Soft Dynamics simulation. 1. Normal approach of two deformable particles in a viscous fluid and optimal-approach...

Discrete simulation methods are efficient tools to investigate the behaviors of complex fluids such as dry granular materials or dilute suspensions of hard particles. By contrast, materials made of soft and/or concentrated units (emulsions, foams, vesicles, dense suspensions) can exhibit both significant elastic particle deflections (Hertz-like response) and strong viscous forces (squeezed liquid). We point out that the gap between two particles is then not determined solely by the positions of their centers, but rather exhibits its own dynamics. We provide the first ingredients of a new discrete numerical method, named Soft Dynamics, to simulate the combined dynamics of particles and contacts. As an illustration, we present the results for the approach of two particles. We recover the scaling behaviors expected in three limits: the Stokes limit for very large gaps, the Poiseuille-lubricated limit for small gaps and even smaller surface deflections, and the Hertz limit for significant surface deflections. We find that for each gap value, an optimal force achieves the fastest approach velocity. The principle of larger-scale simulations with this new method is provided. They will consitute a promising tool for investigating the collective behaviors of many complex materials.