Abstract
Colloidal suspensions of buoyancy neutral particles flowing in circular pipes focus into narrow distributions near the wall due to lateral migration effects associated with fluid inertia. In curving flows, these distributions are altered by Dean currents and the interplay between Reynolds and Dean numbers is used to predict equilibrium positions. Here, we propose a new description of inertial lateral migration in curving flows that expands current understanding of both focusing dynamics and equilibrium distributions. We find that at low Reynolds numbers, the ratio δ between lateral inertial migration and Dean forces scales simply with the particle radius, coil curvature and pipe radius as . A critical value δc = 0.148 of this parameter is identified along with two related inertial focusing mechanisms. In the regime below δc, coined subcritical, Dean forces generate permanently circulating, twinned annuli, each with intricate equilibrium particle distributions including eyes and trailing arms. At δ > δc (supercritical regime) inertial lateral migration forces are dominant and particles focus to a single stable equilibrium position.
Highlights
Colloidal suspensions of buoyancy neutral particles flowing in circular pipes focus into narrow distributions near the wall due to lateral migration effects associated with fluid inertia
In pipes coiled into a circle of radius R, Dean flows are generated by the fluid inertia and the velocity field develops a two-vortex transverse flow defined by[10] ur (r,y)~Um2 sin y(a2{r2)2(4a2 288a4vR
To account for the dynamics of the particles toward the equilibrium positions as well as the topology of stable and unstable equilibrium configurations, we have developed a simple numerical model based on the superposition of the two velocity fields as shown in Eq (5) and (6)
Summary
Colloidal suspensions of buoyancy neutral particles flowing in circular pipes focus into narrow distributions near the wall due to lateral migration effects associated with fluid inertia. In curving flows, these distributions are altered by Dean currents and the interplay between Reynolds and Dean numbers is used to predict equilibrium positions. The particle dynamics in an inertial migration process as well as accurate theoretical models and related physical quantities to describe this dynamics remain challenging We investigate both theoretically and experimentally the inertial lateral migration effect in curving flows and highlight several unique features in the spatial distributions of focused particles in a regime where Dean flows dominate over inertial lateral migration effects. Confocal microscopy measurements of fast flowing particles are presented in order to corroborate these theoretical findings
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