Internship on lubrication forces between objects near contact in a fluid

The Inria center at Université Côte d'Azur includes 42 research teams and 9 support services. The center’s staff (about 500 people) is made up of scientists of different nationalities, engineers, technicians and administrative staff. The teams are mainly located on the university campuses of Sophia Antipolis and Nice as well as Montpellier, in close collaboration with research and higher education laboratories and establishments (Université Côte d'Azur, CNRS, INRAE, INSERM ...), but also with the regional economic players.

With a presence in the fields of computational neuroscience and biology, data science and modeling, software engineering and certification, as well as collaborative robotics, the Inria Centre at Université Côte d'Azur  is a major player in terms of scientific excellence through its results and collaborations at both European and international levels.

Context

Particles are omnipresent in our daily lives and the environment. To name a few examples, particles are present in atmospheric sciences (dispersion of pollutants, aerosols and/or pollens in the air) or in marine sciences (plastic contamination in rivers or oceans) or in medical applications (microswimmers in blood for drug delivery). These particles can be either passive (i.e. transported by the underlying flow) or active (i.e. with their own self-motility). When two objects are immersed in a fluid, specific forces arise as these objects come close to each other. These specific interactions govern the way particles interact with each other, possibly leading to the formation of aggregates or clusters. This implies that accurate models are key to properly predict the formation of aggregates/clusters. The aim of this internship is to propose and validate a numerical scheme based on solvation forces, well-known in the field of chemistry for nanoscale molecules, to compute inter-particle interactions in the framework of continuum fluid mechanics, called lubrication forces.

Partners involved

The student will be in contact with researchers that collaborate with the team members on this topic across both France (in particular Strasbourg, Paris and Marseille) and Europe (mostly in Germany).

Objectives :

The dynamics of objects immersed in a fluid flow is described using Newton’s second law of motion. It describes the evolution in tme of the object’s position Xp, its translational velocity Up, its rotational velocity Ωp. It includes the expression of the forces and torques acting on the object. Yet, behind this apparent simplicity lies complex modeling issues.

In particular, when two objects approach each other, various forces arise [4]

• The lubrication forces, which result from the viscous forces generated when the fluid is squeezed out of the gap
  between the objects [1,2,3].
• The contact forces, which result from the collision between the two objects in contact.

In the fluid mechanics community, lubrication forces can be approximated numerically by solving the fluid flow around each individual object. This implies that the grid size used to compute the fluid flow has to be smaller than the gap between the objects. Yet, close to the contact point, the separation distance eventually becomes smaller than the grid size, implying that lubrication forces have to be modeled. Since these lubrication forces usually diverge when the separation distance nears 0, cut-off distances are introduced to obtain a finite value of the lubrication at contact [4].

Alternatively, in the field of interface chemistry, solvation forces are the equivalent of lubrication forces, except that they designate forces acting within the nanometre scale. Models for solvation force are thus derived from descriptions at the molecular level, i.e. from the motion of each water molecules squeezed between the two objects. Such models thus apply to scales at which the continuum level of description used for fluid mechanics breaks down [5].

References

[1] Lefebvre-Lepot, A., Merlet, B., & Nguyen, T. N. (2015). Journal of Fluid Mechanics, 769, 369-386.
[2] Khabthani, S., Sellier, A., & Feuillebois, F. (2019). Journal of Fluid Mechanics, 867, 949-968.
[3] Cox, R. G., & Brenner, H. (1967): Chemical Engineering Science, 22(12), 1753-1777.
[4] Kempe, T., & Fröhlich, J. (2012). Journal of Fluid Mechanics, 709, 445-489.
[5] Israelachvili, J. N. (2011). Intermolecular and surface forces. Academic press.

A more complete description is available on the team webpage.

The aim of this internship is to develop more advanced lubrication models that bridge the gap between theories developed in the two communities (namely fluid mechanics and interface chemistry). Depending on the student preferences, a number of topics are foreseen, among which:

1. a detailed review of the literature on lubrication and solvation forces;
2. the development of a theoretical model that combines ideas coming from fluid mechanics (lubrication forces) and interface chemistry (solvation forces);
3. the implementation of a new model in a solver for the dynamics of particles in suspension;
4. the assessment of the model performance and its accuracy, as well as a detailed evaluation of the sensitivity of the model to the input parameters.

The student will be encouraged to write a publication in an international journal at the end of the internship. Motivated
students will be encouraged to pursue their work on this topic with a PhD thesis.

Candidates should be fluent in English, have a good experience in programming and in data analysis.

We will appreciate candidates with the following skills (optional):

• Knowledge in fluid dynamics
• Knowledge in statistical physics
• Rigorous, autonomous and creative thinking
• Interest in environmental/medical applications

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Contribution to mutual insurance (subject to conditions)

Traineeship grant depending on attendance hours.