(47d) Hydrodynamics, Conjugate Mass Transfer and Chemical Reaction from a Rising Spherical Droplet

The improvement and optimization of separation processes, such as liquid-liquid extraction, are based most importantly on a clear understanding and precise modeling of the hydrodynamic coupling between the two phases yielding mass transfer across the interface. Chemical reaction in the extracting solvent is often used to enhance interfacial mass transfer. Given the complexity of an accurate description of the different coupling phenomena, the investigation of mass transfer at the microscale around a rising single droplet is still of major interest [1, 2].

Our study represents a significant step towards a complete prediction of general and reliable mass transfer resistance correlations. Many key physical parameters (such as the viscosity ratio, diffusivity ratio, flow configuration [3], and kinetics of chemical reaction) may impact directly both the hydrodynamics of the flow inside and outside the droplet yielding extraction efficiency variations.

A wide numerical investigation has been carried out using Direct Numerical Simulations to investigate the coupling between the internal and the external flows and their respective effects on mass transfer coefficient. The CFD code, developed at IMFT [4], was adapted and used to this aim including the effect of chemical reaction. We consider that the droplet has a constant spherical shape [5]. A specific jump condition has been implemented in order to accurately represent the convection/diffusion and mass transfer coupling at the interface between the droplet and the surrounding liquid. The finite volume code JADIM, together with the use of an orthogonal curvilinear refined mesh close to the interface permit accurate simulations of interfacial phenomena over a large range of fluid flow regimes and conjugate mass transfer.

Original simulations have been made to investigate the interaction between the internal and the external flows related to the motion of a single droplet, and the evolution of the Sherwood number through the influence of the dimensionless numbers that control the physical system (Reynolds, Schmidt and Hatta numbers). The results revealed very good agreement with available experimental and numerical data for validation on external and internal mass coefficients [6]. Moreover, the respective effects of internal flow circulation and external convection was evidenced [7]. Drastic changes of the internal and external resistances to mass transfer with increasing values of the Péclet number were predicted [8]. Under specific flow conditions, 3D instabilities of internal and external fluid circulations were observed leading to drastic modifications of mass transfer. The effect of an external chemical reaction has been correlated to the classic Hatta number with very good collapse of all the data on a mastercurve.

References

[1] Wegener, M., N. Paul, and M. Kraume. "Fluid dynamics and mass transfer at single droplets in liquid/liquid systems." International Journal of Heat and Mass Transfer 71 (2014): 475-495.

[2] Nemer, Martin B., et al. "Drop mass transfer in a microfluidic chip compared to a centrifugal contactor." AIChE Journal 60.8 (2014): 3071-3078.

[3] Michaelides, E. E. (2003). Hydrodynamic force and heat/mass transfer from particles, bubbles, and drops—the Freeman scholar lecture. Journal of Fluids Engineering, 125(2),209-238.

[4] Legendre, D. and Magnaudet, J., (1998). The lift force on a spherical bubble in a viscous linear shear flow. Journal of Fluid Mechanics, 368, pp.81-126.

[5] Grace, J.R., T. Wairegi. and T. H. Nguyen (1967). Shapes and velocities of single drops and bubbles moving freely through immiscible liquids. Trans. Instn Chem. Engrs, 54

[6] Oliver, D. L., & Chung, J. N. (1986). Conjugate unsteady heat transfer from a spherical droplet at low Reynolds numbers. International journal of heat and mass transfer, 29(6), 879-887.

[7] Juncu, G. (2010). A numerical study of the unsteady heat/mass transfer inside a circulating sphere. International Journal of Heat and Mass Transfer, 53(15), 3006-3012.

[8] Numerical study of conjugate mass transfer from a spherical droplet at moderate Reynolds number. (2020) A. Rachih, E. Climent, D. Legendre, S. Charton. Int. J. of Heat and Mass Transfer, 157, 119958.