Dynamics of particles in the steady flows of an inviscid fluid

Modeling and Simulation in Science, Engineering and Technology, 2000

A number of problems related to particle trajectories in ideal 2D flows are discussed. Both regular particle paths, corresponding to integrable dynamics, and irregular or chaotic paths may arise. Examples of both types are shown. Sometimes, in the same flow, certain particles will follow regular paths while others follow irregular paths. Even in the chaotic region the amount of regularity or irregularity of a path depends on initial conditions and system parameters. The notion of a transported fluid region or ''atmosphere'' is mentioned. Various conclusions, ideas and queries are formulated based on the examples given. The intimate mix of regular and chaotic trajectories complicates a purely Lagrangian approach to fluid flow problems.

Physical Review Letters, 2007

We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion, and assume that both processes can be described by independent characteristic time-scales. We show the occurrence of a complex transient that can exhibit a series of alternating regimes of motion, for two different angular dynamics which correspond to persistent and directed random walks. We also show additive corrections to the diffusion coefficient. The characteristic time-scales are also exposed in the velocity autocorrelation, which is a sum of exponential forms. PACS numbers: 05.40.Jc,87.17.Jj

Doklady Physics, 2010

Coherent structures in …, 2001

The study of trajectories of particles suspended in a fluid in motion is of relevance to many problems; as much those in applied technology as those of theoretical interest. Properties of emulsions, dispersion of contaminants in the atmosphere or the oceans, sedimentation, and mixing, are just a few applications. From the point of view of dynamical systems, this type of problem motivates the study of models with a dimension that is relatively low, but sufficient to encounter theoretical aspects that are as yet little understood.

The Journal of Chemical Physics, 2021

We study a self-propelled particle moving in a solvent with the active Ornstein Uhlenbeck dynamics in the underdamped regime to evaluate the influence of the inertia. We focus on the properties of potential-free and harmonically confined underdamped active particles, studying how the singleparticle trajectories modify for different values of the drag coefficient. In both cases, we solve the dynamics in terms of correlation matrices and steady-state probability distribution functions revealing the explicit correlations between velocity and active force. We also evaluate the influence of the inertia on the time-dependent properties of the system, discussing the mean square displacement and the time-correlations of particle positions and velocities. Particular attention is devoted to the study of the Virial active pressure unveiling the role of the inertia on this observable.

New Journal of Physics, 2012

We have performed numerical simulations of inertial particles in random model flows in the white-noise limit (at zero Kubo number, Ku = 0) and at finite Kubo numbers. Our results for the moments of relative inertial particle velocities are in good agreement with recent theoretical results (Gustavsson & Mehlig 2011a) based on the formation of phase-space singularities in the inertial particle dynamics (caustics). We discuss the relation between three recent approaches describing the dynamics and spatial distribution of inertial particles suspended in turbulent flows: caustic formation, real-space singularities of the deformation tensor, and random uncorrelated motion. We discuss how the phase-and real-space singularities are related. Their formation is well understood in terms of a local theory. We discuss implications for random uncorrelated motion.

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1984

Computer Methods in Applied Mechanics and Engineering, 2014

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 [F. Balboa Usabiaga, I. Pagonabarraga, and R. Delgado-Buscalioni, J. Comp. Phys., 235:701-722, 2013 ]. 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 allow the blob to provide an effective model of a particle; specifically, the volume, mass, and hydrodynamic properties of the blob are remarkably grid-independent. 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. In the deterministic setting, we find the blob to be a remarkably robust approximation to a rigid sphere, at both low and high Reynolds numbers. In the stochastic setting, we study in detail the short and long-time behavior of the velocity autocorrelation function and observe agreement with all of the known behavior for rigid sphere immersed in a fluctuating fluid. The proposed inertial coupling method provides a low-cost coarse-grained (minimal resolution) model of particulate flows over a wide range of time-scales ranging from Brownian to convection-driven motion. -resolved particulate flows for example, semi-implicit CFD schemes. Moreover, they cannot be adapted to efficiently treat the natural time scales governing the different dynamical regimes (e.g., the Brownian or overdamped limit). Similar advantages and drawbacks also apply to the lattice Boltzmann (LB) method [3], although the LB approach has proven to be a rather flexible framework .

Understanding Complex Systems, 2010

We review recent advances on the dynamics of finite-size particles advected by chaotic fluid flows, focusing on the phenomena caused by the inertia of finite-size particles which have no counterpart in traditionally studied passive tracers. Particle inertia enlarges the phase space and makes the advection dynamics much richer than the passive tracer dynamics, because particles' trajectories can diverge from the trajectories of fluid parcels. We cover both confined and open flow regimes, and we also discuss the dynamics of interacting particles, which can undergo fragmentation and coagulation. A. de Moura (B)