Sketch of the HS cell of thickness and width . Also shown are the velocity profiles obtained at low frequency in the planes located at and at .
Time evolution of a chemical front (in plane) in a pulsative flow field of period and velocity amplitude . Time increases from left to right and from top to bottom. Two images are separated by time intervals. The distance between two dashes is .
Time evolution of the front position, ( in mm, in s), for different values of the periods and velocity amplitudes corresponding to (, ) ( in s and in ). (a) (25, 70.4), (b) (50, 69.1), (c) (12.5, 140.7), and (d) (25, 138.2).
Normalized drift velocity of the chemical front vs the normalized flow velocity amplitude .
Experimental oscillation frequency of the front width vs the imposed oscillation frequency of the flow (in Hz). The straight line is .
2D numerical simulation of the front displacement (in the gap of the cell, plane), which is obtained with an imposed flow of period and amplitude, and . The product of the reaction is in gray and the reactant is in dark. From top to bottom, time increases by time steps. The lattice dimensions are . Note that the aspect ratio of the pictures is not 1.
Time evolution of the front position, ( in mm, in s). –: Experimental data and – –: numerical simulations. The experimental values (, ) ( in s and in ) are (a) (1.12, 100, 70.4), (b) (0.55, 100, 34.6), (c) (0.14, 25, 35.2), and (d) (0.14, 12.5, 70.4).
Normalized relative front velocity, , vs , where and are the Poiseuille flow and lattice parameters. The symbols pertain to different values of . ●: (0.75, 15.8), ▲: (0.75, 31.6), ▼: (1.5, 15.8), ◼: (1.5, 31.6), ◆: (4.5, 15.8), and ▶: (4.5, 31.6). The open symbols correspond to negative values of . The line is the theoretical prediction of Eq. (7).
Ratio of the normalized relative front velocity to the mixing regime contribution, , vs . The symbols are the same as in Fig. 8. The straight line is the theoretical prediction of Eq. (7).
Normalized time-averaged front velocity versus the flow period (inset) and versus the normalized flow period . The symbols correspond to different values of . ●: , ◆: , and ◻: . The solid line corresponds to Taylor’s mixing regime prediction, which is given by Eq. (9). The dashed line corresponds to analytical fit of Ref. 20.
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