(a) Schematic view of a DNA chip. The labeled free targets hybridize to their complementary probes on the chip, if present. (b) Protocol used here, which operates with two pumps switched alternately. A pump always pushes the fluid in the same direction or else is inactive.
Sketch of the chip: there are 53 round spots of targets. (a) Initial condition for the static hybridization. The repartition of targets is random. (b) Same for dynamic hybridization. The targets are initially located around the source on the bottom left; only their heights z are random.
Comparison of two Poincaré sections (the successive positions of given particles taken at each period is accumulated on the section) of the same protocol 15 with the same period T = 4 s in a square chamber. The left one is calculated with the 3D model, while the right one results from a complete 3D calculation.
Decay of free targets as a function of time; blue ×: static case; red +: with chaotic advection. The diffusion coefficient is in both cases . The straight line in log-lin scale indicates that the decay is of the type .
Homogeneity of hybridization; blue ×: static case; red +: with chaotic advection. The green line corresponds to 2 periods of the flow-field. The diffusion coefficient is in both cases .
(a) Typical time of decay of free target τ (log-log plot) in the static case as a function of dh for different values of D. Red symbols: ; green symbols: ; blue symbols: ; (b) decay of free targets for the same values of D (log-lin plot) as a function of the non-dimensional time (which takes into account the initial distance between two free targets) for : the three curves collapse.
Typical time of decay of free target τ (log-log plot) in the dynamical case as a function of dh for different values of D. Red symbols: ; green symbols: ; blue symbols: .
Typical mechanisms of renewing of fluid inside the hybridization volume: advection is very weak near the bottom, while the very small height of the volume allows a good vertical exchange of fluid by molecular diffusion.
Top: at a given time t, we suppose that there are no more targets above a spot. At a time , when considering the sole action of advection, some targets have been moved above the spot by the velocity field; they can be brought back inside the hybridization volume by molecular diffusion.
Non-dimensional τ (log-log plot) in the dynamical case using Eq. (30) as a function of non-dimensional dh using Eq. (25) for different values of D from up to (same as in Fig. 7 ). The values of and are given, respectively, in Eqs. (26) and (31) . The three sets of points collapse on the same curve.
τ (log-log plot) in the dynamical case as a function of the diameter of the spots Ls ; the fit is a power law with slope −5/3.
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