Deterministic particle transport in a ratchet flow

Abstract

This study is motivated by the issue of the pumping of particle through a periodic modulated channel. We focus on a simplified deterministic model of small inertia particles within the Stokes flow framework that we call "ratchet flow." A path-following method is employed in the parameter space in order to retrace the scenario which from bounded periodic solutions leads to particle transport. Depending on whether the magnitude of the particle drag is moderate or large, two main transport mechanisms are identified in which the role of the parity symmetry of the flow differs. For large drag, transport is induced by flow asymmetry, while for moderate drag, since the full transport solution bifurcation structure already exists for symmetric settings, flow asymmetry only makes the transport effective. We analyzed the scenarios of current reversals for each mechanism as well as the role of synchronization. In particular we show that, for large drag, the particle drift is similar to phase slip in a synchronization problem.

Selective Transport of Airborne Microparticles Through Micro-channels Under Microgravity

“…The consistency of these approximations with the parameter domains of the transport solution is discussed in Section "Domain of Validity of the Assumptions". Without particles, the quasi-static velocity field V 0 ( R, t) at the position R and time t reads V 0 ( R, t) = U 0 ( R)A(t), where A(t) is the pumping amplitude at time t and U 0 ( R) is a stationary velocity field of periodicity L in x-direction (Kettner et al 2000;Beltrame et al 2016). Because of the L-periodicity, the pressure difference, noted [p], between the pore inlet and outlet is constant.…”

“…of Beltrame et al (2016) by the fields γ (x) and u eq (x). Both fields were given without any relation with pore shape, especially γ was assumed constant, contrary to the present study.…”

“…The advantage of the temporal asymmetry compared to the asymmetric geometry is that the particle direction can be controlled by changing only the pumping. According to Beltrame et al (2016), particle transport via the ratchet effect is a generic feature of equations of the same kind as Eq. 6 which have a spatial and temporal periodicity.…”

“…P γ = +∞, the particle trajectories are oscillations synchronized with the fluid. According to Beltrame et al (2016), even for a finite value of P γ but for sufficiently low values of P v , i.e. the pumping amplitude, there are two kinds of periodic solutions of the particle motion which are centered at the extrema of the velocity field u eq noted s 0 for the maximum and s m for the minimum.…”

“…The main goal of this paper was to determine whether such longitudinal transport mechanisms as in (Beltrame et al 2016) exist in a micro-gravity environment for metal particles in suspension in the air. To answer this question, we consider a simplified model in which the particle is constrained to move along the channel axis and the fluid inertia is neglected (Section "Modeling").…”