Particle hydrodynamics: beyond the Stokes force
By: Rafael Delgado-Buscalioni
From: Universidad Autónoma de Madrid
At: Instituto de Investigação Interdisciplinar, Anfiteatro
[2012-03-27]
I will present "FLUAM", a new algorithm designed to solve the hydrodynamics of particles immersed in a Newtonian solvent. Although the scheme is quite general and can be easily generalized to solve dispersions of  large particles (dust)  or even fluid-structure interactions, we envisage applications at the micron scale involving solutions of macromolecules (colloids or polymeric chains). At these scales hydrodynamic fluctuations become important and have to be consistently included in the fluid solver. In particular, the Navier-Stokes-Landau-Lifshitz equations (for either   compressible  or   incompresible  liquids) are solved using a finite volume method [1]. Concering the solute description, at  this coarsed-grained level I will focus on the so called "point-particle" representation, where each particle (macromolecule) is described by translational (also if required rotational) degrees of freedom and of course might feel inter-molecular (effective potential) forces as well.
In these kind of schemes, the force between particle and fluid have been usually assumed to be frictional, based on the Stokes drag. This assumption  is limitted  to  "slow" fluid-particle  interactions developing at times much larger than the friction time (inverse of the friction coefficient). By contrast, our approach is based on imposing a "no-slip" constraint to the fluid velocity at the particle domain which ensures that particle and fluid momentum is instantaneously exchanged over their interaction [2,3]. In this way we can tackle phenomena occurring at high frequencies (such as inertial effects). In particular we are interested in applications involving acoustic forces [3] (ultrasound) on colloidal particles (and soft matter, in general).
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Finally, I'd also like to briefly discuss some of the applications we have in mind; such as the effect of hydrodynamics on the gelation process or in the self-assembly of patchy colloids.
[1] F. Balboa and J. Bell and R. Delgado-Buscalioniand A. Donev and T. Fai and B. Griffit and C. S. Peskin. Staggered Schemes for Fluctuating Hydrodynamics, arXiv:1108.5188v1, (submitted, 2011)
[2] F. Balboa and R. Delgado-Buscalioni, Particle Hydrodynamics using Hybrid Models: from Molecular to Colloidal Fluids,  Particles 2011 (to appear)
[3] F. Balboa, I. Pagonabarraga and R. Delgado-Buscalioni, Inertial coupling for point particle fluctuating hydrodynamics, (submitted, J. Comp. Physics, 2011)