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 Peskin's 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) agree with spherical colloids and provide consistent effective radii. A remarkable property of the present multiblob model is that it naturally provides zero relative mobility at some finite inter-particle distance. In terms of mutual friction, this divergent force accurately represents the “soft” lubrication regime of spherical colloids and permits to resolve the increase of the solution viscosity up to moderately dense systems with volume fraction up to about 0.50. This 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 such as the cube of the particle radius, this result brings about a significant computational speed-up. Our code Fluam works in Graphics Processor Units and uses Fast Fourier Transform for the Poisson solver, which further improves its efficiency.