Particle hydrodynamics

Eulerian-Lagrangian Hybrids

This research aims to develop minimal models to resolve particle hydrodynamics in a robust and quite general way. The novelty resides in the type of coupling between the fluid and the small particles immersed in it, which is based on a "coarse-grained" no-slip constraint which enforces equal particle velocity and local average of fluid velocity within the particle "volume". This non-linear "inertial coupling", permits to consistently solve both, the fluid and particle inertia and conserves momentum and energy. Owing to the non-dissipative nature of the no-slip coupling, the fluctuation-dissipation balance is possible without addition of extra particle noise. Thus, we just take into account thermal fluctuations in the fluid momentum equation, as expressed in the Landau-Lifshitz formalism for fluctuating hydrodynamics. The local averaging and spreading operations are accomplished using compact kernels used in immersed boundary methods. These kernels are soft, so the particle model resembles a "blob" which however has surprisingly physically-consistent volume, mass, and hydrodynamic properties. The present inertial coupling method can model particulate flows in a wide range of time-scales ranging from Brownian to convection-driven motion, using a minimal cost. It can be naturally extended to polymeric fluids and other types of physico/chemical phenomena. In the incompressible formulation, the code is able to reach large particle Reynolds numbers (about 200) and consistently reproduce the increase of fluid drag and transient effects due to particle-wake interaction at large Re.

FLUAM code

Florencio Balboa has developed a code written in CUDA, which works nicely and extremely fast in GPU cards. It can be downloaded at https://code.google.com/p/fluam

Inertial Coupling Method: Ultrasound - soft matter interaction

We have recently developed a method for particle hydrodynamics based on an hybrid Eulerian-Lagrangian approach. Particle dynamics are solved in continuum space while the fluid is solved in an Eulerian mesh, and described by finite volume fluctuating hydrodynamics. This set-up is particularly suited for micron-size devices where the Reynolds number is small but thermal fluctuations are important. The particle-fluid coupling force is obtained by imposing zero relative (particle-fluid) velocity at a local average over the particle volume. In doing so the momentum exchanged between fluid and particle is transferred instantaneously ensuring a correct treatment of inertia and proper particle velocity fluctuations uniquely driven by fluid thermal forces. Using a compressible fluid formulation at low Mach number, we are studying acoustic forces on small particles (colloids) driven by standing pressure waves at ultrasound frequencies (MHz or more). Acoustic forces are excellent agreement with the theoretical expressions. This opens the possibility of including a large number of colloidal particles in acoustic manipulation, and other studies with important technological applications involving soft matter and ultrasound interaction.

Recent publications

Florencio Balboa Usabiaga, Ignacio Pagonabarraga, Rafael Delgado-Buscalioni, Inertial coupling for point particle fluctuating hydrodynamics , Journal of Computational Physics 235, 701 (2013)

F. Balboa Usabiaga, R. Delgado-Buscalioni, B. E. Griffith, A. Donev Inertial Coupling Method for particles in an incompressible fluctuating fluid , submitted - (2013)

Selected talks

Inertial coupling method for blob particle models. given at HYBRID2013, Julich, Germany, March 2013.

Coworkers

Florencio Balboa Usabiaga (UAM)
Aleks Donev (Courant Institute of New York) ,
Ignacio Pagonabarraga (Universidad de Barcelona)