# Transport Engineering of complex fluids: Phenomenology, rheology, processes, modelling, data analysis and numerical simulation

## Transport Engineering of complex fluids: Phenomenology, rheology, processes, modelling, data analysis and numerical simulation

This theme concerns the whole modeling chain linked to the phenomenon of phosphate pulp transport, from experiments and data analysis in the laboratory to the delivery port. It covers all aspects, physical, mathematical and numerical, and is declined in 4 main axes.

1. Phenomenology and rheology

2. Mathematical modeling

3. Data analysis and processes

4. Numerical simulation

When a physical or economic problem arises, it is usually desirable to characterize the key processes that control it (for example, diffusion, viscosity, transportation, friction or stochastic aspects), and those that can be ignored are the focus of part of the first axis.The other component, rheology, is studying the deformation of matter and its flow. There is simultaneous scientific and industrial interest in the rheological analysis of complex fluids. The rheological analysis of the fluids based on condensed suspensions is of particular interest here. It is a mixture of fluid and colloidal particles and non-colloidal ones. Such materials include paints, emulsions, charged greases, charged polymers, drilling mud, natural fine or coarse mud, inks, slurry, granular pastes, etc.We then have the Mathematical Modeling axis where it is a question of translating into equations the phenomena selected, their behavioral laws and their interactions; and analyzing these equations in terms of existence of solutions, regularity and stability. Generally, in simplified configurations.

The Data and Process Analysis axis is fundamental for this type of study. It is a question of collecting data resulting from the exploitation on the ground (here phosphate extraction, treatment, routing) and to analyze it by the modern methods of the discipline in order, on the one hand, to better to define the laws of behavior and their parameters, and on the other hand to propose alternative operating modes in order to improve the processes.

Finally comes the Numerical Modeling dimension where it’s a matter of identifying methods for approximating equations and converting them into computer-usable calculation algorithms. This axis is strongly connected with the other three and needs a considerable degree of interdisciplinarity. The methods used come both from the numerical analysis algorithmic geometry and from high-performance computing. Here, we focus on the equations of non-Newtonian flows, approximated in particular by finite volume diagrams. The scientific discussions will concentrate on: I) how the relevent rheological behavior laws of such materials can be developed. Ii) How to use these laws to model flows and transport by correct calculation codes in industrial processes, based on numerical simulation.