PHD offer: Design of a robotic simulator modelling capillary forces using SPH (Smoothed Particle Hydrodynamics) method

Context: The AS2M department of the FEMTO-ST institute specialises in small-scale robotics (microrobotics). Its researchers develop millimetric and submillimetric robots for medical and industrial applications. At small scales, the deformation of robots and their interactions with their environment is difficult to predict. In particular, capillary forces resulting from the surface tension between two fluids are particularly important at scales of between one micrometre and one millimetre. They can therefore have a major influence on the deformation of a structure and its adhesion to an object in humid environments. In nature, many mechanisms rely on these forces, such as the propulsion of insects on the surface of water, illustrated in Figure 1. Properly understood, they can be used as the basis for flexible droplet based micromechanisms. It is therefore essential to propose simulation tools for deformable robots that incorporate capillary force models.

Topic: Among simulation methods, finite elements enable capillary problems to be solved very accurately. However, the problem definition , multiphysics interactions and boundary conditions definition (in particular the zones in contact with the liquid) are complicated to set up and vary greatly from one simulation to another. Alternatively, minimisation of the surface energy can also be carried out, allowing a rapid resolution of the problem, but limited to a quasi-static approach.

The aim of this thesis is to study the relevance of the Smooth Particle Hydrodynamic (SPH) method for simulating deformable microrobots interacting with liquid at millimetre and sub-millimetre scales. The SPH method represents the fluid by particles of constant mass, so the equations of the medium are approximated by interaction forces between these particles. The advantage of this method is that it is very versatile, offering a simple definition of the wetting boundary conditions by representing the surface energy as an interaction force between the particles.

Expected results: This thesis first objective  will be to implement surface tension in SPH models by adding an inter-particle force. The expression of this force will be studied in order to be robust to changes in resolution and materials, as well as to changes in topology such as the division of a drop into two sub-parts. The coupling between fluid mechanics and continuum mechanics will then be studied in order to propose a stable and efficient scheme for elasto-capillary problems (such as for example, the deformation of hairs by water). After validation of the method on case studies from the literature, its implementation in an existing calculation code will be considered. Finally, demonstrators will be produced, for example enabling the design and control of a micro-actuator based on the formation and destruction of drops or the design of a robot propelling itself on the surface of water inspired by water strider insect.