(342a) Hydrodynamics and Conjugate Mass Transfer from a Translating Spherical Droplet in a Continuous Phase

Hydrodynamics
and Conjugate Mass Transfer from a Translating Spherical Droplet in a
Continuous Phase

Azeddine
RACHIH ^1,2,
Dominique LEGENDRE²,
Eric CLIMENT² ,
Sophie CHARTON^‡1

¹
CEA, DEN, Research Department of Mining and Fuel Recycling, SA2I,
F-30207 Bagnols-sur-Cèze, France
²
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de
Toulouse, CNRS, Toulouse France

Mass
Transfer, Droplet hydrodynamics, Multiphase flow, Sherwood number,
Interfacial phenomena

The
optimization of separation processes, like liquid-liquid extraction,
and improvement of separation apparatus design start most importantly
with a good understanding of the hydrodynamic coupling between the
two phases and the mass transfer across the interface. This task
becomes challenging for complex polydisperse systems. Population of
droplets or bubbles is often considered in these processes. Given the
complexity of an accurate description of the system, the
investigation of mass transfer at the microscale of a single droplet
moving in the surrounding immiscible phase is of prime importance.
This study represents a major step towards derivation of general and
reliable mass transfer resistance correlations.

Many
experimental attempts have been made so far using single droplet
configuration [1,2]. However the empirical correlations found are
neither general nor fully reliable due to parasite phenomena. Direct
numerical simulation on the other hand appears to be an effective
tool to address interface mass transfer issues.

Many
key physical parameters (such as the viscosity ratio, diffusivity
ratio, flow configuration, etc.) may impact directly both the
hydrodynamics of a moving droplet in a continuous phase and
extraction efficiency as well [3]. In this study, efforts 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 various
values of these main key parameters. The temporal evolution and the
spatial concentration distribution have been studied, analyzed and
then validated on reference test cases.

Since
under the hydrodynamic conditions typical of solvent extraction
processes, the droplets usually achieve a spherical shape [4], a
fixed (i.e. non deformable) mesh is considered in this study. A
numerical investigation has been conducted by DNS to investigate the
coupling between the internal and the external flows and their
respective effects on mass transfer. JADIM, the CFD code developed at
IMFT, was used and adapted in this aim. The finite volume scheme
implemented, together with the use of an orthogonal curvilinear mesh,
was shown to enable good description of interfacial phenomena [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.

In
this contribution, the numerical model were used to study the
sensitivity of the transfer’s rate of a non reactive solute to the
various hydrodynamic and chemical parameters, accounted thanks to the
Reynolds, Peclet, Fourier, Henri numbers. The results revealed good
agreement with available experimental and numerical data [6,7]. The
model predicts correctly the effect of relevant physical parameters
on the transfer process. Moreover the respective effect of internal
flow circulation and external convection was evidenced and drastic
changes of the internal and external resistances to mass transfer
with increasing values of the Peclet number were predicted.

Figure:
Time-evolution of an inert solute’s concentration due to mass
transfer under creeping flow (Re=0.1, Pe=1000, Henry coefficient=1 )

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]
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

[5]
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.

[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.