Minimal model for acoustic forces on Brownian particles

Abstract

We present a generalization of inertial coupling (IC) [Balboa Usabiaga et al., J. Comput. Phys. 235, 701 (2013)], which permits the resolution of radiation forces on small particles with arbitrary acoustic contrast factor. The IC method is based on a Eulerian-Lagrangian approach: particles move in continuum space while the fluid equations are solved in a regular mesh (here we use the finite volume method). Thermal fluctuations in the fluid stress, important below the micron scale, are also taken into account following the Landau-Lifshitz fluid description. Each particle is described by a minimal cost resolution which consists of a single small kernel (bell-shaped function) concomitant to the particle. The main role of the particle kernel is to interpolate fluid properties and spread particle forces. Here, we extend the kernel functionality to allow for an arbitrary particle compressibility. The particle-fluid force is obtained from an imposed "no-slip" constraint which enforces similar particle and kernel fluid velocities. This coupling is instantaneous and permits the capture of the fast, nonlinear effects underlying the radiation forces on particles. Acoustic forces arise because of an excess either in particle compressibility (monopolar term) or in mass (dipolar contribution) over the fluid values. Comparison with theoretical expressions shows that the present generalization of the IC method correctly reproduces both contributions. Due to its low computational cost, the present method allows for simulations with many [O(10 4 )] particles using a standard graphical processor unit.

Inertial coupling method for particles in an incompressible fluctuating fluid

“…It is possible to include additional transport processes in the minimally-resolved approach we employ here, however, the specifics of how to express the surface boundary conditions to a volumetric blob condition are very problem specific and need to be carefully constructed on a case by case basis. In this respect, recently, reaction-diffusion processes have been included in the type of method studied here [49], and compressible blobs have been considered and found to adequately describe coupling between ultrasound waves and small particles [50].…”

Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics

“…This happens, for example, when the distinguished particle is simply a tagged fluid molecule. This may also be a good approximation for neutrally buoyant particles that do not have a strong chemical interaction with the surrounding fluid, and the majority of prior work in the literature has in fact used the simplified model c 0 = c, with the notable exception of [37].…”

“…Here the fluid velocity is defined via v = g/ρ, and σ denotes the viscous stress (deterministic and fluctuating components) with a form identical to ours. The volume associated to the particle can be expressed in our notation as V ≡ m 0 /ρ eq but is interpreted differently in [37] to be a geometric rather than an inertial quantity. Note that we have set here the excess mass of the particle [37] over the fluid m e = 0 because in our notation ρ includes the total mass of the particle (see additional discussion in Section VI).…”

“…Such a fluctuating hydrodynamic model [11,[28][29][30] explains the appearance of giant nonequilibrium fluctuations in the concentration of colloidal particles, justifies the Stokes-Einstein relation in the limit of large Schmidt numbers [33], and describes the important influence of boundaries in confined suspensions [23,29]. If one wants to further account for inertial effects and compressibility of the fluid, as crucial for modeling the effect of ultrasound on colloidal particles [34] or the acoustic vibrations produced by suspended particles [35] or micro-organisms [36], one can use a similar model but describe the fluid using compressible fluctuating hydrodynamics [34,37,38].…”

Solvent Hydrodynamics Enhances the Collective Diffusion of Membrane Lipids

“…On one hand, we used the standard pure Brownian dynamics (BD) method, whereby lipids random displacements are completely uncorrelated. The second approach is based on an implicit hydrodynamic solvent solved by the FLUAM package [30]. It basicly consists on an immersed boundary description in fluctuating hydrodynamics [20,31,32].…”