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Job Record #18966
TitleCFD and mass transfer in the acoustic resonance mixing process
CategoryPostDoc Position
LocationFrance, Bordeaux (Talence)
InternationalYes, international applications are welcome
Closure DateWednesday, May 01, 2024

Many industrial sectors, such as pharmaceuticals or civil and military 
aeronautics, require the use of raw materials made from mixtures of constituents 
that are as homogeneous as possible to ensure the efficiency of the raw 
material. The most common industrial mixers are intrusive because they use 
rotating blades or a grid and require relatively long process times. To reduce 
mixing times, a new, non-intrusive technology using acoustic resonance (RAM) has 
been developed, based on vertical oscillation of the container containing the 
components. This induces both macroscopic convective movements and vortex micro-
movements. The latter are generated throughout the volume to be mixed, unlike 
intrusive technologies where they are only present in areas close to the 
rotating blades, which improves mixing and enables a homogenous mixture to be 
obtained very quickly. As part of an ANR ASTRID project (SINRAM), a liquid 
(binder) and particles (fillers) are mixed in a tank partially filled with air 
at low pressure. The tank is set in oscillation, which generates complex 
physical phenomena: instabilities at the interface between the air and the 
binder, vortex micro-movements, collisions of solid particles with each other, 
variable rheology, viscous dissipation, and so on.


The aim of this 2-year post-doctorate is to propose a 3D numerical simulation 
code for the RAM mixer, which will be used to understand the physical phenomena, 
to design highly homogeneous mixtures and to optimise the sizing of the mixer.  
More specifically, it will take into account: i) the effects of air 
compressibility, ii) instabilities at the air/binder interface (without 
particles and then in monodisperse solution), iii) the anisothermal conditions 
of the flow, and iv) the degassing kinetics taking into account the transport of 
air trapped in the binder and its transfer to the interface (but without 
interaction with the particles). All of this work will be carried out using the 
free and open source Notus code ( More specifically, the 
proposed work will focus on 2 aspects:

    1) Compressible/incompressible two-phase solver

The simulation of the process must be able to take into account the non-
negligible effects of compressibility in air and the incompressibility of the 
binder. Initially, we propose to continue the work developed in the laboratory 
[1] on a class of pressure correction type methods [2,3], based on the pressure 
evolution equation [4] and leading to the solution of a Poisson equation similar 
to that which would be solved for an incompressible flow, but including terms 
and specific coefficients relative to the compressibility of the flow. The 
proposed formulation will be compatible with the Volume-of-Fluid two-phase 
approach, and the interface between the binder and the air will be reconstructed 
linearly in the mesh using Weymouth's VOF-PLIC method [5]. Surface tensions will 
be taken into account by the Continuum Surface Force model and curvature by the 
height function method [6]. A non-Newtonian rheology of the binder could be 
considered, as well as heat transfer in the flow. In a second phase, the Philips 
model [7] and Krieger's law [8], which have already been implemented, will also 
be used to take account of the particles in the binder. Together, these methods 
will make it possible to simulate the tank containing the binder in vibration 
for different air pressures, and thus to reproduce the instabilities of the 
interface and the temperature increase of the mixture.

    2) Outgassing and transfer at interfaces

In order to take account of the outgassing phenomenon in numerical simulations, 
it is necessary to develop suitable physical models that deals with the mechano-
chemical coupling of air transport in the binder and its transfer to the 
binder/air interface, while respecting the concentration jump at the interface 
in accordance with thermodynamic equilibrium. At this stage, we will consider 
air as a dissolved entity in order to solve the transport and transfer at the 
interfaces using a single macroscopic advection/diffusion equation [9,10]. The 
1-fluid model described in the previous paragraph will therefore be extended to 
take account of an air concentration. The equivalent fluid will be reconstructed 
as a function of the volume fraction of the fluid in the mesh and the air 
concentration. We propose to use a methodology developed in the laboratory and 
based on a species diffusion potential that has been used to simulate 
dissolution/precipitation mechanisms [11]. This diffusion potential, which is 
continuous across the interface, would include in this project, in addition to 
the classical concentration-dependent term, terms relating to gravity and 

Candidate profile

The post-doctoral student we are looking for should have strong skills in 
physical and numerical modelling of two-phase flows. He/she should have 
experience both in the use of parallel CFD codes (MPI) and in the implementation 
of numerical methods (FORTRAN2008).


Please send a CV, a covering letter detailing your interest in the subject, PhD. 
thesis reports (manuscript and defence), and contact details of referees to the 
contacts below.


Dr. Stéphane Glockner - I2M

Dr. Sylvie Bordère – I2M


[1] J.-P. Caltagirone, S. Vincent, C. Caruyer, A multiphase compressible model 
for the simulation of multiphase flows, J. Comput. Phys. 50 (201

[2] G. Huber, S. Tanguy, J.-C. Béra, B. Gilles, A time splitting projection 
scheme for compressible two-phase flows. Application to the interaction of 
bubbles with ultrasound waves, J. Comput. Phys. 302 (2015) 439–468.

[3] A Urbano, M Bibal, S Tanguy, A semi-implicit compressible solver for two-
phase flows of real fluids, Journal of Computational Physics 456, 111034, 2022.

[4] A Toutant, General and exact pressure evolution equation - Physics Letters 
A, Volume 381, Issue 44, 29 November 2017.

[5] G.D. Weymouth and D.K.-P. Yue. Conservative Volume-of-Fluid method for free-
surface simulations on Cartesian-grids. J. Comput. Phys., 229:2853-2865, 2010

[6] M Owkes, O Desjardins, A mesh-decoupled height function method for computing 
interface curvature, Journal of Computational Physics 281, 285-300, 2015.

[7] Krieger, I. M. (1972). Rheology of monodisperse latices. Advances in Colloid 
and Interface science, 3(2), 111-136.

[8] Phillips, R. J., Armstrong, R. C., Brown, R. A., Graham, A. L., & Abbott, J. 
R. (1992). A constitutive equation for concentrated suspensions that accounts 
for shear‐induced particle migration. Physics of Fluids A: Fluid Dynamics, 4(1), 

[9] Maes, J. and Soulaine, C. (2020). A unified single-field volume-of-fluid-
based formulation for multi-component interfacial transfer with local volume 
changes. Journal of Computational Physics, 402.

[10] Zanutto, C. P., Paladino, E. E., Evrard, F., van Wachem, B., and Denner, F. 
(2022b). Modeling of interfacial mass transfer based on a single-field 
formulation and an algebraic vof method considering non-isothermal systems and 
large volume changes. Chemical Engineering Science, 247.

[11] Bordère, S. and Glockner, S. (2021). Numerical modeling of diffusion-
controlled phase transformation using the darken method: Application to the 
dissolution/precipitation processes in materials. Computational Materials 
Science, 186.
Contact Information:
Please mention the CFD Jobs Database, record #18966 when responding to this ad.
NameStéphane Glockner
Email ApplicationYes
Record Data:
Last Modified09:14:51, Tuesday, January 30, 2024

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