Modeling of granular segregation phenomena using inhomogeneous Markov chains

Powder mixing is an essential unit process when raw materials are handled in the form of divided solids. The mixing of a minority active ingredient and an excipient in the pharmaceutical industry, the manufacture of a recycled nuclear fuel unit from grains of different types, and the production of dry mixtures in the agri-food industry are all examples where the technical issue of powder mixing is central. The challenge is not only to achieve a homogeneous final mixture that guarantees proper use later in the process, but also to optimize the mixing time, which affects the efficiency and profitability of the process as a whole. In addition to these technical requirements, there is the phenomenon of segregation, which prevents the components from mixing. Segregation manifests itself in the spontaneous formation of areas rich in one or other of the components. Cases of segregation are very varied but occur when powders with contrasting properties in terms of grain size, density, surface condition or geometry, etc. are mixed. A common example is the rise of the largest blocks to the surface of a granular flow when falling on an inclined plane, or the rise of the largest grains to the surface in the case of a granular medium in a vibrating cylindrical container. Stochastic modelling of a mixing process using Markov chains to describe the evolution of the position of the grains that make up the mixture is an approach that allows the overall state of the mixture to be described at the mixer level, without going into an individual description of each grain making up the granular medium. In the case of a mixture of mechanically identical grains in a granular medium, intergranular diffusion processes localized in the shear zones when the medium is set in motion explain the mixing. The geometric division of the flow into different zones allows this diffusion to be modelled using transition rates from a homogeneous Markov chain, i.e. one whose parameters are constant. In the case of mixtures of grains with stark contrasts in mechanical or geometric properties, stochastic modelling of the dynamics of the mixture is based on transition rates that depend on the state of the mixture. The use of a non-homogeneous Markov chain then becomes necessary.

The aim of this M2 internship will be to use numerical results from DEM simulations of different grain mixtures to propose a stochastic model capable of reproducing the effects of segregation. This work will complement a thesis that confirmed that knowledge of the individual position of each grain in a granular mixture obtained using a finite-time DEM simulation allows for effective prediction of its subsequent evolution using a Markov chain. The modelling approaches that will be explored during this internship will extend these results to the case of segregation.

Why choose this internship ?

✅ The simulation of granular processes is a major challenge for the development of digital twins of processes in many industrial sectors such as pharmaceuticals and agri-food, but also in civil engineering, energy and materials manufacturing.

✅ The proposed granular flow modelling method will also enable you to develop fundamental knowledge of the flow and mixing of granular media.

👉 This is therefore a project of great industrial and academic interest, which you can easily leverage as an engineer in industry or to pursue a PhD in the field of granular media.

📅 Dates:

6 months starting in the first semester of 2026 (date to be specified depending on your training program)

📍Supervision and location of the internship:

This internship will be co-supervised by research teams from the RAPSODEE center at IMT Mines Albi (Henri Berthiaux, Cendrine Gatumel) and the SPIN center at IMT Mines Saint-Etienne (Guillaume Dumazer, Eric Serris). It may take place at either of the two laboratories, depending on your availability.

@ Contacts:

Cendrine Gatumel, IMT Mines Albi

gatumel@mines-albi.fr

Guillaume Dumazer, IMT Mines Saint-Etienne

guillaume.dumazer@emse.fr