Mass transport

Introduction to the page under construction

Role of hydrodynamics on surface capture

PhD Thesis of Donatien Mottin, in collaboration with Florence Razan, Frédéric Kanoufi and Claude Noguès

Out-of-Equilibrium Measurements of Kinetic Constants on a Biosensor

Conventional measurements of kinetic constants currently in use are performed at equilibrium and may require large volumes, especially at low association rate constant kon. If the measurements are made out of equilibrium, the values obtained may be biased by dilution of the sample with the flow of the running buffer. In some applications, the available sample volume can be very critical and requires the development of tools to measure kinetic constants with low volumes. In this paper, through experimental, numerical simulation and a modeling combined approach, we propose a SPR-based method that relies on an out-of-equilibrium measurement, using the effect of dilution by flow to its advantage. This new method should have a significant impact in biochemistry and medical research.

Motin et al., Anal. Chem., 2021.

Mixing in microfluidics

This topic corresponds to my transition towards microfluidics. This work was done through two collaborations, with P. tabeling from ESPCI and with J. Delaire from ENS-Cachan.

Mixing in a microfluidic system and spatio-temporal resonances

in collaboration with A. Dodge and P. Tabeling - ESPCI

In this work we concentrate on a particular micromixer that exploits chaotic trajectories to achieve mixing. The micromixer we consider here is a cross-channel intersection, in which a main stream is perturbed by an oscillatory flow, driven by an external source. Depending on the amplitude and frequency of the oscillatory flow, one obtains wavy and chaotic regimes, reminiscent of a tendril-whorl mapping. The chaotic states, in which material lines are stretched and folded, favour mixing. A

spatiotemporal resonance phenomenon, in which the material-line deformation is transient, is shown. An experiment using soft lithography and integrated valves, in which the resonant states are revealed, is described. From a practical viewpoint, the cross-channel micromixer offers a variety of regimes, which can be exploited to mix fluids or separate particles of different sizes. In the context of microsystems, it can be viewed as a ‘smart’ elementary system.

Papers: 2004 and 2005

A novel microfluidic flow-injection analysis device with fluorescence detection for cation sensing. Application to potassium

in collaboration with S. Desportes and J. Delaire - ENS-Cachan

A microfabricated device has been developed for fluorimetric detection of potassium ions without previous separation. It is based on use of a fluorescent molecular sensor, calix–bodipy, specially designed to be sensitive to and selective for the target ion. The device is essentially made of a Y-shape microchannel moulded in PDMS fixed on a glass substrate. A passive mixer is used for mixing the reactant and the analyte. The optical detection arrangement uses two optical fibres, one for excitation by a lightemitting diode, the other for collection of the fluorescence.This system enabled the flow-injection analysis of the concentration of potassium ions in aqueous solutions with a detection limit of 0.5 mmol L−1 and without interference with sodium ions. A calibration plot was constructed using potassium standard solutions in the range 0–16 mmol L−1,

and was used for the determination of the potassium content of a pharmaceutical pill.

Paper : 2007

Mixing Regime :

Resonant regime :

Dodge et al., Phys. Rev. 2005.

Dodge et al., C. R. Physique 2004.

Tabeling et al., Phil. Trans. Roy. Soc. Lond. (A) 2004.

Destandau et al., ,Anal. Bioanal. Chem. 2007.

Dispersion of passive tracers in an experimental two-dimensional turbulent flow (my PhD)

We present an experimental study of the dispersion of passive tracers in a forced two-dimensional turbulence. The experiments are performed in electromagnetically driven flows, using thin, stably-stratified layers. Instantaneous velocity fields are measured using particle imaging velocimetry techniques.

The dispersion of passive tracers is studied in the direct enstrophy cascade and in the inverse energy cascade, in accordance with the conjecture formulated by Kraichnan in 1967 about the double cascade mechanism in 2D forced turbulence.

In a first approach, the evolution of a blob of fluoresceine is studied in both cascade. The enstrophy cascade has the particularity to concentrate the strain at large scales, the velocity field is then Taylor expandable at first order. Due to the simplicity of the velocity field, it is possible to developp analytic exact solutions. We show that the spectrum of the concentration fluctuations follows Batchelor's spectrum k-1. In addition, analytic solutions found by Chertkhov et al. are in good agreement with our experiment : exponential tails for both fluctuation distributions and increment distributions, logarithmic behaviour for the structure function of order 2.In the inverse energy cascade, we show that Corrsin-Obukhov analysis is in good agreemnt with our experiment concerning statistics of order 2. A further analysis shows that higher orders deviate strongly from Kolmogorov arguments, and the exponents of structure functions saturate to a constant value.

An other approach is a lagrangian one. Pairs of particles are followed along their trajectories. This study is done in the inverse energy cascade. The statistical properties of the process are obtained by numerically integrating the Lagrangian trajectories of the particles, using the experimentally obtained velocity fields. The hyperdiffusive Richardson t3 law is observed, and strongly non-gaussian behavior is obtained for the distributions of pair separation. The process is shown to be self-similar in time and that strong temporal correlations are present . The observations, which fit well in the Kolmogorov framework, jeopardize the relevance of the Lévy walk approach.

Jullien et al., Phys. Rev. Lett., 1999

Paret et al., Phys. Rev. Lett., 1999

Jullien et al., Phys. Rev. Lett., 2000

Jullien et al., Phys. Rev. E, 2001

Jullien, Phys. of Fluids, 2003

Batchelor dispersion in the 2D enstrophy cascade :

Dispersion of passive tracer in the inverse energy cascade :