Ordering of Small Particles in One-Dimensional Coherent Structures by Time-Periodic Flows

Abstract

Small particles transported by a fluid medium do not necessarily have to follow the flow. We show that for a wide class of time-periodic incompressible flows inertial particles have a tendency to spontaneously align in one-dimensional dynamic coherent structures. This effect may take place for particles so small that often they would be expected to behave as passive tracers and be used in PIV measurement technique. We link the particle tendency to form one-dimensional structures to the nonlinear phenomenon of phase locking. We propose that this general mechanism is, in particular, responsible for the enigmatic formation of the "particle accumulation structures" discovered experimentally in thermocapillary flows more than a decade ago and unexplained until now.

Assessment of the role of axial vorticity in the formation of particle accumulation structures in supercritical Marangoni and hybrid thermocapillary-rotation-driven flows

“…In the present work the phenomenon is investigated resorting to direct numerical solution 17 lies in the use of "injected" vorticity to allow a variation of the particle characteristic turnover motion at a fixed (supercritical) value of the Marangoni number (to see how this "added" vorticity interferes with the oscillatory instability of Marangoni convection and the fundamental mechanism supporting PAS formation).…”

On the variety of particle accumulation structures under the effect of g-jitters

“…As the characteristic flow time scale of the Marangoni flow we assume here (as in other studies, see, e.g., Pushkin et al, 2011):…”

“…As expected, in this region some interesting and exotic dynamics can be discerned and described (they are the main subject of the present section). These behaviors are driven by the competition between the two involved counteracting forces exerting their influence on the considered phenomena, these being: the "capturing" action exerted on solid particles by the attractive close manifold existing in the traveling wave state of supercritical Marangoni flow as discussed by Pushkin et al (2011) and Lappa (2013a) (on which particles would tend to accumulate and order in the absence of vibrations), and the disturbing effect played on each particle by the inertial disturbances produced by vibration-induced accelerations (eq. 2).…”

“…( 1 8 ) is the general parameter that can be used (see, e.g., Pushkin et al, 2011, Lappa, 2013a to account for the combined effect of particle inertia and drag ( =O(10 -5 ) for the conditions considered in the present work). The limit St v 0 represents the condition for which a fixed viewer would see the particle moving with the same amplitude as the imposed vibration, i.e.…”

Measurement of permeability of microfluidic porous media with finite-sized colloidal tracers

“…This, however, is often difficult or even impossible to achieve, for example, in random porous media with a broad range of length scales. In addition, deviations from fluid flow lines due to inertial effects can occur even for small particles, as recently shown for time-periodic and chaotic flows (Ouellette et al 2008;Pushkin 2011). Consequently, the impact of particle size within inhomogeneous flow fields has to be considered, which leads to relevant hydrodynamic effects even in simple geometries (Segre and Silberberg 1962;Staben et al 2003).…”