Numerical modeling of DNA-chip hybridization with chaotic advection

Abstract

We present numerical simulations of DNA-chip hybridization, both in the "static" and "dynamical" cases. In the static case, transport of free targets is limited by molecular diffusion; in the dynamical case, an efficient mixing is achieved by chaotic advection, with a periodic protocol using pumps in a rectangular chamber. This protocol has been shown to achieve rapid and homogeneous mixing. We suppose in our model that all free targets are identical; the chip has different spots on which the probes are fixed, also all identical, and complementary to the targets. The reaction model is an infinite sink potential of width dh , i.e., a target is captured as soon as it comes close enough to a probe, at a distance lower than dh . Our results prove that mixing with chaotic advection enables much more rapid hybridization than the static case. We show and explain why the potential width dh does not play an important role in the final results, and we discuss the role of molecular diffusion. We also recover realistic reaction rates in the static case.

Diffusiophoresis at the macroscale

“…Since we are interested in mixing, the relevant parameter is the Péclet number, which measures the relative effect of advection compared to diffusion. Because in a Hele-Shaw flow chaotic mixing essentially takes place in the horizontal direction [21], we use the Péclet number based on the width L of the cell,…”

The distribution of “time of flight” in three dimensional stationary chaotic advection

“…The shape of the distribution can be further explained as follows: during a lapse of time dt, less particles of the flow cross the section near the walls than in the core where the velocity is maximum; therefore the probability density for the single particle to cross the section at a given point must also follow this flux of particles. This last property was also used in a 3D-model of chaotic flow with sources and sinks in a Hele-Shaw cell, where the flow was calculated first in 2D, and the z-dependence was modeled by a parabolic reinjection rate from the source, with surprisingly good agreement between the model and 3D-calculations 48 . Using these model flows, it is possible to obtain an analytical expression for the distributions of time of flight.…”

Chaotic mixing in an acoustically driven cavity flow

“…The acoustic beam enters with an angle π/4, reflects on the walls, and leaves the cavity at the place where it entered. advection has many fields of application in mixing, like microfluidics [39][40][41] or heat exchangers at the macroscale [42][43][44].…”