Time reversibility and non-deterministic behaviour in oscillatorily sheared suspensions of non-interacting particles at high Reynolds numbers

Abstract

Collections of inertial particles suspended in a viscous fluid and subjected to oscillatory shear have recently attracted much attention due to their relevance to a number of industrial applications and natural phenomena. It is known that, even at very low values of the flow Reynolds number, particle-to-particle interactions can lead to complex chaotic displacements despite the reversibility of the overarching fluid-dynamics (Stokes) equations. For high-Re flows, the loss of predictability after a finite time horizon is generically ascribed to the non-linear nature of the Navier-Stokes equations. Where the sources of nonlinearity are located exactly and how they influence the motion of particles, however, has not been clarified yet. We show that assuming particle interactions to be negligible, surprisingly, at high values of the Reynolds number the major source of non-deterministic behaviour comes from effects of stationary nature in the carrier flow. We report numerical simulations showing precisely how for geometries of finite extent such stationary effects emerge as the time-averaged non-linear response of the Navier-Stokes equations to the applied oscillatory forcing. They cause small deviations of the inertial particle's trajectory from the streamlines of the instantaneous oscillatory flow, which accumulate in time until the system behaviour becomes essentially non reversible. Nomenclature A cavity aspect ratio d cavity thickness [m] M Cycles of modulation p Nondimensional pressure R solid particle radius [m] Re Reynolds number

Symmetry breaking phenomena in thermovibrationally driven particle accumulation structures

“…O(10 4 )Ra  O(10 6 ), O(10 7 ) O(10 9 ), O(10 3 ) O(10 4 ) and 0.12.0. Before embarking into the description of the present results, we wish to put some emphasis on the fact that the present study was motivated by a recent companion work 56 dealing with collections of inertial particles suspended in an isothermal viscous fluid and subjected to oscillatory shear (no thermal effects). Starting from a ordered distribution of particles concentrated in an area having circular shape (initial conditions corresponding to a particle-dense 'ball') and repeating several cycles of shear in time, it was found that while in the absence of non-linear time-averaged effects the set of particles could behave as a cohesive entity for long times (being stretched periodically but maintaining a sharp boundary between its particle-filled interior and the clear fluid outside), the initial ball was quickly turned into a completely disordered distribution of particles when a steady component of velocity was present in the fluid.…”

“…As illustrated for a companion (isothermal) problem by Lappa 56 , the presence of a non-negligible self-generated steady fluid velocity is expected to determine symmetry breaking phenomena in otherwise perfect and highly ordered particle structures. By proposing to analyze situations where thermovibrational convection includes both non-zero time-averaged and instantaneous velocity components, we aim to develop new principles to enable increased control over the ability of particles to target desired locations depending on the prevailing (steady or oscillatory) behavior of the flow.…”

Spatial and temporal evolution of three-dimensional thermovibrational convection in a cubic cavity with various thermal boundary conditions

“…An exciting prospect for the future is to enrich this problem with the addition of solid particles, thereby, giving rise to a new line of inquiry running in parallel with that where the interplay of thermovibrational effects and particle inertial effects in cubic cavities with vibrations perpendicular to the temperature gradient has been found to support fascinating particle self-organization phenomena (formation of highly ordered, high resolution structures with the morphology of quadric surfaces [44][45][46][47][48] ).…”

Characterization of two-way coupled thermovibrationally driven particle attractee

“…The so-called "one-way" class of numerical methods 24,25,28,29,31,56,74,76 relies on the assumption that the particle mass loading v ¼ nu (ratio of the overall solid mass and liquid mass, where u is the ratio of the volume globally occupied by the particles and the volume of the computational domain, i.e., the "volume fraction") is so small that the influence of the dispersed phase on the liquid can be ignored. In such a context, one is therefore allowed to account for the effect of the local fluid-phase velocity on particle motion, whereas vice versa is not mandatorily required.…”