## 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 willÃ‚Â present "FLUAM", a newÃ‚Â algorithm designedÃ‚Â toÃ‚Â solveÃ‚Â the hydrodynamics of particles immersedÃ‚Â in a Newtonian solvent.Ã‚Â Although the schemeÃ‚Â is quiteÃ‚Â general and canÃ‚Â be easily generalizedÃ‚Â to solve dispersionsÃ‚Â ofÃ‚Â Ã‚Â largeÃ‚Â particlesÃ‚Â (dust)Ã‚Â Ã‚Â orÃ‚Â evenÃ‚Â fluid-structure interactions, weÃ‚Â envisage applications at theÃ‚Â micron scale involving solutions of macromolecules (colloidsÃ‚Â or polymeric chains).Ã‚Â At these scalesÃ‚Â hydrodynamic fluctuations becomeÃ‚Â important and have to be consistently included in the fluidÃ‚Â solver. In particular, the Navier-Stokes-Landau-LifshitzÃ‚Â equationsÃ‚Â (for eitherÃ‚Â Ã‚Â Ã‚Â compressibleÃ‚Â Ã‚Â orÃ‚Â Ã‚Â Ã‚Â incompresibleÃ‚Â Ã‚Â liquids) are solved using a finite volume method [1].Ã‚Â Concering the solute description, atÃ‚Â Ã‚Â this coarsed-grained levelÃ‚Â I will focus on theÃ‚Â so called "point-particle" representation,Ã‚Â where each particleÃ‚Â (macromolecule) isÃ‚Â described by translational (also if requiredÃ‚Â rotational) degrees of freedom and of course might feel inter-molecular (effective potential) forces as well.

In theseÃ‚Â kind of schemes, theÃ‚Â force between particleÃ‚Â and fluid have been usually assumed to be frictional, based on the Stokes drag.Ã‚Â This assumptionÃ‚Â Ã‚Â isÃ‚Â limittedÃ‚Â Ã‚Â toÃ‚Â Ã‚Â "slow"Ã‚Â fluid-particleÃ‚Â Ã‚Â interactions developing at times much larger than the friction time (inverse of the friction coefficient).Ã‚Â By contrast, our approach is based on imposing a "no-slip"Ã‚Â constraint to theÃ‚Â fluid velocity at theÃ‚Â particle domainÃ‚Â which ensures thatÃ‚Â particle and fluid momentum is instantaneously exchanged over their interaction [2,3].Ã‚Â In this wayÃ‚Â we can tackleÃ‚Â phenomena occurringÃ‚Â at highÃ‚Â frequencies (such asÃ‚Â inertial effects). InÃ‚Â particular weÃ‚Â are interestedÃ‚Â in applicationsÃ‚Â involving acousticÃ‚Â forces [3]Ã‚Â (ultrasound) on colloidalÃ‚Â particles (and softÃ‚Â matter, inÃ‚Â general).

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Finally, I'd also like to briefly discuss someÃ‚Â of the applications we have in mind; suchÃ‚Â as theÃ‚Â effect ofÃ‚Â hydrodynamicsÃ‚Â 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.Ã‚Â Griffit and C.Ã‚Â S. Peskin. Staggered SchemesÃ‚Â for Fluctuating Hydrodynamics, arXiv:1108.5188v1, (submitted, 2011)

[2] F.Ã‚Â BalboaÃ‚Â and R.Ã‚Â Delgado-Buscalioni,Ã‚Â Particle HydrodynamicsÃ‚Â using Hybrid Models:Ã‚Â from MolecularÃ‚Â to Colloidal Fluids,Ã‚Â Ã‚Â Particles 2011 (to appear)

[3] F.Ã‚Â Balboa,Ã‚Â I.Ã‚Â PagonabarragaÃ‚Â andÃ‚Â R.Ã‚Â Delgado-Buscalioni,Ã‚Â Inertial couplingÃ‚Â for pointÃ‚Â particleÃ‚Â fluctuating hydrodynamics,Ã‚Â (submitted, J. Comp. Physics, 2011)