Numerical study of conjugate mass transfer from a spherical droplet at moderate Reynolds number

Abstract

Hydrodynamics and conjugate mass transfer from a spherical droplet at low to moderate Reynolds number have been investigated by direct numerical simulation. The study particularly focuses on the coupling between the internal and external flows, and their respective effects on the resulting mass transfer of a solute under 2D axi-symmetric configuration. The influence of the viscosity, density, and diffusivity ratios ( μ * , ρ * and D * respectively) between the two phases, as well as that of the equilibrium constant k (or Henry's number) characterizing thermodynamic equilibrium at the interface, has been studied in a range of flow Reynolds numbers relevant for solvent extraction processes (up to Reynolds number 100).The temporal evolution of the Sherwood number has been analyzed and a general correlation is proposed for its steady state regime. Interestingly, simulation results show that correlations available in the literature in the limiting cases k √ D * 1 and k √ D * 1 , referred to as internal and external mass transfer regimes, are not always appropriate in the context of conjugate mass transfer. This limits the use of the addition rule of transfer resistances, which reflects the flux continuity in the double stagnant film model. Indeed, a significant discrepancy is observed under specific configurations, especially at low Péclet number ( Pe ≤ 500) where non uniform interface concentration prevails.

Bubble-mediated transfer of dilute gas in turbulence

“…Dilute gas diffusion from a bubble is similar to conjugate mass transfer from a spherical droplet (Rachih et al. 2020). However, in the present study, the fluid inside the spherical cavity is considerably less dense than the surrounding fluid and hence is called a bubble.…”

Tropfenbewegung und Stofftransport in technischen Flüssig/flüssig‐Systemen. Teil 1: Einzeltropfensedimentation ohne Grenzflächeneffekte

“…Vom Dichteverhältnis ist der Widerstandsbeiwert hingegen nahezu unabhängig 13, 33, wodurch die Abschätzung bezüglich Dichteänderungen auf Basis von Gl. 1 erfolgen kann.…”

“…Es hat sich gezeigt, dass im Falle eines konjugierten Problems in der Regel eine aufwendigere numerische Evaluierung nötig ist 1 und die Additionsregel zur Berechnung des Stoffdurchgangskoeffizienten k d gemäß Gl. 4 nur eine unzureichende Genauigkeit besitzt 33, 45.…”

“…In welchen Grenzen die für konjugierte Systeme gängige Additionsregel der Stofftransportwiderstände Gültigkeit besitzt und in welche Richtung Abweichungen auftreten, evaluieren u. a. Juncu 45 und Rachih et al. 33 numerisch. Eine Übersicht über numerische Betrachtungen und die zugrunde liegenden numerischen Ansätze zur Einzeltropensedimentation ist in Zhang et al.…”

Simulation of conjugate mass transfer in multiphase flow: A new unified approach based on the phase field method

“…Generally, according to the dominant mass transfer resistance, the interphase mass transfer phenomena can fall into three categories: (1) internal problem where the greatest resistance is located in dispersed phases, (2) external problem in which the dominant resistance appears in continuous phases, and (3) conjugate problem when the mass transfer resistances of both dispersed and continuous phases are comparable. Among them, the conjugate problem is the most challengeable, for which the temporal/spatial variation of concentration in both dispersed and continuous phases should be considered and the interfacial concentration is ruled by both thermodynamic equilibrium (Henry's law) and the continuity of mass flux [4].…”