A minimal model for acoustic forces on Brownian particles

We present a generalization of the inertial coupling (IC) [Usabiaga et al. J. Comp. Phys. 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 on 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 to capture the fast, non-linear effects underlying the radiation forces on particles. Acoustic forces arise either because an excess in particle compressibility (monopolar term) or in mass (dipolar contribution) over the fluid values. Comparison with theoretical expressions show 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 particles using a standard Graphical Processor Unit (GPU)

Particle hydrodynamics: from molecular to colloidal fluids

A method for particle hydrodynamics based on an hybrid Eulerian-Lagrangian approach is presented. Particles are solved in the continuum space while the fluid is solved in an Eulerian mesh, and described by finite volume fluctuating hydrodynamics. This set-up is particulary suited for micron-size devices where the Reynolds number is small but thermal fluctuations are important. The fluid-particle coupling force is obtained by imposing zero relative (particle-fluid) velocity at discrete points representing the particle sites. In this work particles are described by an only site which neglect rotation. The momentum exchanged between fluid and particle is transfered instantaneously and this brings about several benefits such as a correct treatment of inertia and proper particle velocity fluctuations uniquely driven by the fluid thermal forces. The present scheme is designed for incompressible and compressible fluids at low Mach number. This is theoretically shown by analyzing the consistency between the Eulerian and Lagrangian momentum balance.A series of tests up to moderate Reynolds number and acoustic forces under ultrasound waves are also presented. 1 INTRODUCTIO

Swimming Efficiently by Wrapping

Single flagellated bacteria are ubiquitous in nature. They exhibit various swimming modes using their flagella to explore complex surroundings such as soil and porous polymer networks. Some single-flagellated bacteria swim with two distinct modes, one with its flagellum extended away from its body and another with its flagellum wrapped around it. The wrapped mode has been observed when the bacteria swim under tight confinements or in highly viscous polymeric melts. In this study we investigate the hydrodynamics of these two modes inside a circular pipe. We find that the wrap mode is slower than the extended mode in bulk but more efficient under strong confinement due to a hydrodynamic increased of its flagellum translation-rotation coupling.Comment: 10 pages, 5 figure

Inertial Coupling Method for particles in an incompressible fluctuating fluid

We develop an inertial coupling method for modeling the dynamics of point-like 'blob' particles immersed in an incompressible fluid, generalizing previous work for compressible fluids. The coupling consistently includes excess (positive or negative) inertia of the particles relative to the displaced fluid, and accounts for thermal fluctuations in the fluid momentum equation. The coupling between the fluid and the blob is based on a no-slip constraint equating the particle velocity with the local average of the fluid velocity, and conserves momentum and energy. We demonstrate that the formulation obeys a fluctuation-dissipation balance, owing to the non-dissipative nature of the no-slip coupling. We develop a spatio-temporal discretization that preserves, as best as possible, these properties of the continuum formulation. In the spatial discretization, the local averaging and spreading operations are accomplished using compact kernels commonly used in immersed boundary methods. We find that the special properties of these kernels make the discrete blob a particle with surprisingly physically-consistent volume, mass, and hydrodynamic properties. We develop a second-order semi-implicit temporal integrator that maintains discrete fluctuation-dissipation balance, and is not limited in stability by viscosity. Furthermore, the temporal scheme requires only constant-coefficient Poisson and Helmholtz linear solvers, enabling a very efficient and simple FFT-based implementation on GPUs. We numerically investigate the performance of the method on several standard test problems...Comment: Contains a number of corrections and an additional Figure 7 (and associated discussion) relative to published versio

Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally-resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. For unbounded suspensions and suspensions sedimented against a single no-slip boundary, we rely on existing analytical expressions for the Rotne-Prager tensor combined with a fast multipole method or a direct summation on a Graphical Processing Unit to obtain an simple yet efficient and scalable implementation. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently-developed rigid-body immersed boundary method to suspensions of freely-moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid body equations converges in a bounded number of iterations regardless of the system size. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201

On the formation and morphology of coherent particulate structures in non-isothermal enclosures subjected to rotating g-jitters

The strategy undertaken in the author's earlier work [M. Lappa, "The patterning behaviour and accumulation of spherical particles in a vibrated non-isothermal liquid," Phys. Fluids 26(9), 093301 (2014) and M. Lappa, "On the multiplicity and symmetry of particle attractors in confined non-isothermal fluids subjected to inclined vibrations," Int. J. Multiphase Flow 93, 71-83 (2017)] based on the use of polarized (purely translational) vibrations for achieving the segregation or accumulation of solid particles in specific regions of an initially dilute dispersion is further pursued by allowing the direction of vibrations to change in time with respect to the applied temperature difference. In particular, the potential of the considered approach in separating the particles from the liquid is explored under the assumption that the angular velocity by which the vibrations axis rotates about a fixed axis is of the same order of magnitude or smaller (one or two orders of magnitude) than the frequency of shaking. A new family of particle coherent structures is identified in the physical space, which can be distinguished from the companion category of particle attractors for fixed vibration direction due to its increased symmetry properties. It is shown how the average nonlinear effects produced by the rotation of the vibration axis, together with those induced by the finite size of the enclosure, accumulate over time leading to the observed fascinating variety of symmetrical patterns

Applications of computational geometry to the molecular simulation of interfaces

The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry, where the definition of the "shape" of a set of point is a well-known problem. In particular, we employ the $\alpha$-shape construction which, applied to the positions of the molecules, selects a shape and identifies its boundary points, which we will take to define our interfacial molecules. A single parameter needs to be fixed (the "$\alpha$" of the $\alpha$-shape), and several proposals are examined, all leading to very similar choices. Results of this methodology are evaluated against previous proposals, and seen to be reasonable.Comment: 22 pages, 8 figure