Active chaotic mixing in a channel with rotating arc-walls

Abstract

An active inline mixer suitable for flows at low Reynolds number and high Péclet number is studied. An alternated oscillatory forcing protocol is imposed by three rotating circular arc-walls in a straight channel. In the two-dimensional case, simple phenomenological arguments are used to estimate heuristically the mixing efficiency with two non-dimensional control parameters: the Strouhal number based on the bulk flow velocity, and the strength of the cross flow relative to the transport flow. The validity and limitations of the proposed mixing conditions are explained by the transport mechanisms in the mixer. The beneficial role of the elliptic flow regions for stretching and folding the passive scalar interfaces is highlighted, as well as a correlation between good mixing ability and the chaotic advection of tracers in the mixing zone.

Experimental study of chaotic flow and mixing of Newtonian fluid in a rotating arc-wall mixer

“…The previous study, presented in Ref. [18], helped to validate this new mixing concept. It has shown that the non-dimensional numbers that control the flow are: the Strouhal number St = W TU which represents the ratio of a characteristic time of the flow to the rotational period of the cylinders T, and the velocity ratio k = RW 0 U of the largest angular speed of the cylinders to the axial velocity of the flow.…”

“…A detailed explanation of the choice of the rotational protocol of the cylinders is given in Ref. [18]. We have shown that the modulation of the angular velocities of the cylinders with a sine function and with opposite directions of rotation generate two flow topologies that alternate smoothly between each other.…”

“…Given the above mentioned reasons, we proposed in previous study [18,49] a new continuous active mixer with three rotating cylinders located on the walls. A theoretical study was carried out based on two simple phenomenological arguments, one for folding the fluid elements and the other for mixing by molecular diffusion.…”

Residence time distributions for in-line chaotic mixers

“…Moreover the least noisy tail is that of the MLLM (figure 4d), for which we have twice as much data as for the two other mixers, but that also corresponds to the more correlated mixer. Finally, note that El Omary et al [29] also found a t −3 tail when properly weighting their statistics.…”

Chaotic mixing in an acoustically driven cavity flow

“…The matter further triggered a great amount of theoretical, numerical, or experimental works on the subject (see, for instance, Refs. [25][26][27][28][29][30][31][32][33]). Note finally that chaotic advection also applies for dynamical systems of higher dimension, as, for instance, 3D time-periodic flows [34][35][36][37][38].…”