A multiblob approach to colloidal hydrodynamics with inherent lubrication

This work presents an intermediate resolution model of the hydrodynamics of colloidal particles based on a mixed Eulerian-Lagrangian formulation. The particle is constructed with a small set of overlapping Peskins Immersed Boundary kernels (blobs) which are held together by springs to build up a particle impenetrable core. Here, we used 12 blobs placed in the vertexes of an icosahedron with an extra one in its center. Although the particle surface is not explicitly resolved, we show that the short-distance hydrodynamic responses (flow profiles, translational and rotational mobilities, lubrication, etc) agree with spherical colloids and provide consistent effective radii. A remarkable property of the present multiblob model is that it naturally presents a divergent lubrication force at finite inter-particle distance. This permits to resolve the large viscosity increase at dense colloidal volume fractions. The intermediate resolution model is able to recover highly non-trivial (many-body) hydrodynamics using small particles whose radii are similar to the grid size $h$ (in the range $[1.6-3.2],h$). Considering that the cost of the embedding fluid phase scales like the cube of the particle radius, this result brings about a significant computational speed-up. Our code Fluam works in Graphics Processor Units (GPUs) and uses Fast Fourier Transform for the Poisson solver, which further improves its efficiency.