In this thesis, although the resource demand of 3D calculation was very large, preliminary results with a coarser grid achieved laid a solid basis for the subsequent work with reasonable meshing and massive parallelization.