By: Rafael Delgado-Buscalioni

From: Universidad Autónoma de Madrid

At: Instituto de Investigação Interdisciplinar, Anfiteatro

[2012-03-27] 11:30

I willÂ present "FLUAM", a newÂ algorithm designedÂ toÂ solveÂ the hydrodynamics of particles immersedÂ in a Newtonian solvent.Â Although the schemeÂ is quiteÂ general and canÂ be easily generalizedÂ to solve dispersionsÂ ofÂ Â largeÂ particlesÂ (dust)Â Â orÂ evenÂ fluid-structure interactions, weÂ envisage applications at theÂ micron scale involving solutions of macromolecules (colloidsÂ or polymeric chains).Â At these scalesÂ hydrodynamic fluctuations becomeÂ important and have to be consistently included in the fluidÂ solver. In particular, the Navier-Stokes-Landau-LifshitzÂ equationsÂ (for eitherÂ Â Â compressibleÂ Â orÂ Â Â incompresibleÂ Â liquids) are solved using a finite volume method [1].Â Concering the solute description, atÂ Â this coarsed-grained levelÂ I will focus on theÂ so called "point-particle" representation,Â where each particleÂ (macromolecule) isÂ described by translational (also if requiredÂ rotational) degrees of freedom and of course might feel inter-molecular (effective potential) forces as well.

In theseÂ kind of schemes, theÂ force between particleÂ and fluid have been usually assumed to be frictional, based on the Stokes drag.Â This assumptionÂ Â isÂ limittedÂ Â toÂ Â "slow"Â fluid-particleÂ Â interactions developing at times much larger than the friction time (inverse of the friction coefficient).Â By contrast, our approach is based on imposing a "no-slip"Â constraint to theÂ fluid velocity at theÂ particle domainÂ which ensures thatÂ particle and fluid momentum is instantaneously exchanged over their interaction [2,3].Â In this wayÂ we can tackleÂ phenomena occurringÂ at highÂ frequencies (such asÂ inertial effects). InÂ particular weÂ are interestedÂ in applicationsÂ involving acousticÂ forces [3]Â (ultrasound) on colloidalÂ particles (and softÂ matter, inÂ general).

Â

Finally, I'd also like to briefly discuss someÂ of the applications we have in mind; suchÂ as theÂ effect ofÂ hydrodynamicsÂ 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.Â Griffit and C.Â S. Peskin. Staggered SchemesÂ for Fluctuating Hydrodynamics, arXiv:1108.5188v1, (submitted, 2011)

[2] F.Â BalboaÂ and R.Â Delgado-Buscalioni,Â Particle HydrodynamicsÂ using Hybrid Models:Â from MolecularÂ to Colloidal Fluids,Â Â Particles 2011 (to appear)

[3] F.Â Balboa,Â I.Â PagonabarragaÂ andÂ R.Â Delgado-Buscalioni,Â Inertial couplingÂ for pointÂ particleÂ fluctuating hydrodynamics,Â (submitted, J. Comp. Physics, 2011)